The Principia Machina/TPC-PY/vectors/module corpus.json/2: Difference between revisions
TPC-PY source vectors/module_corpus.json (0.2.0), page 2 of 3, SHA-256 381c135752b8d8e6; conformed TPS 0.3.0; PROPOSED, not declared (CO-8) |
m 1 revision imported |
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Revision as of 04:39, 28 September 2026
"{\"ID\": \"AIR-LINEAR\", \"VERSION\": \"1.0.0\", \"TITLE\": \"Air resistance at sea level, linear in the speed (Stokes drag on a sphere)\", \"SOURCE\": \"ISO 2533:1975, Standard Atmosphere, sea-level values: density 1.225 kg m-3, dynamic viscosity 1.7894e-5 Pa s\", \"PREREQUISITES\": [{\"SLOT\": \"VELOCITY\", \"KIND\": \"DOF\", \"DIMENSION\": \"L1 T-1\", \"MIN\": 1, \"MAX\": 3, \"LABEL\": \"the velocity components of the body, one per axis\"}], \"PARAMETERS\": [{\"NAME\": \"rho_air\", \"DIMENSION\": \"L-3 M1\", \"SUPPLY\": \"DECLARED\", \"VALUE\": \"1.225\", \"UNIT\": \"kg m-3\", \"OVERRIDABLE\": \"NO\", \"LABEL\": \"the density of air at sea level\"}, {\"NAME\": \"mu_air\", \"DIMENSION\": \"L-1 M1 T-1\", \"SUPPLY\": \"DECLARED\", \"VALUE\": \"1.7894e-5\", \"UNIT\": \"Pa s\", \"OVERRIDABLE\": \"NO\", \"LABEL\": \"the dynamic viscosity of air at sea level\"}, {\"NAME\": \"pi_c\", \"DIMENSION\": \"1\", \"SUPPLY\": \"DECLARED\", \"VALUE\": \"3.141592653589793\", \"UNIT\": \"1\", \"OVERRIDABLE\": \"NO\", \"LABEL\": \"pi, to 16 significant digits\"}, {\"NAME\": \"R_s\", \"DIMENSION\": \"L1\", \"SUPPLY\": \"AUTHOR\", \"LABEL\": \"the radius of the sphere\"}], \"SUMS\": [{\"NAME\": \"SPEED2\", \"OVER\": \"VELOCITY\", \"EACH\": \"VELOCITY^2\"}], \"TERMS\": [{\"TARGET\": \"VELOCITY\", \"SIGN\": \"-\", \"EXPR\": \"6*pi_c*mu_air*R_s*VELOCITY\", \"LABEL\": \"the linear (Stokes) drag\"}], \"ASSUMPTIONS\": [{\"NAME\": \"air_still\", \"PROPOSITION\": \"the air is at rest in the frame of the body's velocity\", \"REFS\": [\"VELOCITY\"]}, {\"NAME\": \"air_uniform\", \"PROPOSITION\": \"the air density is uniform over the region of motion\", \"REFS\": [\"rho_air\"]}, {\"NAME\": \"drag_sphere\", \"PROPOSITION\": \"the body is a rigid sphere of radius R_s\", \"REFS\": [\"R_s\"]}], \"BOUNDARIES\": [{\"NAME\": \"drag_linear_regime\", \"PREDICATE\": \"2 rho_air |v| R_s / mu_air < 1: the regime of the linear law\", \"CONDITION\": \"mu_air != 0 and SPEED2 >= 0 and 2*rho_air*sqrt(SPEED2)*R_s/mu_air < 1\"}], \"NOT_CHOSEN\": \"No linear (Stokes) air resistance.\", \"NOT_INCLUDED\": [\"No wind: the air is at rest.\", \"No change of air density or viscosity with altitude or temperature.\", \"No drag outside the regime of the linear law.\"], \"EXCLUDES\": [], \"INTERACTS_WITH\": [], \"TEST_BINDINGS\": [{\"NAME\": \"PROJECTILE_2D\", \"TPK\": {\"DOF\": [{\"NAME\": \"t\", \"DIMENSION\": \"T1\"}, {\"NAME\": \"x\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"z\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"v_x\", \"DIMENSION\": \"L1 T-1\"}, {\"NAME\": \"v_z\", \"DIMENSION\": \"L1 T-1\"}], \"CONSTANT\": [{\"NAME\": \"m\", \"DIMENSION\": \"M1\"}], \"LAW\": [{\"NAME\": \"KIN_X\", \"STATEMENT\": \"dx/dt = v_x\", \"REFS\": [\"t\", \"v_x\", \"x\"], \"ROLE\": \"EOM(x)\", \"EQUATION\": \"D(x,t)=v_x\"}, {\"NAME\": \"KIN_Z\", \"STATEMENT\": \"dz/dt = v_z\", \"REFS\": [\"t\", \"v_z\", \"z\"], \"ROLE\": \"EOM(z)\", \"EQUATION\": \"D(z,t)=v_z\"}, {\"NAME\": \"EOM_X\", \"STATEMENT\": \"m dv_x/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_x\"], \"ROLE\": \"EOM(v_x)\", \"EQUATION\": \"m*D(v_x,t)=0\"}, {\"NAME\": \"EOM_Z\", \"STATEMENT\": \"m dv_z/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_z\"], \"ROLE\": \"EOM(v_z)\", \"EQUATION\": \"m*D(v_z,t)=0\"}], \"ASSUMPTION\": [{\"NAME\": \"point_mass\", \"PROPOSITION\": \"the body is treated as a point mass\", \"REFS\": [\"m\"]}]}, \"BIND\": {\"VELOCITY\": [\"v_x\", \"v_z\"]}, \"VALUES\": {\"R_s\": {}}, \"ANSWERS\": {}}]}",
"{\"ID\": \"AIR-QUADRATIC\", \"VERSION\": \"1.0.0\", \"TITLE\": \"Air resistance at sea level, quadratic in the speed\", \"SOURCE\": \"ISO 2533:1975, Standard Atmosphere, sea-level values: density 1.225 kg m-3, dynamic viscosity 1.7894e-5 Pa s\", \"PREREQUISITES\": [{\"SLOT\": \"VELOCITY\", \"KIND\": \"DOF\", \"DIMENSION\": \"L1 T-1\", \"MIN\": 1, \"MAX\": 3, \"LABEL\": \"the velocity components of the body, one per axis\"}], \"PARAMETERS\": [{\"NAME\": \"rho_air\", \"DIMENSION\": \"L-3 M1\", \"SUPPLY\": \"DECLARED\", \"VALUE\": \"1.225\", \"UNIT\": \"kg m-3\", \"OVERRIDABLE\": \"NO\", \"LABEL\": \"the density of air at sea level\"}, {\"NAME\": \"mu_air\", \"DIMENSION\": \"L-1 M1 T-1\", \"SUPPLY\": \"DECLARED\", \"VALUE\": \"1.7894e-5\", \"UNIT\": \"Pa s\", \"OVERRIDABLE\": \"NO\", \"LABEL\": \"the dynamic viscosity of air at sea level\"}, {\"NAME\": \"C_d\", \"DIMENSION\": \"1\", \"SUPPLY\": \"AUTHOR\", \"LABEL\": \"the drag coefficient of the body\"}, {\"NAME\": \"A_ref\", \"DIMENSION\": \"L2\", \"SUPPLY\": \"AUTHOR\", \"LABEL\": \"the reference area of the drag coefficient\"}, {\"NAME\": \"L_ref\", \"DIMENSION\": \"L1\", \"SUPPLY\": \"AUTHOR\", \"LABEL\": \"the reference length of the Reynolds number\"}], \"SUMS\": [{\"NAME\": \"SPEED2\", \"OVER\": \"VELOCITY\", \"EACH\": \"VELOCITY^2\"}], \"TERMS\": [{\"TARGET\": \"VELOCITY\", \"SIGN\": \"-\", \"EXPR\": \"0.5*rho_air*C_d*A_ref*sqrt(SPEED2)*VELOCITY\", \"LABEL\": \"the quadratic drag\"}], \"ASSUMPTIONS\": [{\"NAME\": \"air_still\", \"PROPOSITION\": \"the air is at rest in the frame of the body's velocity\", \"REFS\": [\"VELOCITY\"]}, {\"NAME\": \"air_uniform\", \"PROPOSITION\": \"the air density is uniform over the region of motion\", \"REFS\": [\"rho_air\"]}, {\"NAME\": \"drag_cd_constant\", \"PROPOSITION\": \"the drag coefficient C_d is constant over the motion\", \"REFS\": [\"C_d\"]}, {\"NAME\": \"drag_no_lift\", \"PROPOSITION\": \"the body experiences no lift force\", \"REFS\": [\"VELOCITY\"]}, {\"NAME\": \"drag_no_magnus\", \"PROPOSITION\": \"the body experiences no Magnus force\", \"REFS\": [\"VELOCITY\"]}], \"BOUNDARIES\": [{\"NAME\": \"drag_quadratic_regime\", \"PREDICATE\": \"1e3 < rho_air |v| L_ref / mu_air < 2e5: the Reynolds window of the quadratic law\", \"CONDITION\": \"mu_air != 0 and SPEED2 >= 0 and rho_air*sqrt(SPEED2)*L_ref/mu_air > 1000 and rho_air*sqrt(SPEED2)*L_ref/mu_air < 200000\"}], \"NOT_CHOSEN\": \"No quadratic air resistance.\", \"NOT_INCLUDED\": [\"No wind: the air is at rest.\", \"No change of air density or viscosity with altitude or temperature.\", \"No lift, Magnus or added-mass force.\", \"No drag outside the Reynolds window of the quadratic law.\"], \"EXCLUDES\": [\"AIR-LINEAR\"], \"INTERACTS_WITH\": [], \"TEST_BINDINGS\": [{\"NAME\": \"PROJECTILE_2D\", \"TPK\": {\"DOF\": [{\"NAME\": \"t\", \"DIMENSION\": \"T1\"}, {\"NAME\": \"x\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"z\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"v_x\", \"DIMENSION\": \"L1 T-1\"}, {\"NAME\": \"v_z\", \"DIMENSION\": \"L1 T-1\"}], \"CONSTANT\": [{\"NAME\": \"m\", \"DIMENSION\": \"M1\"}], \"LAW\": [{\"NAME\": \"KIN_X\", \"STATEMENT\": \"dx/dt = v_x\", \"REFS\": [\"t\", \"v_x\", \"x\"], \"ROLE\": \"EOM(x)\", \"EQUATION\": \"D(x,t)=v_x\"}, {\"NAME\": \"KIN_Z\", \"STATEMENT\": \"dz/dt = v_z\", \"REFS\": [\"t\", \"v_z\", \"z\"], \"ROLE\": \"EOM(z)\", \"EQUATION\": \"D(z,t)=v_z\"}, {\"NAME\": \"EOM_X\", \"STATEMENT\": \"m dv_x/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_x\"], \"ROLE\": \"EOM(v_x)\", \"EQUATION\": \"m*D(v_x,t)=0\"}, {\"NAME\": \"EOM_Z\", \"STATEMENT\": \"m dv_z/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_z\"], \"ROLE\": \"EOM(v_z)\", \"EQUATION\": \"m*D(v_z,t)=0\"}], \"ASSUMPTION\": [{\"NAME\": \"point_mass\", \"PROPOSITION\": \"the body is treated as a point mass\", \"REFS\": [\"m\"]}]}, \"BIND\": {\"VELOCITY\": [\"v_x\", \"v_z\"]}, \"VALUES\": {\"A_ref\": {}, \"C_d\": {}, \"L_ref\": {}}, \"ANSWERS\": {}}]}",
"{\"ID\": \"GRAV-UNIFORM\", \"VERSION\": \"1.0.0\", \"TITLE\": \"Uniform gravity at the standard value g_n\", \"SOURCE\": \"g_n = 9.80665 m s-2, exact by definition: 3rd CGPM (1901), declaration on the unit of mass and on the definition of weight\", \"PREREQUISITES\": [{\"SLOT\": \"MASS\", \"KIND\": \"CONSTANT\", \"DIMENSION\": \"M1\", \"MIN\": 1, \"MAX\": 1, \"LABEL\": \"the mass of the body\"}, {\"SLOT\": \"UP_VELOCITY\", \"KIND\": \"DOF\", \"DIMENSION\": \"L1 T-1\", \"MIN\": 1, \"MAX\": 1, \"LABEL\": \"the velocity component pointing up; its equation of motion receives the weight\"}, {\"SLOT\": \"HEIGHT\", \"KIND\": \"DOF\", \"DIMENSION\": \"L1\", \"MIN\": 1, \"MAX\": 1, \"LABEL\": \"the position along the same upward axis\"}], \"PARAMETERS\": [{\"NAME\": \"g_n\", \"DIMENSION\": \"L1 T-2\", \"SUPPLY\": \"DECLARED\", \"VALUE\": \"9.80665\", \"UNIT\": \"m s-2\", \"OVERRIDABLE\": \"NO\", \"LABEL\": \"the standard acceleration of gravity\"}, {\"NAME\": \"h_max\", \"DIMENSION\": \"L1\", \"SUPPLY\": \"AUTHOR\", \"LABEL\": \"the largest height, above or below the origin, over which the field is taken as uniform\"}], \"SUMS\": [], \"TERMS\": [{\"TARGET\": \"UP_VELOCITY\", \"SIGN\": \"-\", \"EXPR\": \"MASS*g_n\", \"LABEL\": \"the weight\"}], \"ASSUMPTIONS\": [{\"NAME\": \"gravity_uniform\", \"PROPOSITION\": \"the gravitational field is uniform over the region abs({HEIGHT}) < h_max\", \"REFS\": [\"HEIGHT\", \"h_max\"]}, {\"NAME\": \"gravity_standard\", \"PROPOSITION\": \"the local gravitational acceleration equals the conventional standard value g_n\", \"REFS\": [\"g_n\"]}, {\"NAME\": \"frame_inertial\", \"PROPOSITION\": \"the frame in which {HEIGHT} is measured is treated as inertial\", \"REFS\": [\"HEIGHT\"]}], \"BOUNDARIES\": [{\"NAME\": \"gravity_region\", \"PREDICATE\": \"abs({HEIGHT}) < h_max\", \"CONDITION\": \"abs(HEIGHT) < h_max\"}], \"NOT_CHOSEN\": \"No gravity: no weight acts on any DOF.\", \"NOT_INCLUDED\": [\"No variation of gravity with height or latitude beyond what g_n contains.\", \"No Earth rotation (Coriolis or centrifugal force) beyond what g_n contains.\", \"No gravity of bodies other than the Earth.\"], \"EXCLUDES\": [], \"INTERACTS_WITH\": [{\"WITH\": \"AIR-*\", \"QUESTION_ID\": \"BUOYANCY\", \"QUESTION\": \"Does the air's buoyancy (upthrust) act on the body in the system you mean?\", \"YES_LINE\": \"Buoyancy acts (your answer): no module adds it; it acts in this kernel only where one of your own laws states it.\", \"NO_LINE\": \"No buoyancy: the air's upthrust on the body is not included.\"}], \"TEST_BINDINGS\": [{\"NAME\": \"PROJECTILE_2D\", \"TPK\": {\"DOF\": [{\"NAME\": \"t\", \"DIMENSION\": \"T1\"}, {\"NAME\": \"x\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"z\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"v_x\", \"DIMENSION\": \"L1 T-1\"}, {\"NAME\": \"v_z\", \"DIMENSION\": \"L1 T-1\"}], \"CONSTANT\": [{\"NAME\": \"m\", \"DIMENSION\": \"M1\"}], \"LAW\": [{\"NAME\": \"KIN_X\", \"STATEMENT\": \"dx/dt = v_x\", \"REFS\": [\"t\", \"v_x\", \"x\"], \"ROLE\": \"EOM(x)\", \"EQUATION\": \"D(x,t)=v_x\"}, {\"NAME\": \"KIN_Z\", \"STATEMENT\": \"dz/dt = v_z\", \"REFS\": [\"t\", \"v_z\", \"z\"], \"ROLE\": \"EOM(z)\", \"EQUATION\": \"D(z,t)=v_z\"}, {\"NAME\": \"EOM_X\", \"STATEMENT\": \"m dv_x/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_x\"], \"ROLE\": \"EOM(v_x)\", \"EQUATION\": \"m*D(v_x,t)=0\"}, {\"NAME\": \"EOM_Z\", \"STATEMENT\": \"m dv_z/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_z\"], \"ROLE\": \"EOM(v_z)\", \"EQUATION\": \"m*D(v_z,t)=0\"}], \"ASSUMPTION\": [{\"NAME\": \"point_mass\", \"PROPOSITION\": \"the body is treated as a point mass\", \"REFS\": [\"m\"]}]}, \"BIND\": {\"HEIGHT\": [\"z\"], \"MASS\": [\"m\"], \"UP_VELOCITY\": [\"v_z\"]}, \"VALUES\": {\"h_max\": {\"VALUE\": \"100\", \"UNIT\": \"m\"}}, \"ANSWERS\": {}}, {\"NAME\": \"TABLE\", \"TPK\": {\"DOF\": [{\"NAME\": \"t\", \"DIMENSION\": \"T1\"}, {\"NAME\": \"x\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"z\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"v_x\", \"DIMENSION\": \"L1 T-1\"}, {\"NAME\": \"v_z\", \"DIMENSION\": \"L1 T-1\"}], \"CONSTANT\": [{\"NAME\": \"m\", \"DIMENSION\": \"M1\"}], \"LAW\": [{\"NAME\": \"KIN_X\", \"STATEMENT\": \"dx/dt = v_x\", \"REFS\": [\"t\", \"v_x\", \"x\"], \"ROLE\": \"EOM(x)\", \"EQUATION\": \"D(x,t)=v_x\"}, {\"NAME\": \"KIN_Z\", \"STATEMENT\": \"dz/dt = v_z\", \"REFS\": [\"t\", \"v_z\", \"z\"], \"ROLE\": \"CONSTRAINT\", \"EQUATION\": \"D(z,t)=v_z\"}, {\"NAME\": \"EOM_X\", \"STATEMENT\": \"m dv_x/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_x\"], \"ROLE\": \"EOM(v_x)\", \"EQUATION\": \"m*D(v_x,t)=0\"}], \"CONSTRAINT\": [{\"NAME\": \"C_Z\", \"TARGET\": \"z\", \"ACTION\": \"FIX\", \"VALUE\": \"0\", \"UNIT\": \"m\", \"STATEMENT\": \"the puck stays on the table top, z = 0\"}, {\"NAME\": \"C_VZ\", \"TARGET\": \"v_z\", \"ACTION\": \"FIX\", \"VALUE\": \"0\", \"UNIT\": \"m s-1\", \"STATEMENT\": \"the puck has no vertical velocity\"}]}, \"BIND\": {\"HEIGHT\": [\"z\"], \"MASS\": [\"m\"], \"UP_VELOCITY\": [\"v_z\"]}, \"VALUES\": {\"h_max\": {\"VALUE\": \"1\", \"UNIT\": \"m\"}}, \"ANSWERS\": {\"FIXED:v_z\": \"YES\"}}]}",
"{\"ID\": \"MATH\", \"VERSION\": \"1.0.0\", \"TITLE\": \"The mathematical constant pi, as the CONSTANT pi_c\", \"SOURCE\": \"pi to 16 significant digits, 3.141592653589793, the nearest IEEE 754 binary64 value\", \"PREREQUISITES\": [], \"PARAMETERS\": [{\"NAME\": \"pi_c\", \"DIMENSION\": \"1\", \"SUPPLY\": \"DECLARED\", \"VALUE\": \"3.141592653589793\", \"UNIT\": \"1\", \"OVERRIDABLE\": \"NO\", \"LABEL\": \"pi, to 16 significant digits\"}], \"SUMS\": [], \"TERMS\": [], \"ASSUMPTIONS\": [], \"BOUNDARIES\": [], \"NOT_CHOSEN\": \"No mathematical constant: pi exists only if you declare it.\", \"NOT_INCLUDED\": [\"pi_c is pi rounded to 16 significant digits; no other mathematical constant is declared.\"], \"EXCLUDES\": [], \"INTERACTS_WITH\": [], \"TEST_BINDINGS\": [{\"NAME\": \"PROJECTILE_2D\", \"TPK\": {\"DOF\": [{\"NAME\": \"t\", \"DIMENSION\": \"T1\"}, {\"NAME\": \"x\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"z\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"v_x\", \"DIMENSION\": \"L1 T-1\"}, {\"NAME\": \"v_z\", \"DIMENSION\": \"L1 T-1\"}], \"CONSTANT\": [{\"NAME\": \"m\", \"DIMENSION\": \"M1\"}], \"LAW\": [{\"NAME\": \"KIN_X\", \"STATEMENT\": \"dx/dt = v_x\", \"REFS\": [\"t\", \"v_x\", \"x\"], \"ROLE\": \"EOM(x)\", \"EQUATION\": \"D(x,t)=v_x\"}, {\"NAME\": \"KIN_Z\", \"STATEMENT\": \"dz/dt = v_z\", \"REFS\": [\"t\", \"v_z\", \"z\"], \"ROLE\": \"EOM(z)\", \"EQUATION\": \"D(z,t)=v_z\"}, {\"NAME\": \"EOM_X\", \"STATEMENT\": \"m dv_x/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_x\"], \"ROLE\": \"EOM(v_x)\", \"EQUATION\": \"m*D(v_x,t)=0\"}, {\"NAME\": \"EOM_Z\", \"STATEMENT\": \"m dv_z/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_z\"], \"ROLE\": \"EOM(v_z)\", \"EQUATION\": \"m*D(v_z,t)=0\"}], \"ASSUMPTION\": [{\"NAME\": \"point_mass\", \"PROPOSITION\": \"the body is treated as a point mass\", \"REFS\": [\"m\"]}]}, \"BIND\": {}, \"VALUES\": {}, \"ANSWERS\": {}}]}"
]
},
"expected": "[\"REFUSED\",\"CLAIM GRAV-UNIFORM 1.1.0: no module text\"]",
"fn": "module_expand",
"hand_checked": true,
"name": "X36 a claimed version with no text"
},
{
"args": {
"claims": [
{
"ANSWERS": {},
"BIND": {
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"z"
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"MASS": [
"m"
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"UP_VELOCITY": [
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},
"DIGEST": "24877ccb5c8ec300d29ed82ce6650592f35cf8899a3d878ccce9c08d4c72c025",
"ID": "GRAV-UNIFORM",
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"UNIT": "m",
"VALUE": "100"
}
},
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},
{
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},
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"ID": "GRAV-UNIFORM",
"VALUES": {
"h_max": {
"UNIT": "m",
"VALUE": "100"
}
},
"VERSION": "1.0.0"
}
],
"draft": {
"TPK": {
"ASSUMPTION": [
{
"NAME": "point_mass",
"PROPOSITION": "the body is treated as a point mass",
"REFS": [
"m"
]
}
],
"CONSTANT": [
{
"DIMENSION": "M1",
"NAME": "m"
}
],
"DOF": [
{
"DIMENSION": "T1",
"NAME": "t"
},
{
"DIMENSION": "L1",
"NAME": "x"
},
{
"DIMENSION": "L1",
"NAME": "z"
},
{
"DIMENSION": "L1 T-1",
"NAME": "v_x"
},
{
"DIMENSION": "L1 T-1",
"NAME": "v_z"
}
],
"LAW": [
{
"EQUATION": "D(x,t)=v_x",
"NAME": "KIN_X",
"REFS": [
"t",
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"x"
],
"ROLE": "EOM(x)",
"STATEMENT": "dx/dt = v_x"
},
{
"EQUATION": "D(z,t)=v_z",
"NAME": "KIN_Z",
"REFS": [
"t",
"v_z",
"z"
],
"ROLE": "EOM(z)",
"STATEMENT": "dz/dt = v_z"
},
{
"EQUATION": "m*D(v_x,t)=0",
"NAME": "EOM_X",
"REFS": [
"m",
"t",
"v_x"
],
"ROLE": "EOM(v_x)",
"STATEMENT": "m dv_x/dt = 0"
},
{
"EQUATION": "m*D(v_z,t)=0",
"NAME": "EOM_Z",
"REFS": [
"m",
"t",
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],
"ROLE": "EOM(v_z)",
"STATEMENT": "m dv_z/dt = 0"
}
]
}
},
"modules": [
"{\"ID\": \"AIR-LINEAR\", \"VERSION\": \"1.0.0\", \"TITLE\": \"Air resistance at sea level, linear in the speed (Stokes drag on a sphere)\", \"SOURCE\": \"ISO 2533:1975, Standard Atmosphere, sea-level values: density 1.225 kg m-3, dynamic viscosity 1.7894e-5 Pa s\", \"PREREQUISITES\": [{\"SLOT\": \"VELOCITY\", \"KIND\": \"DOF\", \"DIMENSION\": \"L1 T-1\", \"MIN\": 1, \"MAX\": 3, \"LABEL\": \"the velocity components of the body, one per axis\"}], \"PARAMETERS\": [{\"NAME\": \"rho_air\", \"DIMENSION\": \"L-3 M1\", \"SUPPLY\": \"DECLARED\", \"VALUE\": \"1.225\", \"UNIT\": \"kg m-3\", \"OVERRIDABLE\": \"NO\", \"LABEL\": \"the density of air at sea level\"}, {\"NAME\": \"mu_air\", \"DIMENSION\": \"L-1 M1 T-1\", \"SUPPLY\": \"DECLARED\", \"VALUE\": \"1.7894e-5\", \"UNIT\": \"Pa s\", \"OVERRIDABLE\": \"NO\", \"LABEL\": \"the dynamic viscosity of air at sea level\"}, {\"NAME\": \"pi_c\", \"DIMENSION\": \"1\", \"SUPPLY\": \"DECLARED\", \"VALUE\": \"3.141592653589793\", \"UNIT\": \"1\", \"OVERRIDABLE\": \"NO\", \"LABEL\": \"pi, to 16 significant digits\"}, {\"NAME\": \"R_s\", \"DIMENSION\": \"L1\", \"SUPPLY\": \"AUTHOR\", \"LABEL\": \"the radius of the sphere\"}], \"SUMS\": [{\"NAME\": \"SPEED2\", \"OVER\": \"VELOCITY\", \"EACH\": \"VELOCITY^2\"}], \"TERMS\": [{\"TARGET\": \"VELOCITY\", \"SIGN\": \"-\", \"EXPR\": \"6*pi_c*mu_air*R_s*VELOCITY\", \"LABEL\": \"the linear (Stokes) drag\"}], \"ASSUMPTIONS\": [{\"NAME\": \"air_still\", \"PROPOSITION\": \"the air is at rest in the frame of the body's velocity\", \"REFS\": [\"VELOCITY\"]}, {\"NAME\": \"air_uniform\", \"PROPOSITION\": \"the air density is uniform over the region of motion\", \"REFS\": [\"rho_air\"]}, {\"NAME\": \"drag_sphere\", \"PROPOSITION\": \"the body is a rigid sphere of radius R_s\", \"REFS\": [\"R_s\"]}], \"BOUNDARIES\": [{\"NAME\": \"drag_linear_regime\", \"PREDICATE\": \"2 rho_air |v| R_s / mu_air < 1: the regime of the linear law\", \"CONDITION\": \"mu_air != 0 and SPEED2 >= 0 and 2*rho_air*sqrt(SPEED2)*R_s/mu_air < 1\"}], \"NOT_CHOSEN\": \"No linear (Stokes) air resistance.\", \"NOT_INCLUDED\": [\"No wind: the air is at rest.\", \"No change of air density or viscosity with altitude or temperature.\", \"No drag outside the regime of the linear law.\"], \"EXCLUDES\": [], \"INTERACTS_WITH\": [], \"TEST_BINDINGS\": [{\"NAME\": \"PROJECTILE_2D\", \"TPK\": {\"DOF\": [{\"NAME\": \"t\", \"DIMENSION\": \"T1\"}, {\"NAME\": \"x\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"z\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"v_x\", \"DIMENSION\": \"L1 T-1\"}, {\"NAME\": \"v_z\", \"DIMENSION\": \"L1 T-1\"}], \"CONSTANT\": [{\"NAME\": \"m\", \"DIMENSION\": \"M1\"}], \"LAW\": [{\"NAME\": \"KIN_X\", \"STATEMENT\": \"dx/dt = v_x\", \"REFS\": [\"t\", \"v_x\", \"x\"], \"ROLE\": \"EOM(x)\", \"EQUATION\": \"D(x,t)=v_x\"}, {\"NAME\": \"KIN_Z\", \"STATEMENT\": \"dz/dt = v_z\", \"REFS\": [\"t\", \"v_z\", \"z\"], \"ROLE\": \"EOM(z)\", \"EQUATION\": \"D(z,t)=v_z\"}, {\"NAME\": \"EOM_X\", \"STATEMENT\": \"m dv_x/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_x\"], \"ROLE\": \"EOM(v_x)\", \"EQUATION\": \"m*D(v_x,t)=0\"}, {\"NAME\": \"EOM_Z\", \"STATEMENT\": \"m dv_z/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_z\"], \"ROLE\": \"EOM(v_z)\", \"EQUATION\": \"m*D(v_z,t)=0\"}], \"ASSUMPTION\": [{\"NAME\": \"point_mass\", \"PROPOSITION\": \"the body is treated as a point mass\", \"REFS\": [\"m\"]}]}, \"BIND\": {\"VELOCITY\": [\"v_x\", \"v_z\"]}, \"VALUES\": {\"R_s\": {}}, \"ANSWERS\": {}}]}",
"{\"ID\": \"AIR-QUADRATIC\", \"VERSION\": \"1.0.0\", \"TITLE\": \"Air resistance at sea level, quadratic in the speed\", \"SOURCE\": \"ISO 2533:1975, Standard Atmosphere, sea-level values: density 1.225 kg m-3, dynamic viscosity 1.7894e-5 Pa s\", \"PREREQUISITES\": [{\"SLOT\": \"VELOCITY\", \"KIND\": \"DOF\", \"DIMENSION\": \"L1 T-1\", \"MIN\": 1, \"MAX\": 3, \"LABEL\": \"the velocity components of the body, one per axis\"}], \"PARAMETERS\": [{\"NAME\": \"rho_air\", \"DIMENSION\": \"L-3 M1\", \"SUPPLY\": \"DECLARED\", \"VALUE\": \"1.225\", \"UNIT\": \"kg m-3\", \"OVERRIDABLE\": \"NO\", \"LABEL\": \"the density of air at sea level\"}, {\"NAME\": \"mu_air\", \"DIMENSION\": \"L-1 M1 T-1\", \"SUPPLY\": \"DECLARED\", \"VALUE\": \"1.7894e-5\", \"UNIT\": \"Pa s\", \"OVERRIDABLE\": \"NO\", \"LABEL\": \"the dynamic viscosity of air at sea level\"}, {\"NAME\": \"C_d\", \"DIMENSION\": \"1\", \"SUPPLY\": \"AUTHOR\", \"LABEL\": \"the drag coefficient of the body\"}, {\"NAME\": \"A_ref\", \"DIMENSION\": \"L2\", \"SUPPLY\": \"AUTHOR\", \"LABEL\": \"the reference area of the drag coefficient\"}, {\"NAME\": \"L_ref\", \"DIMENSION\": \"L1\", \"SUPPLY\": \"AUTHOR\", \"LABEL\": \"the reference length of the Reynolds number\"}], \"SUMS\": [{\"NAME\": \"SPEED2\", \"OVER\": \"VELOCITY\", \"EACH\": \"VELOCITY^2\"}], \"TERMS\": [{\"TARGET\": \"VELOCITY\", \"SIGN\": \"-\", \"EXPR\": \"0.5*rho_air*C_d*A_ref*sqrt(SPEED2)*VELOCITY\", \"LABEL\": \"the quadratic drag\"}], \"ASSUMPTIONS\": [{\"NAME\": \"air_still\", \"PROPOSITION\": \"the air is at rest in the frame of the body's velocity\", \"REFS\": [\"VELOCITY\"]}, {\"NAME\": \"air_uniform\", \"PROPOSITION\": \"the air density is uniform over the region of motion\", \"REFS\": [\"rho_air\"]}, {\"NAME\": \"drag_cd_constant\", \"PROPOSITION\": \"the drag coefficient C_d is constant over the motion\", \"REFS\": [\"C_d\"]}, {\"NAME\": \"drag_no_lift\", \"PROPOSITION\": \"the body experiences no lift force\", \"REFS\": [\"VELOCITY\"]}, {\"NAME\": \"drag_no_magnus\", \"PROPOSITION\": \"the body experiences no Magnus force\", \"REFS\": [\"VELOCITY\"]}], \"BOUNDARIES\": [{\"NAME\": \"drag_quadratic_regime\", \"PREDICATE\": \"1e3 < rho_air |v| L_ref / mu_air < 2e5: the Reynolds window of the quadratic law\", \"CONDITION\": \"mu_air != 0 and SPEED2 >= 0 and rho_air*sqrt(SPEED2)*L_ref/mu_air > 1000 and rho_air*sqrt(SPEED2)*L_ref/mu_air < 200000\"}], \"NOT_CHOSEN\": \"No quadratic air resistance.\", \"NOT_INCLUDED\": [\"No wind: the air is at rest.\", \"No change of air density or viscosity with altitude or temperature.\", \"No lift, Magnus or added-mass force.\", \"No drag outside the Reynolds window of the quadratic law.\"], \"EXCLUDES\": [\"AIR-LINEAR\"], \"INTERACTS_WITH\": [], \"TEST_BINDINGS\": [{\"NAME\": \"PROJECTILE_2D\", \"TPK\": {\"DOF\": [{\"NAME\": \"t\", \"DIMENSION\": \"T1\"}, {\"NAME\": \"x\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"z\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"v_x\", \"DIMENSION\": \"L1 T-1\"}, {\"NAME\": \"v_z\", \"DIMENSION\": \"L1 T-1\"}], \"CONSTANT\": [{\"NAME\": \"m\", \"DIMENSION\": \"M1\"}], \"LAW\": [{\"NAME\": \"KIN_X\", \"STATEMENT\": \"dx/dt = v_x\", \"REFS\": [\"t\", \"v_x\", \"x\"], \"ROLE\": \"EOM(x)\", \"EQUATION\": \"D(x,t)=v_x\"}, {\"NAME\": \"KIN_Z\", \"STATEMENT\": \"dz/dt = v_z\", \"REFS\": [\"t\", \"v_z\", \"z\"], \"ROLE\": \"EOM(z)\", \"EQUATION\": \"D(z,t)=v_z\"}, {\"NAME\": \"EOM_X\", \"STATEMENT\": \"m dv_x/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_x\"], \"ROLE\": \"EOM(v_x)\", \"EQUATION\": \"m*D(v_x,t)=0\"}, {\"NAME\": \"EOM_Z\", \"STATEMENT\": \"m dv_z/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_z\"], \"ROLE\": \"EOM(v_z)\", \"EQUATION\": \"m*D(v_z,t)=0\"}], \"ASSUMPTION\": [{\"NAME\": \"point_mass\", \"PROPOSITION\": \"the body is treated as a point mass\", \"REFS\": [\"m\"]}]}, \"BIND\": {\"VELOCITY\": [\"v_x\", \"v_z\"]}, \"VALUES\": {\"A_ref\": {}, \"C_d\": {}, \"L_ref\": {}}, \"ANSWERS\": {}}]}",
"{\"ID\": \"GRAV-UNIFORM\", \"VERSION\": \"1.0.0\", \"TITLE\": \"Uniform gravity at the standard value g_n\", \"SOURCE\": \"g_n = 9.80665 m s-2, exact by definition: 3rd CGPM (1901), declaration on the unit of mass and on the definition of weight\", \"PREREQUISITES\": [{\"SLOT\": \"MASS\", \"KIND\": \"CONSTANT\", \"DIMENSION\": \"M1\", \"MIN\": 1, \"MAX\": 1, \"LABEL\": \"the mass of the body\"}, {\"SLOT\": \"UP_VELOCITY\", \"KIND\": \"DOF\", \"DIMENSION\": \"L1 T-1\", \"MIN\": 1, \"MAX\": 1, \"LABEL\": \"the velocity component pointing up; its equation of motion receives the weight\"}, {\"SLOT\": \"HEIGHT\", \"KIND\": \"DOF\", \"DIMENSION\": \"L1\", \"MIN\": 1, \"MAX\": 1, \"LABEL\": \"the position along the same upward axis\"}], \"PARAMETERS\": [{\"NAME\": \"g_n\", \"DIMENSION\": \"L1 T-2\", \"SUPPLY\": \"DECLARED\", \"VALUE\": \"9.80665\", \"UNIT\": \"m s-2\", \"OVERRIDABLE\": \"NO\", \"LABEL\": \"the standard acceleration of gravity\"}, {\"NAME\": \"h_max\", \"DIMENSION\": \"L1\", \"SUPPLY\": \"AUTHOR\", \"LABEL\": \"the largest height, above or below the origin, over which the field is taken as uniform\"}], \"SUMS\": [], \"TERMS\": [{\"TARGET\": \"UP_VELOCITY\", \"SIGN\": \"-\", \"EXPR\": \"MASS*g_n\", \"LABEL\": \"the weight\"}], \"ASSUMPTIONS\": [{\"NAME\": \"gravity_uniform\", \"PROPOSITION\": \"the gravitational field is uniform over the region abs({HEIGHT}) < h_max\", \"REFS\": [\"HEIGHT\", \"h_max\"]}, {\"NAME\": \"gravity_standard\", \"PROPOSITION\": \"the local gravitational acceleration equals the conventional standard value g_n\", \"REFS\": [\"g_n\"]}, {\"NAME\": \"frame_inertial\", \"PROPOSITION\": \"the frame in which {HEIGHT} is measured is treated as inertial\", \"REFS\": [\"HEIGHT\"]}], \"BOUNDARIES\": [{\"NAME\": \"gravity_region\", \"PREDICATE\": \"abs({HEIGHT}) < h_max\", \"CONDITION\": \"abs(HEIGHT) < h_max\"}], \"NOT_CHOSEN\": \"No gravity: no weight acts on any DOF.\", \"NOT_INCLUDED\": [\"No variation of gravity with height or latitude beyond what g_n contains.\", \"No Earth rotation (Coriolis or centrifugal force) beyond what g_n contains.\", \"No gravity of bodies other than the Earth.\"], \"EXCLUDES\": [], \"INTERACTS_WITH\": [{\"WITH\": \"AIR-*\", \"QUESTION_ID\": \"BUOYANCY\", \"QUESTION\": \"Does the air's buoyancy (upthrust) act on the body in the system you mean?\", \"YES_LINE\": \"Buoyancy acts (your answer): no module adds it; it acts in this kernel only where one of your own laws states it.\", \"NO_LINE\": \"No buoyancy: the air's upthrust on the body is not included.\"}], \"TEST_BINDINGS\": [{\"NAME\": \"PROJECTILE_2D\", \"TPK\": {\"DOF\": [{\"NAME\": \"t\", \"DIMENSION\": \"T1\"}, {\"NAME\": \"x\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"z\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"v_x\", \"DIMENSION\": \"L1 T-1\"}, {\"NAME\": \"v_z\", \"DIMENSION\": \"L1 T-1\"}], \"CONSTANT\": [{\"NAME\": \"m\", \"DIMENSION\": \"M1\"}], \"LAW\": [{\"NAME\": \"KIN_X\", \"STATEMENT\": \"dx/dt = v_x\", \"REFS\": [\"t\", \"v_x\", \"x\"], \"ROLE\": \"EOM(x)\", \"EQUATION\": \"D(x,t)=v_x\"}, {\"NAME\": \"KIN_Z\", \"STATEMENT\": \"dz/dt = v_z\", \"REFS\": [\"t\", \"v_z\", \"z\"], \"ROLE\": \"EOM(z)\", \"EQUATION\": \"D(z,t)=v_z\"}, {\"NAME\": \"EOM_X\", \"STATEMENT\": \"m dv_x/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_x\"], \"ROLE\": \"EOM(v_x)\", \"EQUATION\": \"m*D(v_x,t)=0\"}, {\"NAME\": \"EOM_Z\", \"STATEMENT\": \"m dv_z/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_z\"], \"ROLE\": \"EOM(v_z)\", \"EQUATION\": \"m*D(v_z,t)=0\"}], \"ASSUMPTION\": [{\"NAME\": \"point_mass\", \"PROPOSITION\": \"the body is treated as a point mass\", \"REFS\": [\"m\"]}]}, \"BIND\": {\"HEIGHT\": [\"z\"], \"MASS\": [\"m\"], \"UP_VELOCITY\": [\"v_z\"]}, \"VALUES\": {\"h_max\": {\"VALUE\": \"100\", \"UNIT\": \"m\"}}, \"ANSWERS\": {}}, {\"NAME\": \"TABLE\", \"TPK\": {\"DOF\": [{\"NAME\": \"t\", \"DIMENSION\": \"T1\"}, {\"NAME\": \"x\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"z\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"v_x\", \"DIMENSION\": \"L1 T-1\"}, {\"NAME\": \"v_z\", \"DIMENSION\": \"L1 T-1\"}], \"CONSTANT\": [{\"NAME\": \"m\", \"DIMENSION\": \"M1\"}], \"LAW\": [{\"NAME\": \"KIN_X\", \"STATEMENT\": \"dx/dt = v_x\", \"REFS\": [\"t\", \"v_x\", \"x\"], \"ROLE\": \"EOM(x)\", \"EQUATION\": \"D(x,t)=v_x\"}, {\"NAME\": \"KIN_Z\", \"STATEMENT\": \"dz/dt = v_z\", \"REFS\": [\"t\", \"v_z\", \"z\"], \"ROLE\": \"CONSTRAINT\", \"EQUATION\": \"D(z,t)=v_z\"}, {\"NAME\": \"EOM_X\", \"STATEMENT\": \"m dv_x/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_x\"], \"ROLE\": \"EOM(v_x)\", \"EQUATION\": \"m*D(v_x,t)=0\"}], \"CONSTRAINT\": [{\"NAME\": \"C_Z\", \"TARGET\": \"z\", \"ACTION\": \"FIX\", \"VALUE\": \"0\", \"UNIT\": \"m\", \"STATEMENT\": \"the puck stays on the table top, z = 0\"}, {\"NAME\": \"C_VZ\", \"TARGET\": \"v_z\", \"ACTION\": \"FIX\", \"VALUE\": \"0\", \"UNIT\": \"m s-1\", \"STATEMENT\": \"the puck has no vertical velocity\"}]}, \"BIND\": {\"HEIGHT\": [\"z\"], \"MASS\": [\"m\"], \"UP_VELOCITY\": [\"v_z\"]}, \"VALUES\": {\"h_max\": {\"VALUE\": \"1\", \"UNIT\": \"m\"}}, \"ANSWERS\": {\"FIXED:v_z\": \"YES\"}}]}",
"{\"ID\": \"MATH\", \"VERSION\": \"1.0.0\", \"TITLE\": \"The mathematical constant pi, as the CONSTANT pi_c\", \"SOURCE\": \"pi to 16 significant digits, 3.141592653589793, the nearest IEEE 754 binary64 value\", \"PREREQUISITES\": [], \"PARAMETERS\": [{\"NAME\": \"pi_c\", \"DIMENSION\": \"1\", \"SUPPLY\": \"DECLARED\", \"VALUE\": \"3.141592653589793\", \"UNIT\": \"1\", \"OVERRIDABLE\": \"NO\", \"LABEL\": \"pi, to 16 significant digits\"}], \"SUMS\": [], \"TERMS\": [], \"ASSUMPTIONS\": [], \"BOUNDARIES\": [], \"NOT_CHOSEN\": \"No mathematical constant: pi exists only if you declare it.\", \"NOT_INCLUDED\": [\"pi_c is pi rounded to 16 significant digits; no other mathematical constant is declared.\"], \"EXCLUDES\": [], \"INTERACTS_WITH\": [], \"TEST_BINDINGS\": [{\"NAME\": \"PROJECTILE_2D\", \"TPK\": {\"DOF\": [{\"NAME\": \"t\", \"DIMENSION\": \"T1\"}, {\"NAME\": \"x\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"z\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"v_x\", \"DIMENSION\": \"L1 T-1\"}, {\"NAME\": \"v_z\", \"DIMENSION\": \"L1 T-1\"}], \"CONSTANT\": [{\"NAME\": \"m\", \"DIMENSION\": \"M1\"}], \"LAW\": [{\"NAME\": \"KIN_X\", \"STATEMENT\": \"dx/dt = v_x\", \"REFS\": [\"t\", \"v_x\", \"x\"], \"ROLE\": \"EOM(x)\", \"EQUATION\": \"D(x,t)=v_x\"}, {\"NAME\": \"KIN_Z\", \"STATEMENT\": \"dz/dt = v_z\", \"REFS\": [\"t\", \"v_z\", \"z\"], \"ROLE\": \"EOM(z)\", \"EQUATION\": \"D(z,t)=v_z\"}, {\"NAME\": \"EOM_X\", \"STATEMENT\": \"m dv_x/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_x\"], \"ROLE\": \"EOM(v_x)\", \"EQUATION\": \"m*D(v_x,t)=0\"}, {\"NAME\": \"EOM_Z\", \"STATEMENT\": \"m dv_z/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_z\"], \"ROLE\": \"EOM(v_z)\", \"EQUATION\": \"m*D(v_z,t)=0\"}], \"ASSUMPTION\": [{\"NAME\": \"point_mass\", \"PROPOSITION\": \"the body is treated as a point mass\", \"REFS\": [\"m\"]}]}, \"BIND\": {}, \"VALUES\": {}, \"ANSWERS\": {}}]}"
]
},
"expected": "[\"REFUSED\",\"CLAIMS: duplicate module GRAV-UNIFORM\"]",
"fn": "module_expand",
"hand_checked": true,
"name": "X37 two claims of one module"
},
{
"args": {
"claims": {
"ANSWERS": {},
"BIND": {
"HEIGHT": [
"z"
],
"MASS": [
"m"
],
"UP_VELOCITY": [
"v_z"
]
},
"DIGEST": "24877ccb5c8ec300d29ed82ce6650592f35cf8899a3d878ccce9c08d4c72c025",
"ID": "GRAV-UNIFORM",
"VALUES": {
"h_max": {
"UNIT": "m",
"VALUE": "100"
}
},
"VERSION": "1.0.0"
},
"draft": {
"TPK": {
"ASSUMPTION": [
{
"NAME": "point_mass",
"PROPOSITION": "the body is treated as a point mass",
"REFS": [
"m"
]
}
],
"CONSTANT": [
{
"DIMENSION": "M1",
"NAME": "m"
}
],
"DOF": [
{
"DIMENSION": "T1",
"NAME": "t"
},
{
"DIMENSION": "L1",
"NAME": "x"
},
{
"DIMENSION": "L1",
"NAME": "z"
},
{
"DIMENSION": "L1 T-1",
"NAME": "v_x"
},
{
"DIMENSION": "L1 T-1",
"NAME": "v_z"
}
],
"LAW": [
{
"EQUATION": "D(x,t)=v_x",
"NAME": "KIN_X",
"REFS": [
"t",
"v_x",
"x"
],
"ROLE": "EOM(x)",
"STATEMENT": "dx/dt = v_x"
},
{
"EQUATION": "D(z,t)=v_z",
"NAME": "KIN_Z",
"REFS": [
"t",
"v_z",
"z"
],
"ROLE": "EOM(z)",
"STATEMENT": "dz/dt = v_z"
},
{
"EQUATION": "m*D(v_x,t)=0",
"NAME": "EOM_X",
"REFS": [
"m",
"t",
"v_x"
],
"ROLE": "EOM(v_x)",
"STATEMENT": "m dv_x/dt = 0"
},
{
"EQUATION": "m*D(v_z,t)=0",
"NAME": "EOM_Z",
"REFS": [
"m",
"t",
"v_z"
],
"ROLE": "EOM(v_z)",
"STATEMENT": "m dv_z/dt = 0"
}
]
}
},
"modules": [
"{\"ID\": \"AIR-LINEAR\", \"VERSION\": \"1.0.0\", \"TITLE\": \"Air resistance at sea level, linear in the speed (Stokes drag on a sphere)\", \"SOURCE\": \"ISO 2533:1975, Standard Atmosphere, sea-level values: density 1.225 kg m-3, dynamic viscosity 1.7894e-5 Pa s\", \"PREREQUISITES\": [{\"SLOT\": \"VELOCITY\", \"KIND\": \"DOF\", \"DIMENSION\": \"L1 T-1\", \"MIN\": 1, \"MAX\": 3, \"LABEL\": \"the velocity components of the body, one per axis\"}], \"PARAMETERS\": [{\"NAME\": \"rho_air\", \"DIMENSION\": \"L-3 M1\", \"SUPPLY\": \"DECLARED\", \"VALUE\": \"1.225\", \"UNIT\": \"kg m-3\", \"OVERRIDABLE\": \"NO\", \"LABEL\": \"the density of air at sea level\"}, {\"NAME\": \"mu_air\", \"DIMENSION\": \"L-1 M1 T-1\", \"SUPPLY\": \"DECLARED\", \"VALUE\": \"1.7894e-5\", \"UNIT\": \"Pa s\", \"OVERRIDABLE\": \"NO\", \"LABEL\": \"the dynamic viscosity of air at sea level\"}, {\"NAME\": \"pi_c\", \"DIMENSION\": \"1\", \"SUPPLY\": \"DECLARED\", \"VALUE\": \"3.141592653589793\", \"UNIT\": \"1\", \"OVERRIDABLE\": \"NO\", \"LABEL\": \"pi, to 16 significant digits\"}, {\"NAME\": \"R_s\", \"DIMENSION\": \"L1\", \"SUPPLY\": \"AUTHOR\", \"LABEL\": \"the radius of the sphere\"}], \"SUMS\": [{\"NAME\": \"SPEED2\", \"OVER\": \"VELOCITY\", \"EACH\": \"VELOCITY^2\"}], \"TERMS\": [{\"TARGET\": \"VELOCITY\", \"SIGN\": \"-\", \"EXPR\": \"6*pi_c*mu_air*R_s*VELOCITY\", \"LABEL\": \"the linear (Stokes) drag\"}], \"ASSUMPTIONS\": [{\"NAME\": \"air_still\", \"PROPOSITION\": \"the air is at rest in the frame of the body's velocity\", \"REFS\": [\"VELOCITY\"]}, {\"NAME\": \"air_uniform\", \"PROPOSITION\": \"the air density is uniform over the region of motion\", \"REFS\": [\"rho_air\"]}, {\"NAME\": \"drag_sphere\", \"PROPOSITION\": \"the body is a rigid sphere of radius R_s\", \"REFS\": [\"R_s\"]}], \"BOUNDARIES\": [{\"NAME\": \"drag_linear_regime\", \"PREDICATE\": \"2 rho_air |v| R_s / mu_air < 1: the regime of the linear law\", \"CONDITION\": \"mu_air != 0 and SPEED2 >= 0 and 2*rho_air*sqrt(SPEED2)*R_s/mu_air < 1\"}], \"NOT_CHOSEN\": \"No linear (Stokes) air resistance.\", \"NOT_INCLUDED\": [\"No wind: the air is at rest.\", \"No change of air density or viscosity with altitude or temperature.\", \"No drag outside the regime of the linear law.\"], \"EXCLUDES\": [], \"INTERACTS_WITH\": [], \"TEST_BINDINGS\": [{\"NAME\": \"PROJECTILE_2D\", \"TPK\": {\"DOF\": [{\"NAME\": \"t\", \"DIMENSION\": \"T1\"}, {\"NAME\": \"x\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"z\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"v_x\", \"DIMENSION\": \"L1 T-1\"}, {\"NAME\": \"v_z\", \"DIMENSION\": \"L1 T-1\"}], \"CONSTANT\": [{\"NAME\": \"m\", \"DIMENSION\": \"M1\"}], \"LAW\": [{\"NAME\": \"KIN_X\", \"STATEMENT\": \"dx/dt = v_x\", \"REFS\": [\"t\", \"v_x\", \"x\"], \"ROLE\": \"EOM(x)\", \"EQUATION\": \"D(x,t)=v_x\"}, {\"NAME\": \"KIN_Z\", \"STATEMENT\": \"dz/dt = v_z\", \"REFS\": [\"t\", \"v_z\", \"z\"], \"ROLE\": \"EOM(z)\", \"EQUATION\": \"D(z,t)=v_z\"}, {\"NAME\": \"EOM_X\", \"STATEMENT\": \"m dv_x/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_x\"], \"ROLE\": \"EOM(v_x)\", \"EQUATION\": \"m*D(v_x,t)=0\"}, {\"NAME\": \"EOM_Z\", \"STATEMENT\": \"m dv_z/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_z\"], \"ROLE\": \"EOM(v_z)\", \"EQUATION\": \"m*D(v_z,t)=0\"}], \"ASSUMPTION\": [{\"NAME\": \"point_mass\", \"PROPOSITION\": \"the body is treated as a point mass\", \"REFS\": [\"m\"]}]}, \"BIND\": {\"VELOCITY\": [\"v_x\", \"v_z\"]}, \"VALUES\": {\"R_s\": {}}, \"ANSWERS\": {}}]}",
"{\"ID\": \"AIR-QUADRATIC\", \"VERSION\": \"1.0.0\", \"TITLE\": \"Air resistance at sea level, quadratic in the speed\", \"SOURCE\": \"ISO 2533:1975, Standard Atmosphere, sea-level values: density 1.225 kg m-3, dynamic viscosity 1.7894e-5 Pa s\", \"PREREQUISITES\": [{\"SLOT\": \"VELOCITY\", \"KIND\": \"DOF\", \"DIMENSION\": \"L1 T-1\", \"MIN\": 1, \"MAX\": 3, \"LABEL\": \"the velocity components of the body, one per axis\"}], \"PARAMETERS\": [{\"NAME\": \"rho_air\", \"DIMENSION\": \"L-3 M1\", \"SUPPLY\": \"DECLARED\", \"VALUE\": \"1.225\", \"UNIT\": \"kg m-3\", \"OVERRIDABLE\": \"NO\", \"LABEL\": \"the density of air at sea level\"}, {\"NAME\": \"mu_air\", \"DIMENSION\": \"L-1 M1 T-1\", \"SUPPLY\": \"DECLARED\", \"VALUE\": \"1.7894e-5\", \"UNIT\": \"Pa s\", \"OVERRIDABLE\": \"NO\", \"LABEL\": \"the dynamic viscosity of air at sea level\"}, {\"NAME\": \"C_d\", \"DIMENSION\": \"1\", \"SUPPLY\": \"AUTHOR\", \"LABEL\": \"the drag coefficient of the body\"}, {\"NAME\": \"A_ref\", \"DIMENSION\": \"L2\", \"SUPPLY\": \"AUTHOR\", \"LABEL\": \"the reference area of the drag coefficient\"}, {\"NAME\": \"L_ref\", \"DIMENSION\": \"L1\", \"SUPPLY\": \"AUTHOR\", \"LABEL\": \"the reference length of the Reynolds number\"}], \"SUMS\": [{\"NAME\": \"SPEED2\", \"OVER\": \"VELOCITY\", \"EACH\": \"VELOCITY^2\"}], \"TERMS\": [{\"TARGET\": \"VELOCITY\", \"SIGN\": \"-\", \"EXPR\": \"0.5*rho_air*C_d*A_ref*sqrt(SPEED2)*VELOCITY\", \"LABEL\": \"the quadratic drag\"}], \"ASSUMPTIONS\": [{\"NAME\": \"air_still\", \"PROPOSITION\": \"the air is at rest in the frame of the body's velocity\", \"REFS\": [\"VELOCITY\"]}, {\"NAME\": \"air_uniform\", \"PROPOSITION\": \"the air density is uniform over the region of motion\", \"REFS\": [\"rho_air\"]}, {\"NAME\": \"drag_cd_constant\", \"PROPOSITION\": \"the drag coefficient C_d is constant over the motion\", \"REFS\": [\"C_d\"]}, {\"NAME\": \"drag_no_lift\", \"PROPOSITION\": \"the body experiences no lift force\", \"REFS\": [\"VELOCITY\"]}, {\"NAME\": \"drag_no_magnus\", \"PROPOSITION\": \"the body experiences no Magnus force\", \"REFS\": [\"VELOCITY\"]}], \"BOUNDARIES\": [{\"NAME\": \"drag_quadratic_regime\", \"PREDICATE\": \"1e3 < rho_air |v| L_ref / mu_air < 2e5: the Reynolds window of the quadratic law\", \"CONDITION\": \"mu_air != 0 and SPEED2 >= 0 and rho_air*sqrt(SPEED2)*L_ref/mu_air > 1000 and rho_air*sqrt(SPEED2)*L_ref/mu_air < 200000\"}], \"NOT_CHOSEN\": \"No quadratic air resistance.\", \"NOT_INCLUDED\": [\"No wind: the air is at rest.\", \"No change of air density or viscosity with altitude or temperature.\", \"No lift, Magnus or added-mass force.\", \"No drag outside the Reynolds window of the quadratic law.\"], \"EXCLUDES\": [\"AIR-LINEAR\"], \"INTERACTS_WITH\": [], \"TEST_BINDINGS\": [{\"NAME\": \"PROJECTILE_2D\", \"TPK\": {\"DOF\": [{\"NAME\": \"t\", \"DIMENSION\": \"T1\"}, {\"NAME\": \"x\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"z\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"v_x\", \"DIMENSION\": \"L1 T-1\"}, {\"NAME\": \"v_z\", \"DIMENSION\": \"L1 T-1\"}], \"CONSTANT\": [{\"NAME\": \"m\", \"DIMENSION\": \"M1\"}], \"LAW\": [{\"NAME\": \"KIN_X\", \"STATEMENT\": \"dx/dt = v_x\", \"REFS\": [\"t\", \"v_x\", \"x\"], \"ROLE\": \"EOM(x)\", \"EQUATION\": \"D(x,t)=v_x\"}, {\"NAME\": \"KIN_Z\", \"STATEMENT\": \"dz/dt = v_z\", \"REFS\": [\"t\", \"v_z\", \"z\"], \"ROLE\": \"EOM(z)\", \"EQUATION\": \"D(z,t)=v_z\"}, {\"NAME\": \"EOM_X\", \"STATEMENT\": \"m dv_x/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_x\"], \"ROLE\": \"EOM(v_x)\", \"EQUATION\": \"m*D(v_x,t)=0\"}, {\"NAME\": \"EOM_Z\", \"STATEMENT\": \"m dv_z/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_z\"], \"ROLE\": \"EOM(v_z)\", \"EQUATION\": \"m*D(v_z,t)=0\"}], \"ASSUMPTION\": [{\"NAME\": \"point_mass\", \"PROPOSITION\": \"the body is treated as a point mass\", \"REFS\": [\"m\"]}]}, \"BIND\": {\"VELOCITY\": [\"v_x\", \"v_z\"]}, \"VALUES\": {\"A_ref\": {}, \"C_d\": {}, \"L_ref\": {}}, \"ANSWERS\": {}}]}",
"{\"ID\": \"GRAV-UNIFORM\", \"VERSION\": \"1.0.0\", \"TITLE\": \"Uniform gravity at the standard value g_n\", \"SOURCE\": \"g_n = 9.80665 m s-2, exact by definition: 3rd CGPM (1901), declaration on the unit of mass and on the definition of weight\", \"PREREQUISITES\": [{\"SLOT\": \"MASS\", \"KIND\": \"CONSTANT\", \"DIMENSION\": \"M1\", \"MIN\": 1, \"MAX\": 1, \"LABEL\": \"the mass of the body\"}, {\"SLOT\": \"UP_VELOCITY\", \"KIND\": \"DOF\", \"DIMENSION\": \"L1 T-1\", \"MIN\": 1, \"MAX\": 1, \"LABEL\": \"the velocity component pointing up; its equation of motion receives the weight\"}, {\"SLOT\": \"HEIGHT\", \"KIND\": \"DOF\", \"DIMENSION\": \"L1\", \"MIN\": 1, \"MAX\": 1, \"LABEL\": \"the position along the same upward axis\"}], \"PARAMETERS\": [{\"NAME\": \"g_n\", \"DIMENSION\": \"L1 T-2\", \"SUPPLY\": \"DECLARED\", \"VALUE\": \"9.80665\", \"UNIT\": \"m s-2\", \"OVERRIDABLE\": \"NO\", \"LABEL\": \"the standard acceleration of gravity\"}, {\"NAME\": \"h_max\", \"DIMENSION\": \"L1\", \"SUPPLY\": \"AUTHOR\", \"LABEL\": \"the largest height, above or below the origin, over which the field is taken as uniform\"}], \"SUMS\": [], \"TERMS\": [{\"TARGET\": \"UP_VELOCITY\", \"SIGN\": \"-\", \"EXPR\": \"MASS*g_n\", \"LABEL\": \"the weight\"}], \"ASSUMPTIONS\": [{\"NAME\": \"gravity_uniform\", \"PROPOSITION\": \"the gravitational field is uniform over the region abs({HEIGHT}) < h_max\", \"REFS\": [\"HEIGHT\", \"h_max\"]}, {\"NAME\": \"gravity_standard\", \"PROPOSITION\": \"the local gravitational acceleration equals the conventional standard value g_n\", \"REFS\": [\"g_n\"]}, {\"NAME\": \"frame_inertial\", \"PROPOSITION\": \"the frame in which {HEIGHT} is measured is treated as inertial\", \"REFS\": [\"HEIGHT\"]}], \"BOUNDARIES\": [{\"NAME\": \"gravity_region\", \"PREDICATE\": \"abs({HEIGHT}) < h_max\", \"CONDITION\": \"abs(HEIGHT) < h_max\"}], \"NOT_CHOSEN\": \"No gravity: no weight acts on any DOF.\", \"NOT_INCLUDED\": [\"No variation of gravity with height or latitude beyond what g_n contains.\", \"No Earth rotation (Coriolis or centrifugal force) beyond what g_n contains.\", \"No gravity of bodies other than the Earth.\"], \"EXCLUDES\": [], \"INTERACTS_WITH\": [{\"WITH\": \"AIR-*\", \"QUESTION_ID\": \"BUOYANCY\", \"QUESTION\": \"Does the air's buoyancy (upthrust) act on the body in the system you mean?\", \"YES_LINE\": \"Buoyancy acts (your answer): no module adds it; it acts in this kernel only where one of your own laws states it.\", \"NO_LINE\": \"No buoyancy: the air's upthrust on the body is not included.\"}], \"TEST_BINDINGS\": [{\"NAME\": \"PROJECTILE_2D\", \"TPK\": {\"DOF\": [{\"NAME\": \"t\", \"DIMENSION\": \"T1\"}, {\"NAME\": \"x\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"z\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"v_x\", \"DIMENSION\": \"L1 T-1\"}, {\"NAME\": \"v_z\", \"DIMENSION\": \"L1 T-1\"}], \"CONSTANT\": [{\"NAME\": \"m\", \"DIMENSION\": \"M1\"}], \"LAW\": [{\"NAME\": \"KIN_X\", \"STATEMENT\": \"dx/dt = v_x\", \"REFS\": [\"t\", \"v_x\", \"x\"], \"ROLE\": \"EOM(x)\", \"EQUATION\": \"D(x,t)=v_x\"}, {\"NAME\": \"KIN_Z\", \"STATEMENT\": \"dz/dt = v_z\", \"REFS\": [\"t\", \"v_z\", \"z\"], \"ROLE\": \"EOM(z)\", \"EQUATION\": \"D(z,t)=v_z\"}, {\"NAME\": \"EOM_X\", \"STATEMENT\": \"m dv_x/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_x\"], \"ROLE\": \"EOM(v_x)\", \"EQUATION\": \"m*D(v_x,t)=0\"}, {\"NAME\": \"EOM_Z\", \"STATEMENT\": \"m dv_z/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_z\"], \"ROLE\": \"EOM(v_z)\", \"EQUATION\": \"m*D(v_z,t)=0\"}], \"ASSUMPTION\": [{\"NAME\": \"point_mass\", \"PROPOSITION\": \"the body is treated as a point mass\", \"REFS\": [\"m\"]}]}, \"BIND\": {\"HEIGHT\": [\"z\"], \"MASS\": [\"m\"], \"UP_VELOCITY\": [\"v_z\"]}, \"VALUES\": {\"h_max\": {\"VALUE\": \"100\", \"UNIT\": \"m\"}}, \"ANSWERS\": {}}, {\"NAME\": \"TABLE\", \"TPK\": {\"DOF\": [{\"NAME\": \"t\", \"DIMENSION\": \"T1\"}, {\"NAME\": \"x\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"z\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"v_x\", \"DIMENSION\": \"L1 T-1\"}, {\"NAME\": \"v_z\", \"DIMENSION\": \"L1 T-1\"}], \"CONSTANT\": [{\"NAME\": \"m\", \"DIMENSION\": \"M1\"}], \"LAW\": [{\"NAME\": \"KIN_X\", \"STATEMENT\": \"dx/dt = v_x\", \"REFS\": [\"t\", \"v_x\", \"x\"], \"ROLE\": \"EOM(x)\", \"EQUATION\": \"D(x,t)=v_x\"}, {\"NAME\": \"KIN_Z\", \"STATEMENT\": \"dz/dt = v_z\", \"REFS\": [\"t\", \"v_z\", \"z\"], \"ROLE\": \"CONSTRAINT\", \"EQUATION\": \"D(z,t)=v_z\"}, {\"NAME\": \"EOM_X\", \"STATEMENT\": \"m dv_x/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_x\"], \"ROLE\": \"EOM(v_x)\", \"EQUATION\": \"m*D(v_x,t)=0\"}], \"CONSTRAINT\": [{\"NAME\": \"C_Z\", \"TARGET\": \"z\", \"ACTION\": \"FIX\", \"VALUE\": \"0\", \"UNIT\": \"m\", \"STATEMENT\": \"the puck stays on the table top, z = 0\"}, {\"NAME\": \"C_VZ\", \"TARGET\": \"v_z\", \"ACTION\": \"FIX\", \"VALUE\": \"0\", \"UNIT\": \"m s-1\", \"STATEMENT\": \"the puck has no vertical velocity\"}]}, \"BIND\": {\"HEIGHT\": [\"z\"], \"MASS\": [\"m\"], \"UP_VELOCITY\": [\"v_z\"]}, \"VALUES\": {\"h_max\": {\"VALUE\": \"1\", \"UNIT\": \"m\"}}, \"ANSWERS\": {\"FIXED:v_z\": \"YES\"}}]}",
"{\"ID\": \"MATH\", \"VERSION\": \"1.0.0\", \"TITLE\": \"The mathematical constant pi, as the CONSTANT pi_c\", \"SOURCE\": \"pi to 16 significant digits, 3.141592653589793, the nearest IEEE 754 binary64 value\", \"PREREQUISITES\": [], \"PARAMETERS\": [{\"NAME\": \"pi_c\", \"DIMENSION\": \"1\", \"SUPPLY\": \"DECLARED\", \"VALUE\": \"3.141592653589793\", \"UNIT\": \"1\", \"OVERRIDABLE\": \"NO\", \"LABEL\": \"pi, to 16 significant digits\"}], \"SUMS\": [], \"TERMS\": [], \"ASSUMPTIONS\": [], \"BOUNDARIES\": [], \"NOT_CHOSEN\": \"No mathematical constant: pi exists only if you declare it.\", \"NOT_INCLUDED\": [\"pi_c is pi rounded to 16 significant digits; no other mathematical constant is declared.\"], \"EXCLUDES\": [], \"INTERACTS_WITH\": [], \"TEST_BINDINGS\": [{\"NAME\": \"PROJECTILE_2D\", \"TPK\": {\"DOF\": [{\"NAME\": \"t\", \"DIMENSION\": \"T1\"}, {\"NAME\": \"x\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"z\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"v_x\", \"DIMENSION\": \"L1 T-1\"}, {\"NAME\": \"v_z\", \"DIMENSION\": \"L1 T-1\"}], \"CONSTANT\": [{\"NAME\": \"m\", \"DIMENSION\": \"M1\"}], \"LAW\": [{\"NAME\": \"KIN_X\", \"STATEMENT\": \"dx/dt = v_x\", \"REFS\": [\"t\", \"v_x\", \"x\"], \"ROLE\": \"EOM(x)\", \"EQUATION\": \"D(x,t)=v_x\"}, {\"NAME\": \"KIN_Z\", \"STATEMENT\": \"dz/dt = v_z\", \"REFS\": [\"t\", \"v_z\", \"z\"], \"ROLE\": \"EOM(z)\", \"EQUATION\": \"D(z,t)=v_z\"}, {\"NAME\": \"EOM_X\", \"STATEMENT\": \"m dv_x/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_x\"], \"ROLE\": \"EOM(v_x)\", \"EQUATION\": \"m*D(v_x,t)=0\"}, {\"NAME\": \"EOM_Z\", \"STATEMENT\": \"m dv_z/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_z\"], \"ROLE\": \"EOM(v_z)\", \"EQUATION\": \"m*D(v_z,t)=0\"}], \"ASSUMPTION\": [{\"NAME\": \"point_mass\", \"PROPOSITION\": \"the body is treated as a point mass\", \"REFS\": [\"m\"]}]}, \"BIND\": {}, \"VALUES\": {}, \"ANSWERS\": {}}]}"
]
},
"expected": "[\"REFUSED\",\"CLAIMS: not a list\"]",
"fn": "module_expand",
"hand_checked": true,
"name": "X38 claims not a list"
},
{
"args": {
"claims": [
{
"BIND": {
"HEIGHT": [
"z"
],
"MASS": [
"m"
],
"UP_VELOCITY": [
"v_z"
]
},
"DIGEST": "24877ccb5c8ec300d29ed82ce6650592f35cf8899a3d878ccce9c08d4c72c025",
"ID": "GRAV-UNIFORM",
"VALUES": {
"h_max": {
"UNIT": "m",
"VALUE": "100"
}
},
"VERSION": "1.0.0"
}
],
"draft": {
"TPK": {
"ASSUMPTION": [
{
"NAME": "point_mass",
"PROPOSITION": "the body is treated as a point mass",
"REFS": [
"m"
]
}
],
"CONSTANT": [
{
"DIMENSION": "M1",
"NAME": "m"
}
],
"DOF": [
{
"DIMENSION": "T1",
"NAME": "t"
},
{
"DIMENSION": "L1",
"NAME": "x"
},
{
"DIMENSION": "L1",
"NAME": "z"
},
{
"DIMENSION": "L1 T-1",
"NAME": "v_x"
},
{
"DIMENSION": "L1 T-1",
"NAME": "v_z"
}
],
"LAW": [
{
"EQUATION": "D(x,t)=v_x",
"NAME": "KIN_X",
"REFS": [
"t",
"v_x",
"x"
],
"ROLE": "EOM(x)",
"STATEMENT": "dx/dt = v_x"
},
{
"EQUATION": "D(z,t)=v_z",
"NAME": "KIN_Z",
"REFS": [
"t",
"v_z",
"z"
],
"ROLE": "EOM(z)",
"STATEMENT": "dz/dt = v_z"
},
{
"EQUATION": "m*D(v_x,t)=0",
"NAME": "EOM_X",
"REFS": [
"m",
"t",
"v_x"
],
"ROLE": "EOM(v_x)",
"STATEMENT": "m dv_x/dt = 0"
},
{
"EQUATION": "m*D(v_z,t)=0",
"NAME": "EOM_Z",
"REFS": [
"m",
"t",
"v_z"
],
"ROLE": "EOM(v_z)",
"STATEMENT": "m dv_z/dt = 0"
}
]
}
},
"modules": [
"{\"ID\": \"AIR-LINEAR\", \"VERSION\": \"1.0.0\", \"TITLE\": \"Air resistance at sea level, linear in the speed (Stokes drag on a sphere)\", \"SOURCE\": \"ISO 2533:1975, Standard Atmosphere, sea-level values: density 1.225 kg m-3, dynamic viscosity 1.7894e-5 Pa s\", \"PREREQUISITES\": [{\"SLOT\": \"VELOCITY\", \"KIND\": \"DOF\", \"DIMENSION\": \"L1 T-1\", \"MIN\": 1, \"MAX\": 3, \"LABEL\": \"the velocity components of the body, one per axis\"}], \"PARAMETERS\": [{\"NAME\": \"rho_air\", \"DIMENSION\": \"L-3 M1\", \"SUPPLY\": \"DECLARED\", \"VALUE\": \"1.225\", \"UNIT\": \"kg m-3\", \"OVERRIDABLE\": \"NO\", \"LABEL\": \"the density of air at sea level\"}, {\"NAME\": \"mu_air\", \"DIMENSION\": \"L-1 M1 T-1\", \"SUPPLY\": \"DECLARED\", \"VALUE\": \"1.7894e-5\", \"UNIT\": \"Pa s\", \"OVERRIDABLE\": \"NO\", \"LABEL\": \"the dynamic viscosity of air at sea level\"}, {\"NAME\": \"pi_c\", \"DIMENSION\": \"1\", \"SUPPLY\": \"DECLARED\", \"VALUE\": \"3.141592653589793\", \"UNIT\": \"1\", \"OVERRIDABLE\": \"NO\", \"LABEL\": \"pi, to 16 significant digits\"}, {\"NAME\": \"R_s\", \"DIMENSION\": \"L1\", \"SUPPLY\": \"AUTHOR\", \"LABEL\": \"the radius of the sphere\"}], \"SUMS\": [{\"NAME\": \"SPEED2\", \"OVER\": \"VELOCITY\", \"EACH\": \"VELOCITY^2\"}], \"TERMS\": [{\"TARGET\": \"VELOCITY\", \"SIGN\": \"-\", \"EXPR\": \"6*pi_c*mu_air*R_s*VELOCITY\", \"LABEL\": \"the linear (Stokes) drag\"}], \"ASSUMPTIONS\": [{\"NAME\": \"air_still\", \"PROPOSITION\": \"the air is at rest in the frame of the body's velocity\", \"REFS\": [\"VELOCITY\"]}, {\"NAME\": \"air_uniform\", \"PROPOSITION\": \"the air density is uniform over the region of motion\", \"REFS\": [\"rho_air\"]}, {\"NAME\": \"drag_sphere\", \"PROPOSITION\": \"the body is a rigid sphere of radius R_s\", \"REFS\": [\"R_s\"]}], \"BOUNDARIES\": [{\"NAME\": \"drag_linear_regime\", \"PREDICATE\": \"2 rho_air |v| R_s / mu_air < 1: the regime of the linear law\", \"CONDITION\": \"mu_air != 0 and SPEED2 >= 0 and 2*rho_air*sqrt(SPEED2)*R_s/mu_air < 1\"}], \"NOT_CHOSEN\": \"No linear (Stokes) air resistance.\", \"NOT_INCLUDED\": [\"No wind: the air is at rest.\", \"No change of air density or viscosity with altitude or temperature.\", \"No drag outside the regime of the linear law.\"], \"EXCLUDES\": [], \"INTERACTS_WITH\": [], \"TEST_BINDINGS\": [{\"NAME\": \"PROJECTILE_2D\", \"TPK\": {\"DOF\": [{\"NAME\": \"t\", \"DIMENSION\": \"T1\"}, {\"NAME\": \"x\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"z\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"v_x\", \"DIMENSION\": \"L1 T-1\"}, {\"NAME\": \"v_z\", \"DIMENSION\": \"L1 T-1\"}], \"CONSTANT\": [{\"NAME\": \"m\", \"DIMENSION\": \"M1\"}], \"LAW\": [{\"NAME\": \"KIN_X\", \"STATEMENT\": \"dx/dt = v_x\", \"REFS\": [\"t\", \"v_x\", \"x\"], \"ROLE\": \"EOM(x)\", \"EQUATION\": \"D(x,t)=v_x\"}, {\"NAME\": \"KIN_Z\", \"STATEMENT\": \"dz/dt = v_z\", \"REFS\": [\"t\", \"v_z\", \"z\"], \"ROLE\": \"EOM(z)\", \"EQUATION\": \"D(z,t)=v_z\"}, {\"NAME\": \"EOM_X\", \"STATEMENT\": \"m dv_x/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_x\"], \"ROLE\": \"EOM(v_x)\", \"EQUATION\": \"m*D(v_x,t)=0\"}, {\"NAME\": \"EOM_Z\", \"STATEMENT\": \"m dv_z/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_z\"], \"ROLE\": \"EOM(v_z)\", \"EQUATION\": \"m*D(v_z,t)=0\"}], \"ASSUMPTION\": [{\"NAME\": \"point_mass\", \"PROPOSITION\": \"the body is treated as a point mass\", \"REFS\": [\"m\"]}]}, \"BIND\": {\"VELOCITY\": [\"v_x\", \"v_z\"]}, \"VALUES\": {\"R_s\": {}}, \"ANSWERS\": {}}]}",
"{\"ID\": \"AIR-QUADRATIC\", \"VERSION\": \"1.0.0\", \"TITLE\": \"Air resistance at sea level, quadratic in the speed\", \"SOURCE\": \"ISO 2533:1975, Standard Atmosphere, sea-level values: density 1.225 kg m-3, dynamic viscosity 1.7894e-5 Pa s\", \"PREREQUISITES\": [{\"SLOT\": \"VELOCITY\", \"KIND\": \"DOF\", \"DIMENSION\": \"L1 T-1\", \"MIN\": 1, \"MAX\": 3, \"LABEL\": \"the velocity components of the body, one per axis\"}], \"PARAMETERS\": [{\"NAME\": \"rho_air\", \"DIMENSION\": \"L-3 M1\", \"SUPPLY\": \"DECLARED\", \"VALUE\": \"1.225\", \"UNIT\": \"kg m-3\", \"OVERRIDABLE\": \"NO\", \"LABEL\": \"the density of air at sea level\"}, {\"NAME\": \"mu_air\", \"DIMENSION\": \"L-1 M1 T-1\", \"SUPPLY\": \"DECLARED\", \"VALUE\": \"1.7894e-5\", \"UNIT\": \"Pa s\", \"OVERRIDABLE\": \"NO\", \"LABEL\": \"the dynamic viscosity of air at sea level\"}, {\"NAME\": \"C_d\", \"DIMENSION\": \"1\", \"SUPPLY\": \"AUTHOR\", \"LABEL\": \"the drag coefficient of the body\"}, {\"NAME\": \"A_ref\", \"DIMENSION\": \"L2\", \"SUPPLY\": \"AUTHOR\", \"LABEL\": \"the reference area of the drag coefficient\"}, {\"NAME\": \"L_ref\", \"DIMENSION\": \"L1\", \"SUPPLY\": \"AUTHOR\", \"LABEL\": \"the reference length of the Reynolds number\"}], \"SUMS\": [{\"NAME\": \"SPEED2\", \"OVER\": \"VELOCITY\", \"EACH\": \"VELOCITY^2\"}], \"TERMS\": [{\"TARGET\": \"VELOCITY\", \"SIGN\": \"-\", \"EXPR\": \"0.5*rho_air*C_d*A_ref*sqrt(SPEED2)*VELOCITY\", \"LABEL\": \"the quadratic drag\"}], \"ASSUMPTIONS\": [{\"NAME\": \"air_still\", \"PROPOSITION\": \"the air is at rest in the frame of the body's velocity\", \"REFS\": [\"VELOCITY\"]}, {\"NAME\": \"air_uniform\", \"PROPOSITION\": \"the air density is uniform over the region of motion\", \"REFS\": [\"rho_air\"]}, {\"NAME\": \"drag_cd_constant\", \"PROPOSITION\": \"the drag coefficient C_d is constant over the motion\", \"REFS\": [\"C_d\"]}, {\"NAME\": \"drag_no_lift\", \"PROPOSITION\": \"the body experiences no lift force\", \"REFS\": [\"VELOCITY\"]}, {\"NAME\": \"drag_no_magnus\", \"PROPOSITION\": \"the body experiences no Magnus force\", \"REFS\": [\"VELOCITY\"]}], \"BOUNDARIES\": [{\"NAME\": \"drag_quadratic_regime\", \"PREDICATE\": \"1e3 < rho_air |v| L_ref / mu_air < 2e5: the Reynolds window of the quadratic law\", \"CONDITION\": \"mu_air != 0 and SPEED2 >= 0 and rho_air*sqrt(SPEED2)*L_ref/mu_air > 1000 and rho_air*sqrt(SPEED2)*L_ref/mu_air < 200000\"}], \"NOT_CHOSEN\": \"No quadratic air resistance.\", \"NOT_INCLUDED\": [\"No wind: the air is at rest.\", \"No change of air density or viscosity with altitude or temperature.\", \"No lift, Magnus or added-mass force.\", \"No drag outside the Reynolds window of the quadratic law.\"], \"EXCLUDES\": [\"AIR-LINEAR\"], \"INTERACTS_WITH\": [], \"TEST_BINDINGS\": [{\"NAME\": \"PROJECTILE_2D\", \"TPK\": {\"DOF\": [{\"NAME\": \"t\", \"DIMENSION\": \"T1\"}, {\"NAME\": \"x\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"z\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"v_x\", \"DIMENSION\": \"L1 T-1\"}, {\"NAME\": \"v_z\", \"DIMENSION\": \"L1 T-1\"}], \"CONSTANT\": [{\"NAME\": \"m\", \"DIMENSION\": \"M1\"}], \"LAW\": [{\"NAME\": \"KIN_X\", \"STATEMENT\": \"dx/dt = v_x\", \"REFS\": [\"t\", \"v_x\", \"x\"], \"ROLE\": \"EOM(x)\", \"EQUATION\": \"D(x,t)=v_x\"}, {\"NAME\": \"KIN_Z\", \"STATEMENT\": \"dz/dt = v_z\", \"REFS\": [\"t\", \"v_z\", \"z\"], \"ROLE\": \"EOM(z)\", \"EQUATION\": \"D(z,t)=v_z\"}, {\"NAME\": \"EOM_X\", \"STATEMENT\": \"m dv_x/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_x\"], \"ROLE\": \"EOM(v_x)\", \"EQUATION\": \"m*D(v_x,t)=0\"}, {\"NAME\": \"EOM_Z\", \"STATEMENT\": \"m dv_z/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_z\"], \"ROLE\": \"EOM(v_z)\", \"EQUATION\": \"m*D(v_z,t)=0\"}], \"ASSUMPTION\": [{\"NAME\": \"point_mass\", \"PROPOSITION\": \"the body is treated as a point mass\", \"REFS\": [\"m\"]}]}, \"BIND\": {\"VELOCITY\": [\"v_x\", \"v_z\"]}, \"VALUES\": {\"A_ref\": {}, \"C_d\": {}, \"L_ref\": {}}, \"ANSWERS\": {}}]}",
"{\"ID\": \"GRAV-UNIFORM\", \"VERSION\": \"1.0.0\", \"TITLE\": \"Uniform gravity at the standard value g_n\", \"SOURCE\": \"g_n = 9.80665 m s-2, exact by definition: 3rd CGPM (1901), declaration on the unit of mass and on the definition of weight\", \"PREREQUISITES\": [{\"SLOT\": \"MASS\", \"KIND\": \"CONSTANT\", \"DIMENSION\": \"M1\", \"MIN\": 1, \"MAX\": 1, \"LABEL\": \"the mass of the body\"}, {\"SLOT\": \"UP_VELOCITY\", \"KIND\": \"DOF\", \"DIMENSION\": \"L1 T-1\", \"MIN\": 1, \"MAX\": 1, \"LABEL\": \"the velocity component pointing up; its equation of motion receives the weight\"}, {\"SLOT\": \"HEIGHT\", \"KIND\": \"DOF\", \"DIMENSION\": \"L1\", \"MIN\": 1, \"MAX\": 1, \"LABEL\": \"the position along the same upward axis\"}], \"PARAMETERS\": [{\"NAME\": \"g_n\", \"DIMENSION\": \"L1 T-2\", \"SUPPLY\": \"DECLARED\", \"VALUE\": \"9.80665\", \"UNIT\": \"m s-2\", \"OVERRIDABLE\": \"NO\", \"LABEL\": \"the standard acceleration of gravity\"}, {\"NAME\": \"h_max\", \"DIMENSION\": \"L1\", \"SUPPLY\": \"AUTHOR\", \"LABEL\": \"the largest height, above or below the origin, over which the field is taken as uniform\"}], \"SUMS\": [], \"TERMS\": [{\"TARGET\": \"UP_VELOCITY\", \"SIGN\": \"-\", \"EXPR\": \"MASS*g_n\", \"LABEL\": \"the weight\"}], \"ASSUMPTIONS\": [{\"NAME\": \"gravity_uniform\", \"PROPOSITION\": \"the gravitational field is uniform over the region abs({HEIGHT}) < h_max\", \"REFS\": [\"HEIGHT\", \"h_max\"]}, {\"NAME\": \"gravity_standard\", \"PROPOSITION\": \"the local gravitational acceleration equals the conventional standard value g_n\", \"REFS\": [\"g_n\"]}, {\"NAME\": \"frame_inertial\", \"PROPOSITION\": \"the frame in which {HEIGHT} is measured is treated as inertial\", \"REFS\": [\"HEIGHT\"]}], \"BOUNDARIES\": [{\"NAME\": \"gravity_region\", \"PREDICATE\": \"abs({HEIGHT}) < h_max\", \"CONDITION\": \"abs(HEIGHT) < h_max\"}], \"NOT_CHOSEN\": \"No gravity: no weight acts on any DOF.\", \"NOT_INCLUDED\": [\"No variation of gravity with height or latitude beyond what g_n contains.\", \"No Earth rotation (Coriolis or centrifugal force) beyond what g_n contains.\", \"No gravity of bodies other than the Earth.\"], \"EXCLUDES\": [], \"INTERACTS_WITH\": [{\"WITH\": \"AIR-*\", \"QUESTION_ID\": \"BUOYANCY\", \"QUESTION\": \"Does the air's buoyancy (upthrust) act on the body in the system you mean?\", \"YES_LINE\": \"Buoyancy acts (your answer): no module adds it; it acts in this kernel only where one of your own laws states it.\", \"NO_LINE\": \"No buoyancy: the air's upthrust on the body is not included.\"}], \"TEST_BINDINGS\": [{\"NAME\": \"PROJECTILE_2D\", \"TPK\": {\"DOF\": [{\"NAME\": \"t\", \"DIMENSION\": \"T1\"}, {\"NAME\": \"x\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"z\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"v_x\", \"DIMENSION\": \"L1 T-1\"}, {\"NAME\": \"v_z\", \"DIMENSION\": \"L1 T-1\"}], \"CONSTANT\": [{\"NAME\": \"m\", \"DIMENSION\": \"M1\"}], \"LAW\": [{\"NAME\": \"KIN_X\", \"STATEMENT\": \"dx/dt = v_x\", \"REFS\": [\"t\", \"v_x\", \"x\"], \"ROLE\": \"EOM(x)\", \"EQUATION\": \"D(x,t)=v_x\"}, {\"NAME\": \"KIN_Z\", \"STATEMENT\": \"dz/dt = v_z\", \"REFS\": [\"t\", \"v_z\", \"z\"], \"ROLE\": \"EOM(z)\", \"EQUATION\": \"D(z,t)=v_z\"}, {\"NAME\": \"EOM_X\", \"STATEMENT\": \"m dv_x/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_x\"], \"ROLE\": \"EOM(v_x)\", \"EQUATION\": \"m*D(v_x,t)=0\"}, {\"NAME\": \"EOM_Z\", \"STATEMENT\": \"m dv_z/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_z\"], \"ROLE\": \"EOM(v_z)\", \"EQUATION\": \"m*D(v_z,t)=0\"}], \"ASSUMPTION\": [{\"NAME\": \"point_mass\", \"PROPOSITION\": \"the body is treated as a point mass\", \"REFS\": [\"m\"]}]}, \"BIND\": {\"HEIGHT\": [\"z\"], \"MASS\": [\"m\"], \"UP_VELOCITY\": [\"v_z\"]}, \"VALUES\": {\"h_max\": {\"VALUE\": \"100\", \"UNIT\": \"m\"}}, \"ANSWERS\": {}}, {\"NAME\": \"TABLE\", \"TPK\": {\"DOF\": [{\"NAME\": \"t\", \"DIMENSION\": \"T1\"}, {\"NAME\": \"x\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"z\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"v_x\", \"DIMENSION\": \"L1 T-1\"}, {\"NAME\": \"v_z\", \"DIMENSION\": \"L1 T-1\"}], \"CONSTANT\": [{\"NAME\": \"m\", \"DIMENSION\": \"M1\"}], \"LAW\": [{\"NAME\": \"KIN_X\", \"STATEMENT\": \"dx/dt = v_x\", \"REFS\": [\"t\", \"v_x\", \"x\"], \"ROLE\": \"EOM(x)\", \"EQUATION\": \"D(x,t)=v_x\"}, {\"NAME\": \"KIN_Z\", \"STATEMENT\": \"dz/dt = v_z\", \"REFS\": [\"t\", \"v_z\", \"z\"], \"ROLE\": \"CONSTRAINT\", \"EQUATION\": \"D(z,t)=v_z\"}, {\"NAME\": \"EOM_X\", \"STATEMENT\": \"m dv_x/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_x\"], \"ROLE\": \"EOM(v_x)\", \"EQUATION\": \"m*D(v_x,t)=0\"}], \"CONSTRAINT\": [{\"NAME\": \"C_Z\", \"TARGET\": \"z\", \"ACTION\": \"FIX\", \"VALUE\": \"0\", \"UNIT\": \"m\", \"STATEMENT\": \"the puck stays on the table top, z = 0\"}, {\"NAME\": \"C_VZ\", \"TARGET\": \"v_z\", \"ACTION\": \"FIX\", \"VALUE\": \"0\", \"UNIT\": \"m s-1\", \"STATEMENT\": \"the puck has no vertical velocity\"}]}, \"BIND\": {\"HEIGHT\": [\"z\"], \"MASS\": [\"m\"], \"UP_VELOCITY\": [\"v_z\"]}, \"VALUES\": {\"h_max\": {\"VALUE\": \"1\", \"UNIT\": \"m\"}}, \"ANSWERS\": {\"FIXED:v_z\": \"YES\"}}]}",
"{\"ID\": \"MATH\", \"VERSION\": \"1.0.0\", \"TITLE\": \"The mathematical constant pi, as the CONSTANT pi_c\", \"SOURCE\": \"pi to 16 significant digits, 3.141592653589793, the nearest IEEE 754 binary64 value\", \"PREREQUISITES\": [], \"PARAMETERS\": [{\"NAME\": \"pi_c\", \"DIMENSION\": \"1\", \"SUPPLY\": \"DECLARED\", \"VALUE\": \"3.141592653589793\", \"UNIT\": \"1\", \"OVERRIDABLE\": \"NO\", \"LABEL\": \"pi, to 16 significant digits\"}], \"SUMS\": [], \"TERMS\": [], \"ASSUMPTIONS\": [], \"BOUNDARIES\": [], \"NOT_CHOSEN\": \"No mathematical constant: pi exists only if you declare it.\", \"NOT_INCLUDED\": [\"pi_c is pi rounded to 16 significant digits; no other mathematical constant is declared.\"], \"EXCLUDES\": [], \"INTERACTS_WITH\": [], \"TEST_BINDINGS\": [{\"NAME\": \"PROJECTILE_2D\", \"TPK\": {\"DOF\": [{\"NAME\": \"t\", \"DIMENSION\": \"T1\"}, {\"NAME\": \"x\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"z\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"v_x\", \"DIMENSION\": \"L1 T-1\"}, {\"NAME\": \"v_z\", \"DIMENSION\": \"L1 T-1\"}], \"CONSTANT\": [{\"NAME\": \"m\", \"DIMENSION\": \"M1\"}], \"LAW\": [{\"NAME\": \"KIN_X\", \"STATEMENT\": \"dx/dt = v_x\", \"REFS\": [\"t\", \"v_x\", \"x\"], \"ROLE\": \"EOM(x)\", \"EQUATION\": \"D(x,t)=v_x\"}, {\"NAME\": \"KIN_Z\", \"STATEMENT\": \"dz/dt = v_z\", \"REFS\": [\"t\", \"v_z\", \"z\"], \"ROLE\": \"EOM(z)\", \"EQUATION\": \"D(z,t)=v_z\"}, {\"NAME\": \"EOM_X\", \"STATEMENT\": \"m dv_x/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_x\"], \"ROLE\": \"EOM(v_x)\", \"EQUATION\": \"m*D(v_x,t)=0\"}, {\"NAME\": \"EOM_Z\", \"STATEMENT\": \"m dv_z/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_z\"], \"ROLE\": \"EOM(v_z)\", \"EQUATION\": \"m*D(v_z,t)=0\"}], \"ASSUMPTION\": [{\"NAME\": \"point_mass\", \"PROPOSITION\": \"the body is treated as a point mass\", \"REFS\": [\"m\"]}]}, \"BIND\": {}, \"VALUES\": {}, \"ANSWERS\": {}}]}"
]
},
"expected": "[\"REFUSED\",\"CLAIM 1: missing field ANSWERS\"]",
"fn": "module_expand",
"hand_checked": true,
"name": "X39 a claim without ANSWERS"
},
{
"args": {
"claims": [
{
"ANSWERS": {},
"BIND": {
"HEIGHT": [
"z"
],
"MASS": [
"m"
],
"UP_VELOCITY": [
"v_z"
]
},
"DIGEST": "24877ccb5c8ec300d29ed82ce6650592f35cf8899a3d878ccce9c08d4c72c025",
"ID": "GRAV-UNIFORM",
"NOTE": "x",
"VALUES": {
"h_max": {
"UNIT": "m",
"VALUE": "100"
}
},
"VERSION": "1.0.0"
}
],
"draft": {
"TPK": {
"ASSUMPTION": [
{
"NAME": "point_mass",
"PROPOSITION": "the body is treated as a point mass",
"REFS": [
"m"
]
}
],
"CONSTANT": [
{
"DIMENSION": "M1",
"NAME": "m"
}
],
"DOF": [
{
"DIMENSION": "T1",
"NAME": "t"
},
{
"DIMENSION": "L1",
"NAME": "x"
},
{
"DIMENSION": "L1",
"NAME": "z"
},
{
"DIMENSION": "L1 T-1",
"NAME": "v_x"
},
{
"DIMENSION": "L1 T-1",
"NAME": "v_z"
}
],
"LAW": [
{
"EQUATION": "D(x,t)=v_x",
"NAME": "KIN_X",
"REFS": [
"t",
"v_x",
"x"
],
"ROLE": "EOM(x)",
"STATEMENT": "dx/dt = v_x"
},
{
"EQUATION": "D(z,t)=v_z",
"NAME": "KIN_Z",
"REFS": [
"t",
"v_z",
"z"
],
"ROLE": "EOM(z)",
"STATEMENT": "dz/dt = v_z"
},
{
"EQUATION": "m*D(v_x,t)=0",
"NAME": "EOM_X",
"REFS": [
"m",
"t",
"v_x"
],
"ROLE": "EOM(v_x)",
"STATEMENT": "m dv_x/dt = 0"
},
{
"EQUATION": "m*D(v_z,t)=0",
"NAME": "EOM_Z",
"REFS": [
"m",
"t",
"v_z"
],
"ROLE": "EOM(v_z)",
"STATEMENT": "m dv_z/dt = 0"
}
]
}
},
"modules": [
"{\"ID\": \"AIR-LINEAR\", \"VERSION\": \"1.0.0\", \"TITLE\": \"Air resistance at sea level, linear in the speed (Stokes drag on a sphere)\", \"SOURCE\": \"ISO 2533:1975, Standard Atmosphere, sea-level values: density 1.225 kg m-3, dynamic viscosity 1.7894e-5 Pa s\", \"PREREQUISITES\": [{\"SLOT\": \"VELOCITY\", \"KIND\": \"DOF\", \"DIMENSION\": \"L1 T-1\", \"MIN\": 1, \"MAX\": 3, \"LABEL\": \"the velocity components of the body, one per axis\"}], \"PARAMETERS\": [{\"NAME\": \"rho_air\", \"DIMENSION\": \"L-3 M1\", \"SUPPLY\": \"DECLARED\", \"VALUE\": \"1.225\", \"UNIT\": \"kg m-3\", \"OVERRIDABLE\": \"NO\", \"LABEL\": \"the density of air at sea level\"}, {\"NAME\": \"mu_air\", \"DIMENSION\": \"L-1 M1 T-1\", \"SUPPLY\": \"DECLARED\", \"VALUE\": \"1.7894e-5\", \"UNIT\": \"Pa s\", \"OVERRIDABLE\": \"NO\", \"LABEL\": \"the dynamic viscosity of air at sea level\"}, {\"NAME\": \"pi_c\", \"DIMENSION\": \"1\", \"SUPPLY\": \"DECLARED\", \"VALUE\": \"3.141592653589793\", \"UNIT\": \"1\", \"OVERRIDABLE\": \"NO\", \"LABEL\": \"pi, to 16 significant digits\"}, {\"NAME\": \"R_s\", \"DIMENSION\": \"L1\", \"SUPPLY\": \"AUTHOR\", \"LABEL\": \"the radius of the sphere\"}], \"SUMS\": [{\"NAME\": \"SPEED2\", \"OVER\": \"VELOCITY\", \"EACH\": \"VELOCITY^2\"}], \"TERMS\": [{\"TARGET\": \"VELOCITY\", \"SIGN\": \"-\", \"EXPR\": \"6*pi_c*mu_air*R_s*VELOCITY\", \"LABEL\": \"the linear (Stokes) drag\"}], \"ASSUMPTIONS\": [{\"NAME\": \"air_still\", \"PROPOSITION\": \"the air is at rest in the frame of the body's velocity\", \"REFS\": [\"VELOCITY\"]}, {\"NAME\": \"air_uniform\", \"PROPOSITION\": \"the air density is uniform over the region of motion\", \"REFS\": [\"rho_air\"]}, {\"NAME\": \"drag_sphere\", \"PROPOSITION\": \"the body is a rigid sphere of radius R_s\", \"REFS\": [\"R_s\"]}], \"BOUNDARIES\": [{\"NAME\": \"drag_linear_regime\", \"PREDICATE\": \"2 rho_air |v| R_s / mu_air < 1: the regime of the linear law\", \"CONDITION\": \"mu_air != 0 and SPEED2 >= 0 and 2*rho_air*sqrt(SPEED2)*R_s/mu_air < 1\"}], \"NOT_CHOSEN\": \"No linear (Stokes) air resistance.\", \"NOT_INCLUDED\": [\"No wind: the air is at rest.\", \"No change of air density or viscosity with altitude or temperature.\", \"No drag outside the regime of the linear law.\"], \"EXCLUDES\": [], \"INTERACTS_WITH\": [], \"TEST_BINDINGS\": [{\"NAME\": \"PROJECTILE_2D\", \"TPK\": {\"DOF\": [{\"NAME\": \"t\", \"DIMENSION\": \"T1\"}, {\"NAME\": \"x\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"z\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"v_x\", \"DIMENSION\": \"L1 T-1\"}, {\"NAME\": \"v_z\", \"DIMENSION\": \"L1 T-1\"}], \"CONSTANT\": [{\"NAME\": \"m\", \"DIMENSION\": \"M1\"}], \"LAW\": [{\"NAME\": \"KIN_X\", \"STATEMENT\": \"dx/dt = v_x\", \"REFS\": [\"t\", \"v_x\", \"x\"], \"ROLE\": \"EOM(x)\", \"EQUATION\": \"D(x,t)=v_x\"}, {\"NAME\": \"KIN_Z\", \"STATEMENT\": \"dz/dt = v_z\", \"REFS\": [\"t\", \"v_z\", \"z\"], \"ROLE\": \"EOM(z)\", \"EQUATION\": \"D(z,t)=v_z\"}, {\"NAME\": \"EOM_X\", \"STATEMENT\": \"m dv_x/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_x\"], \"ROLE\": \"EOM(v_x)\", \"EQUATION\": \"m*D(v_x,t)=0\"}, {\"NAME\": \"EOM_Z\", \"STATEMENT\": \"m dv_z/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_z\"], \"ROLE\": \"EOM(v_z)\", \"EQUATION\": \"m*D(v_z,t)=0\"}], \"ASSUMPTION\": [{\"NAME\": \"point_mass\", \"PROPOSITION\": \"the body is treated as a point mass\", \"REFS\": [\"m\"]}]}, \"BIND\": {\"VELOCITY\": [\"v_x\", \"v_z\"]}, \"VALUES\": {\"R_s\": {}}, \"ANSWERS\": {}}]}",
"{\"ID\": \"AIR-QUADRATIC\", \"VERSION\": \"1.0.0\", \"TITLE\": \"Air resistance at sea level, quadratic in the speed\", \"SOURCE\": \"ISO 2533:1975, Standard Atmosphere, sea-level values: density 1.225 kg m-3, dynamic viscosity 1.7894e-5 Pa s\", \"PREREQUISITES\": [{\"SLOT\": \"VELOCITY\", \"KIND\": \"DOF\", \"DIMENSION\": \"L1 T-1\", \"MIN\": 1, \"MAX\": 3, \"LABEL\": \"the velocity components of the body, one per axis\"}], \"PARAMETERS\": [{\"NAME\": \"rho_air\", \"DIMENSION\": \"L-3 M1\", \"SUPPLY\": \"DECLARED\", \"VALUE\": \"1.225\", \"UNIT\": \"kg m-3\", \"OVERRIDABLE\": \"NO\", \"LABEL\": \"the density of air at sea level\"}, {\"NAME\": \"mu_air\", \"DIMENSION\": \"L-1 M1 T-1\", \"SUPPLY\": \"DECLARED\", \"VALUE\": \"1.7894e-5\", \"UNIT\": \"Pa s\", \"OVERRIDABLE\": \"NO\", \"LABEL\": \"the dynamic viscosity of air at sea level\"}, {\"NAME\": \"C_d\", \"DIMENSION\": \"1\", \"SUPPLY\": \"AUTHOR\", \"LABEL\": \"the drag coefficient of the body\"}, {\"NAME\": \"A_ref\", \"DIMENSION\": \"L2\", \"SUPPLY\": \"AUTHOR\", \"LABEL\": \"the reference area of the drag coefficient\"}, {\"NAME\": \"L_ref\", \"DIMENSION\": \"L1\", \"SUPPLY\": \"AUTHOR\", \"LABEL\": \"the reference length of the Reynolds number\"}], \"SUMS\": [{\"NAME\": \"SPEED2\", \"OVER\": \"VELOCITY\", \"EACH\": \"VELOCITY^2\"}], \"TERMS\": [{\"TARGET\": \"VELOCITY\", \"SIGN\": \"-\", \"EXPR\": \"0.5*rho_air*C_d*A_ref*sqrt(SPEED2)*VELOCITY\", \"LABEL\": \"the quadratic drag\"}], \"ASSUMPTIONS\": [{\"NAME\": \"air_still\", \"PROPOSITION\": \"the air is at rest in the frame of the body's velocity\", \"REFS\": [\"VELOCITY\"]}, {\"NAME\": \"air_uniform\", \"PROPOSITION\": \"the air density is uniform over the region of motion\", \"REFS\": [\"rho_air\"]}, {\"NAME\": \"drag_cd_constant\", \"PROPOSITION\": \"the drag coefficient C_d is constant over the motion\", \"REFS\": [\"C_d\"]}, {\"NAME\": \"drag_no_lift\", \"PROPOSITION\": \"the body experiences no lift force\", \"REFS\": [\"VELOCITY\"]}, {\"NAME\": \"drag_no_magnus\", \"PROPOSITION\": \"the body experiences no Magnus force\", \"REFS\": [\"VELOCITY\"]}], \"BOUNDARIES\": [{\"NAME\": \"drag_quadratic_regime\", \"PREDICATE\": \"1e3 < rho_air |v| L_ref / mu_air < 2e5: the Reynolds window of the quadratic law\", \"CONDITION\": \"mu_air != 0 and SPEED2 >= 0 and rho_air*sqrt(SPEED2)*L_ref/mu_air > 1000 and rho_air*sqrt(SPEED2)*L_ref/mu_air < 200000\"}], \"NOT_CHOSEN\": \"No quadratic air resistance.\", \"NOT_INCLUDED\": [\"No wind: the air is at rest.\", \"No change of air density or viscosity with altitude or temperature.\", \"No lift, Magnus or added-mass force.\", \"No drag outside the Reynolds window of the quadratic law.\"], \"EXCLUDES\": [\"AIR-LINEAR\"], \"INTERACTS_WITH\": [], \"TEST_BINDINGS\": [{\"NAME\": \"PROJECTILE_2D\", \"TPK\": {\"DOF\": [{\"NAME\": \"t\", \"DIMENSION\": \"T1\"}, {\"NAME\": \"x\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"z\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"v_x\", \"DIMENSION\": \"L1 T-1\"}, {\"NAME\": \"v_z\", \"DIMENSION\": \"L1 T-1\"}], \"CONSTANT\": [{\"NAME\": \"m\", \"DIMENSION\": \"M1\"}], \"LAW\": [{\"NAME\": \"KIN_X\", \"STATEMENT\": \"dx/dt = v_x\", \"REFS\": [\"t\", \"v_x\", \"x\"], \"ROLE\": \"EOM(x)\", \"EQUATION\": \"D(x,t)=v_x\"}, {\"NAME\": \"KIN_Z\", \"STATEMENT\": \"dz/dt = v_z\", \"REFS\": [\"t\", \"v_z\", \"z\"], \"ROLE\": \"EOM(z)\", \"EQUATION\": \"D(z,t)=v_z\"}, {\"NAME\": \"EOM_X\", \"STATEMENT\": \"m dv_x/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_x\"], \"ROLE\": \"EOM(v_x)\", \"EQUATION\": \"m*D(v_x,t)=0\"}, {\"NAME\": \"EOM_Z\", \"STATEMENT\": \"m dv_z/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_z\"], \"ROLE\": \"EOM(v_z)\", \"EQUATION\": \"m*D(v_z,t)=0\"}], \"ASSUMPTION\": [{\"NAME\": \"point_mass\", \"PROPOSITION\": \"the body is treated as a point mass\", \"REFS\": [\"m\"]}]}, \"BIND\": {\"VELOCITY\": [\"v_x\", \"v_z\"]}, \"VALUES\": {\"A_ref\": {}, \"C_d\": {}, \"L_ref\": {}}, \"ANSWERS\": {}}]}",
"{\"ID\": \"GRAV-UNIFORM\", \"VERSION\": \"1.0.0\", \"TITLE\": \"Uniform gravity at the standard value g_n\", \"SOURCE\": \"g_n = 9.80665 m s-2, exact by definition: 3rd CGPM (1901), declaration on the unit of mass and on the definition of weight\", \"PREREQUISITES\": [{\"SLOT\": \"MASS\", \"KIND\": \"CONSTANT\", \"DIMENSION\": \"M1\", \"MIN\": 1, \"MAX\": 1, \"LABEL\": \"the mass of the body\"}, {\"SLOT\": \"UP_VELOCITY\", \"KIND\": \"DOF\", \"DIMENSION\": \"L1 T-1\", \"MIN\": 1, \"MAX\": 1, \"LABEL\": \"the velocity component pointing up; its equation of motion receives the weight\"}, {\"SLOT\": \"HEIGHT\", \"KIND\": \"DOF\", \"DIMENSION\": \"L1\", \"MIN\": 1, \"MAX\": 1, \"LABEL\": \"the position along the same upward axis\"}], \"PARAMETERS\": [{\"NAME\": \"g_n\", \"DIMENSION\": \"L1 T-2\", \"SUPPLY\": \"DECLARED\", \"VALUE\": \"9.80665\", \"UNIT\": \"m s-2\", \"OVERRIDABLE\": \"NO\", \"LABEL\": \"the standard acceleration of gravity\"}, {\"NAME\": \"h_max\", \"DIMENSION\": \"L1\", \"SUPPLY\": \"AUTHOR\", \"LABEL\": \"the largest height, above or below the origin, over which the field is taken as uniform\"}], \"SUMS\": [], \"TERMS\": [{\"TARGET\": \"UP_VELOCITY\", \"SIGN\": \"-\", \"EXPR\": \"MASS*g_n\", \"LABEL\": \"the weight\"}], \"ASSUMPTIONS\": [{\"NAME\": \"gravity_uniform\", \"PROPOSITION\": \"the gravitational field is uniform over the region abs({HEIGHT}) < h_max\", \"REFS\": [\"HEIGHT\", \"h_max\"]}, {\"NAME\": \"gravity_standard\", \"PROPOSITION\": \"the local gravitational acceleration equals the conventional standard value g_n\", \"REFS\": [\"g_n\"]}, {\"NAME\": \"frame_inertial\", \"PROPOSITION\": \"the frame in which {HEIGHT} is measured is treated as inertial\", \"REFS\": [\"HEIGHT\"]}], \"BOUNDARIES\": [{\"NAME\": \"gravity_region\", \"PREDICATE\": \"abs({HEIGHT}) < h_max\", \"CONDITION\": \"abs(HEIGHT) < h_max\"}], \"NOT_CHOSEN\": \"No gravity: no weight acts on any DOF.\", \"NOT_INCLUDED\": [\"No variation of gravity with height or latitude beyond what g_n contains.\", \"No Earth rotation (Coriolis or centrifugal force) beyond what g_n contains.\", \"No gravity of bodies other than the Earth.\"], \"EXCLUDES\": [], \"INTERACTS_WITH\": [{\"WITH\": \"AIR-*\", \"QUESTION_ID\": \"BUOYANCY\", \"QUESTION\": \"Does the air's buoyancy (upthrust) act on the body in the system you mean?\", \"YES_LINE\": \"Buoyancy acts (your answer): no module adds it; it acts in this kernel only where one of your own laws states it.\", \"NO_LINE\": \"No buoyancy: the air's upthrust on the body is not included.\"}], \"TEST_BINDINGS\": [{\"NAME\": \"PROJECTILE_2D\", \"TPK\": {\"DOF\": [{\"NAME\": \"t\", \"DIMENSION\": \"T1\"}, {\"NAME\": \"x\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"z\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"v_x\", \"DIMENSION\": \"L1 T-1\"}, {\"NAME\": \"v_z\", \"DIMENSION\": \"L1 T-1\"}], \"CONSTANT\": [{\"NAME\": \"m\", \"DIMENSION\": \"M1\"}], \"LAW\": [{\"NAME\": \"KIN_X\", \"STATEMENT\": \"dx/dt = v_x\", \"REFS\": [\"t\", \"v_x\", \"x\"], \"ROLE\": \"EOM(x)\", \"EQUATION\": \"D(x,t)=v_x\"}, {\"NAME\": \"KIN_Z\", \"STATEMENT\": \"dz/dt = v_z\", \"REFS\": [\"t\", \"v_z\", \"z\"], \"ROLE\": \"EOM(z)\", \"EQUATION\": \"D(z,t)=v_z\"}, {\"NAME\": \"EOM_X\", \"STATEMENT\": \"m dv_x/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_x\"], \"ROLE\": \"EOM(v_x)\", \"EQUATION\": \"m*D(v_x,t)=0\"}, {\"NAME\": \"EOM_Z\", \"STATEMENT\": \"m dv_z/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_z\"], \"ROLE\": \"EOM(v_z)\", \"EQUATION\": \"m*D(v_z,t)=0\"}], \"ASSUMPTION\": [{\"NAME\": \"point_mass\", \"PROPOSITION\": \"the body is treated as a point mass\", \"REFS\": [\"m\"]}]}, \"BIND\": {\"HEIGHT\": [\"z\"], \"MASS\": [\"m\"], \"UP_VELOCITY\": [\"v_z\"]}, \"VALUES\": {\"h_max\": {\"VALUE\": \"100\", \"UNIT\": \"m\"}}, \"ANSWERS\": {}}, {\"NAME\": \"TABLE\", \"TPK\": {\"DOF\": [{\"NAME\": \"t\", \"DIMENSION\": \"T1\"}, {\"NAME\": \"x\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"z\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"v_x\", \"DIMENSION\": \"L1 T-1\"}, {\"NAME\": \"v_z\", \"DIMENSION\": \"L1 T-1\"}], \"CONSTANT\": [{\"NAME\": \"m\", \"DIMENSION\": \"M1\"}], \"LAW\": [{\"NAME\": \"KIN_X\", \"STATEMENT\": \"dx/dt = v_x\", \"REFS\": [\"t\", \"v_x\", \"x\"], \"ROLE\": \"EOM(x)\", \"EQUATION\": \"D(x,t)=v_x\"}, {\"NAME\": \"KIN_Z\", \"STATEMENT\": \"dz/dt = v_z\", \"REFS\": [\"t\", \"v_z\", \"z\"], \"ROLE\": \"CONSTRAINT\", \"EQUATION\": \"D(z,t)=v_z\"}, {\"NAME\": \"EOM_X\", \"STATEMENT\": \"m dv_x/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_x\"], \"ROLE\": \"EOM(v_x)\", \"EQUATION\": \"m*D(v_x,t)=0\"}], \"CONSTRAINT\": [{\"NAME\": \"C_Z\", \"TARGET\": \"z\", \"ACTION\": \"FIX\", \"VALUE\": \"0\", \"UNIT\": \"m\", \"STATEMENT\": \"the puck stays on the table top, z = 0\"}, {\"NAME\": \"C_VZ\", \"TARGET\": \"v_z\", \"ACTION\": \"FIX\", \"VALUE\": \"0\", \"UNIT\": \"m s-1\", \"STATEMENT\": \"the puck has no vertical velocity\"}]}, \"BIND\": {\"HEIGHT\": [\"z\"], \"MASS\": [\"m\"], \"UP_VELOCITY\": [\"v_z\"]}, \"VALUES\": {\"h_max\": {\"VALUE\": \"1\", \"UNIT\": \"m\"}}, \"ANSWERS\": {\"FIXED:v_z\": \"YES\"}}]}",
"{\"ID\": \"MATH\", \"VERSION\": \"1.0.0\", \"TITLE\": \"The mathematical constant pi, as the CONSTANT pi_c\", \"SOURCE\": \"pi to 16 significant digits, 3.141592653589793, the nearest IEEE 754 binary64 value\", \"PREREQUISITES\": [], \"PARAMETERS\": [{\"NAME\": \"pi_c\", \"DIMENSION\": \"1\", \"SUPPLY\": \"DECLARED\", \"VALUE\": \"3.141592653589793\", \"UNIT\": \"1\", \"OVERRIDABLE\": \"NO\", \"LABEL\": \"pi, to 16 significant digits\"}], \"SUMS\": [], \"TERMS\": [], \"ASSUMPTIONS\": [], \"BOUNDARIES\": [], \"NOT_CHOSEN\": \"No mathematical constant: pi exists only if you declare it.\", \"NOT_INCLUDED\": [\"pi_c is pi rounded to 16 significant digits; no other mathematical constant is declared.\"], \"EXCLUDES\": [], \"INTERACTS_WITH\": [], \"TEST_BINDINGS\": [{\"NAME\": \"PROJECTILE_2D\", \"TPK\": {\"DOF\": [{\"NAME\": \"t\", \"DIMENSION\": \"T1\"}, {\"NAME\": \"x\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"z\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"v_x\", \"DIMENSION\": \"L1 T-1\"}, {\"NAME\": \"v_z\", \"DIMENSION\": \"L1 T-1\"}], \"CONSTANT\": [{\"NAME\": \"m\", \"DIMENSION\": \"M1\"}], \"LAW\": [{\"NAME\": \"KIN_X\", \"STATEMENT\": \"dx/dt = v_x\", \"REFS\": [\"t\", \"v_x\", \"x\"], \"ROLE\": \"EOM(x)\", \"EQUATION\": \"D(x,t)=v_x\"}, {\"NAME\": \"KIN_Z\", \"STATEMENT\": \"dz/dt = v_z\", \"REFS\": [\"t\", \"v_z\", \"z\"], \"ROLE\": \"EOM(z)\", \"EQUATION\": \"D(z,t)=v_z\"}, {\"NAME\": \"EOM_X\", \"STATEMENT\": \"m dv_x/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_x\"], \"ROLE\": \"EOM(v_x)\", \"EQUATION\": \"m*D(v_x,t)=0\"}, {\"NAME\": \"EOM_Z\", \"STATEMENT\": \"m dv_z/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_z\"], \"ROLE\": \"EOM(v_z)\", \"EQUATION\": \"m*D(v_z,t)=0\"}], \"ASSUMPTION\": [{\"NAME\": \"point_mass\", \"PROPOSITION\": \"the body is treated as a point mass\", \"REFS\": [\"m\"]}]}, \"BIND\": {}, \"VALUES\": {}, \"ANSWERS\": {}}]}"
]
},
"expected": "[\"REFUSED\",\"CLAIM 1: unknown field NOTE\"]",
"fn": "module_expand",
"hand_checked": true,
"name": "X40 a claim with an unknown field"
},
{
"args": {
"claims": [
{
"ANSWERS": {},
"BIND": {
"HEIGHT": [
"z"
],
"MASS": [
"m"
],
"UP_VELOCITY": [
"v_z"
]
},
"DIGEST": "XYZ",
"ID": "GRAV-UNIFORM",
"VALUES": {
"h_max": {
"UNIT": "m",
"VALUE": "100"
}
},
"VERSION": "1.0.0"
}
],
"draft": {
"TPK": {
"ASSUMPTION": [
{
"NAME": "point_mass",
"PROPOSITION": "the body is treated as a point mass",
"REFS": [
"m"
]
}
],
"CONSTANT": [
{
"DIMENSION": "M1",
"NAME": "m"
}
],
"DOF": [
{
"DIMENSION": "T1",
"NAME": "t"
},
{
"DIMENSION": "L1",
"NAME": "x"
},
{
"DIMENSION": "L1",
"NAME": "z"
},
{
"DIMENSION": "L1 T-1",
"NAME": "v_x"
},
{
"DIMENSION": "L1 T-1",
"NAME": "v_z"
}
],
"LAW": [
{
"EQUATION": "D(x,t)=v_x",
"NAME": "KIN_X",
"REFS": [
"t",
"v_x",
"x"
],
"ROLE": "EOM(x)",
"STATEMENT": "dx/dt = v_x"
},
{
"EQUATION": "D(z,t)=v_z",
"NAME": "KIN_Z",
"REFS": [
"t",
"v_z",
"z"
],
"ROLE": "EOM(z)",
"STATEMENT": "dz/dt = v_z"
},
{
"EQUATION": "m*D(v_x,t)=0",
"NAME": "EOM_X",
"REFS": [
"m",
"t",
"v_x"
],
"ROLE": "EOM(v_x)",
"STATEMENT": "m dv_x/dt = 0"
},
{
"EQUATION": "m*D(v_z,t)=0",
"NAME": "EOM_Z",
"REFS": [
"m",
"t",
"v_z"
],
"ROLE": "EOM(v_z)",
"STATEMENT": "m dv_z/dt = 0"
}
]
}
},
"modules": [
"{\"ID\": \"AIR-LINEAR\", \"VERSION\": \"1.0.0\", \"TITLE\": \"Air resistance at sea level, linear in the speed (Stokes drag on a sphere)\", \"SOURCE\": \"ISO 2533:1975, Standard Atmosphere, sea-level values: density 1.225 kg m-3, dynamic viscosity 1.7894e-5 Pa s\", \"PREREQUISITES\": [{\"SLOT\": \"VELOCITY\", \"KIND\": \"DOF\", \"DIMENSION\": \"L1 T-1\", \"MIN\": 1, \"MAX\": 3, \"LABEL\": \"the velocity components of the body, one per axis\"}], \"PARAMETERS\": [{\"NAME\": \"rho_air\", \"DIMENSION\": \"L-3 M1\", \"SUPPLY\": \"DECLARED\", \"VALUE\": \"1.225\", \"UNIT\": \"kg m-3\", \"OVERRIDABLE\": \"NO\", \"LABEL\": \"the density of air at sea level\"}, {\"NAME\": \"mu_air\", \"DIMENSION\": \"L-1 M1 T-1\", \"SUPPLY\": \"DECLARED\", \"VALUE\": \"1.7894e-5\", \"UNIT\": \"Pa s\", \"OVERRIDABLE\": \"NO\", \"LABEL\": \"the dynamic viscosity of air at sea level\"}, {\"NAME\": \"pi_c\", \"DIMENSION\": \"1\", \"SUPPLY\": \"DECLARED\", \"VALUE\": \"3.141592653589793\", \"UNIT\": \"1\", \"OVERRIDABLE\": \"NO\", \"LABEL\": \"pi, to 16 significant digits\"}, {\"NAME\": \"R_s\", \"DIMENSION\": \"L1\", \"SUPPLY\": \"AUTHOR\", \"LABEL\": \"the radius of the sphere\"}], \"SUMS\": [{\"NAME\": \"SPEED2\", \"OVER\": \"VELOCITY\", \"EACH\": \"VELOCITY^2\"}], \"TERMS\": [{\"TARGET\": \"VELOCITY\", \"SIGN\": \"-\", \"EXPR\": \"6*pi_c*mu_air*R_s*VELOCITY\", \"LABEL\": \"the linear (Stokes) drag\"}], \"ASSUMPTIONS\": [{\"NAME\": \"air_still\", \"PROPOSITION\": \"the air is at rest in the frame of the body's velocity\", \"REFS\": [\"VELOCITY\"]}, {\"NAME\": \"air_uniform\", \"PROPOSITION\": \"the air density is uniform over the region of motion\", \"REFS\": [\"rho_air\"]}, {\"NAME\": \"drag_sphere\", \"PROPOSITION\": \"the body is a rigid sphere of radius R_s\", \"REFS\": [\"R_s\"]}], \"BOUNDARIES\": [{\"NAME\": \"drag_linear_regime\", \"PREDICATE\": \"2 rho_air |v| R_s / mu_air < 1: the regime of the linear law\", \"CONDITION\": \"mu_air != 0 and SPEED2 >= 0 and 2*rho_air*sqrt(SPEED2)*R_s/mu_air < 1\"}], \"NOT_CHOSEN\": \"No linear (Stokes) air resistance.\", \"NOT_INCLUDED\": [\"No wind: the air is at rest.\", \"No change of air density or viscosity with altitude or temperature.\", \"No drag outside the regime of the linear law.\"], \"EXCLUDES\": [], \"INTERACTS_WITH\": [], \"TEST_BINDINGS\": [{\"NAME\": \"PROJECTILE_2D\", \"TPK\": {\"DOF\": [{\"NAME\": \"t\", \"DIMENSION\": \"T1\"}, {\"NAME\": \"x\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"z\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"v_x\", \"DIMENSION\": \"L1 T-1\"}, {\"NAME\": \"v_z\", \"DIMENSION\": \"L1 T-1\"}], \"CONSTANT\": [{\"NAME\": \"m\", \"DIMENSION\": \"M1\"}], \"LAW\": [{\"NAME\": \"KIN_X\", \"STATEMENT\": \"dx/dt = v_x\", \"REFS\": [\"t\", \"v_x\", \"x\"], \"ROLE\": \"EOM(x)\", \"EQUATION\": \"D(x,t)=v_x\"}, {\"NAME\": \"KIN_Z\", \"STATEMENT\": \"dz/dt = v_z\", \"REFS\": [\"t\", \"v_z\", \"z\"], \"ROLE\": \"EOM(z)\", \"EQUATION\": \"D(z,t)=v_z\"}, {\"NAME\": \"EOM_X\", \"STATEMENT\": \"m dv_x/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_x\"], \"ROLE\": \"EOM(v_x)\", \"EQUATION\": \"m*D(v_x,t)=0\"}, {\"NAME\": \"EOM_Z\", \"STATEMENT\": \"m dv_z/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_z\"], \"ROLE\": \"EOM(v_z)\", \"EQUATION\": \"m*D(v_z,t)=0\"}], \"ASSUMPTION\": [{\"NAME\": \"point_mass\", \"PROPOSITION\": \"the body is treated as a point mass\", \"REFS\": [\"m\"]}]}, \"BIND\": {\"VELOCITY\": [\"v_x\", \"v_z\"]}, \"VALUES\": {\"R_s\": {}}, \"ANSWERS\": {}}]}",
"{\"ID\": \"AIR-QUADRATIC\", \"VERSION\": \"1.0.0\", \"TITLE\": \"Air resistance at sea level, quadratic in the speed\", \"SOURCE\": \"ISO 2533:1975, Standard Atmosphere, sea-level values: density 1.225 kg m-3, dynamic viscosity 1.7894e-5 Pa s\", \"PREREQUISITES\": [{\"SLOT\": \"VELOCITY\", \"KIND\": \"DOF\", \"DIMENSION\": \"L1 T-1\", \"MIN\": 1, \"MAX\": 3, \"LABEL\": \"the velocity components of the body, one per axis\"}], \"PARAMETERS\": [{\"NAME\": \"rho_air\", \"DIMENSION\": \"L-3 M1\", \"SUPPLY\": \"DECLARED\", \"VALUE\": \"1.225\", \"UNIT\": \"kg m-3\", \"OVERRIDABLE\": \"NO\", \"LABEL\": \"the density of air at sea level\"}, {\"NAME\": \"mu_air\", \"DIMENSION\": \"L-1 M1 T-1\", \"SUPPLY\": \"DECLARED\", \"VALUE\": \"1.7894e-5\", \"UNIT\": \"Pa s\", \"OVERRIDABLE\": \"NO\", \"LABEL\": \"the dynamic viscosity of air at sea level\"}, {\"NAME\": \"C_d\", \"DIMENSION\": \"1\", \"SUPPLY\": \"AUTHOR\", \"LABEL\": \"the drag coefficient of the body\"}, {\"NAME\": \"A_ref\", \"DIMENSION\": \"L2\", \"SUPPLY\": \"AUTHOR\", \"LABEL\": \"the reference area of the drag coefficient\"}, {\"NAME\": \"L_ref\", \"DIMENSION\": \"L1\", \"SUPPLY\": \"AUTHOR\", \"LABEL\": \"the reference length of the Reynolds number\"}], \"SUMS\": [{\"NAME\": \"SPEED2\", \"OVER\": \"VELOCITY\", \"EACH\": \"VELOCITY^2\"}], \"TERMS\": [{\"TARGET\": \"VELOCITY\", \"SIGN\": \"-\", \"EXPR\": \"0.5*rho_air*C_d*A_ref*sqrt(SPEED2)*VELOCITY\", \"LABEL\": \"the quadratic drag\"}], \"ASSUMPTIONS\": [{\"NAME\": \"air_still\", \"PROPOSITION\": \"the air is at rest in the frame of the body's velocity\", \"REFS\": [\"VELOCITY\"]}, {\"NAME\": \"air_uniform\", \"PROPOSITION\": \"the air density is uniform over the region of motion\", \"REFS\": [\"rho_air\"]}, {\"NAME\": \"drag_cd_constant\", \"PROPOSITION\": \"the drag coefficient C_d is constant over the motion\", \"REFS\": [\"C_d\"]}, {\"NAME\": \"drag_no_lift\", \"PROPOSITION\": \"the body experiences no lift force\", \"REFS\": [\"VELOCITY\"]}, {\"NAME\": \"drag_no_magnus\", \"PROPOSITION\": \"the body experiences no Magnus force\", \"REFS\": [\"VELOCITY\"]}], \"BOUNDARIES\": [{\"NAME\": \"drag_quadratic_regime\", \"PREDICATE\": \"1e3 < rho_air |v| L_ref / mu_air < 2e5: the Reynolds window of the quadratic law\", \"CONDITION\": \"mu_air != 0 and SPEED2 >= 0 and rho_air*sqrt(SPEED2)*L_ref/mu_air > 1000 and rho_air*sqrt(SPEED2)*L_ref/mu_air < 200000\"}], \"NOT_CHOSEN\": \"No quadratic air resistance.\", \"NOT_INCLUDED\": [\"No wind: the air is at rest.\", \"No change of air density or viscosity with altitude or temperature.\", \"No lift, Magnus or added-mass force.\", \"No drag outside the Reynolds window of the quadratic law.\"], \"EXCLUDES\": [\"AIR-LINEAR\"], \"INTERACTS_WITH\": [], \"TEST_BINDINGS\": [{\"NAME\": \"PROJECTILE_2D\", \"TPK\": {\"DOF\": [{\"NAME\": \"t\", \"DIMENSION\": \"T1\"}, {\"NAME\": \"x\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"z\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"v_x\", \"DIMENSION\": \"L1 T-1\"}, {\"NAME\": \"v_z\", \"DIMENSION\": \"L1 T-1\"}], \"CONSTANT\": [{\"NAME\": \"m\", \"DIMENSION\": \"M1\"}], \"LAW\": [{\"NAME\": \"KIN_X\", \"STATEMENT\": \"dx/dt = v_x\", \"REFS\": [\"t\", \"v_x\", \"x\"], \"ROLE\": \"EOM(x)\", \"EQUATION\": \"D(x,t)=v_x\"}, {\"NAME\": \"KIN_Z\", \"STATEMENT\": \"dz/dt = v_z\", \"REFS\": [\"t\", \"v_z\", \"z\"], \"ROLE\": \"EOM(z)\", \"EQUATION\": \"D(z,t)=v_z\"}, {\"NAME\": \"EOM_X\", \"STATEMENT\": \"m dv_x/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_x\"], \"ROLE\": \"EOM(v_x)\", \"EQUATION\": \"m*D(v_x,t)=0\"}, {\"NAME\": \"EOM_Z\", \"STATEMENT\": \"m dv_z/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_z\"], \"ROLE\": \"EOM(v_z)\", \"EQUATION\": \"m*D(v_z,t)=0\"}], \"ASSUMPTION\": [{\"NAME\": \"point_mass\", \"PROPOSITION\": \"the body is treated as a point mass\", \"REFS\": [\"m\"]}]}, \"BIND\": {\"VELOCITY\": [\"v_x\", \"v_z\"]}, \"VALUES\": {\"A_ref\": {}, \"C_d\": {}, \"L_ref\": {}}, \"ANSWERS\": {}}]}",
"{\"ID\": \"GRAV-UNIFORM\", \"VERSION\": \"1.0.0\", \"TITLE\": \"Uniform gravity at the standard value g_n\", \"SOURCE\": \"g_n = 9.80665 m s-2, exact by definition: 3rd CGPM (1901), declaration on the unit of mass and on the definition of weight\", \"PREREQUISITES\": [{\"SLOT\": \"MASS\", \"KIND\": \"CONSTANT\", \"DIMENSION\": \"M1\", \"MIN\": 1, \"MAX\": 1, \"LABEL\": \"the mass of the body\"}, {\"SLOT\": \"UP_VELOCITY\", \"KIND\": \"DOF\", \"DIMENSION\": \"L1 T-1\", \"MIN\": 1, \"MAX\": 1, \"LABEL\": \"the velocity component pointing up; its equation of motion receives the weight\"}, {\"SLOT\": \"HEIGHT\", \"KIND\": \"DOF\", \"DIMENSION\": \"L1\", \"MIN\": 1, \"MAX\": 1, \"LABEL\": \"the position along the same upward axis\"}], \"PARAMETERS\": [{\"NAME\": \"g_n\", \"DIMENSION\": \"L1 T-2\", \"SUPPLY\": \"DECLARED\", \"VALUE\": \"9.80665\", \"UNIT\": \"m s-2\", \"OVERRIDABLE\": \"NO\", \"LABEL\": \"the standard acceleration of gravity\"}, {\"NAME\": \"h_max\", \"DIMENSION\": \"L1\", \"SUPPLY\": \"AUTHOR\", \"LABEL\": \"the largest height, above or below the origin, over which the field is taken as uniform\"}], \"SUMS\": [], \"TERMS\": [{\"TARGET\": \"UP_VELOCITY\", \"SIGN\": \"-\", \"EXPR\": \"MASS*g_n\", \"LABEL\": \"the weight\"}], \"ASSUMPTIONS\": [{\"NAME\": \"gravity_uniform\", \"PROPOSITION\": \"the gravitational field is uniform over the region abs({HEIGHT}) < h_max\", \"REFS\": [\"HEIGHT\", \"h_max\"]}, {\"NAME\": \"gravity_standard\", \"PROPOSITION\": \"the local gravitational acceleration equals the conventional standard value g_n\", \"REFS\": [\"g_n\"]}, {\"NAME\": \"frame_inertial\", \"PROPOSITION\": \"the frame in which {HEIGHT} is measured is treated as inertial\", \"REFS\": [\"HEIGHT\"]}], \"BOUNDARIES\": [{\"NAME\": \"gravity_region\", \"PREDICATE\": \"abs({HEIGHT}) < h_max\", \"CONDITION\": \"abs(HEIGHT) < h_max\"}], \"NOT_CHOSEN\": \"No gravity: no weight acts on any DOF.\", \"NOT_INCLUDED\": [\"No variation of gravity with height or latitude beyond what g_n contains.\", \"No Earth rotation (Coriolis or centrifugal force) beyond what g_n contains.\", \"No gravity of bodies other than the Earth.\"], \"EXCLUDES\": [], \"INTERACTS_WITH\": [{\"WITH\": \"AIR-*\", \"QUESTION_ID\": \"BUOYANCY\", \"QUESTION\": \"Does the air's buoyancy (upthrust) act on the body in the system you mean?\", \"YES_LINE\": \"Buoyancy acts (your answer): no module adds it; it acts in this kernel only where one of your own laws states it.\", \"NO_LINE\": \"No buoyancy: the air's upthrust on the body is not included.\"}], \"TEST_BINDINGS\": [{\"NAME\": \"PROJECTILE_2D\", \"TPK\": {\"DOF\": [{\"NAME\": \"t\", \"DIMENSION\": \"T1\"}, {\"NAME\": \"x\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"z\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"v_x\", \"DIMENSION\": \"L1 T-1\"}, {\"NAME\": \"v_z\", \"DIMENSION\": \"L1 T-1\"}], \"CONSTANT\": [{\"NAME\": \"m\", \"DIMENSION\": \"M1\"}], \"LAW\": [{\"NAME\": \"KIN_X\", \"STATEMENT\": \"dx/dt = v_x\", \"REFS\": [\"t\", \"v_x\", \"x\"], \"ROLE\": \"EOM(x)\", \"EQUATION\": \"D(x,t)=v_x\"}, {\"NAME\": \"KIN_Z\", \"STATEMENT\": \"dz/dt = v_z\", \"REFS\": [\"t\", \"v_z\", \"z\"], \"ROLE\": \"EOM(z)\", \"EQUATION\": \"D(z,t)=v_z\"}, {\"NAME\": \"EOM_X\", \"STATEMENT\": \"m dv_x/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_x\"], \"ROLE\": \"EOM(v_x)\", \"EQUATION\": \"m*D(v_x,t)=0\"}, {\"NAME\": \"EOM_Z\", \"STATEMENT\": \"m dv_z/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_z\"], \"ROLE\": \"EOM(v_z)\", \"EQUATION\": \"m*D(v_z,t)=0\"}], \"ASSUMPTION\": [{\"NAME\": \"point_mass\", \"PROPOSITION\": \"the body is treated as a point mass\", \"REFS\": [\"m\"]}]}, \"BIND\": {\"HEIGHT\": [\"z\"], \"MASS\": [\"m\"], \"UP_VELOCITY\": [\"v_z\"]}, \"VALUES\": {\"h_max\": {\"VALUE\": \"100\", \"UNIT\": \"m\"}}, \"ANSWERS\": {}}, {\"NAME\": \"TABLE\", \"TPK\": {\"DOF\": [{\"NAME\": \"t\", \"DIMENSION\": \"T1\"}, {\"NAME\": \"x\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"z\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"v_x\", \"DIMENSION\": \"L1 T-1\"}, {\"NAME\": \"v_z\", \"DIMENSION\": \"L1 T-1\"}], \"CONSTANT\": [{\"NAME\": \"m\", \"DIMENSION\": \"M1\"}], \"LAW\": [{\"NAME\": \"KIN_X\", \"STATEMENT\": \"dx/dt = v_x\", \"REFS\": [\"t\", \"v_x\", \"x\"], \"ROLE\": \"EOM(x)\", \"EQUATION\": \"D(x,t)=v_x\"}, {\"NAME\": \"KIN_Z\", \"STATEMENT\": \"dz/dt = v_z\", \"REFS\": [\"t\", \"v_z\", \"z\"], \"ROLE\": \"CONSTRAINT\", \"EQUATION\": \"D(z,t)=v_z\"}, {\"NAME\": \"EOM_X\", \"STATEMENT\": \"m dv_x/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_x\"], \"ROLE\": \"EOM(v_x)\", \"EQUATION\": \"m*D(v_x,t)=0\"}], \"CONSTRAINT\": [{\"NAME\": \"C_Z\", \"TARGET\": \"z\", \"ACTION\": \"FIX\", \"VALUE\": \"0\", \"UNIT\": \"m\", \"STATEMENT\": \"the puck stays on the table top, z = 0\"}, {\"NAME\": \"C_VZ\", \"TARGET\": \"v_z\", \"ACTION\": \"FIX\", \"VALUE\": \"0\", \"UNIT\": \"m s-1\", \"STATEMENT\": \"the puck has no vertical velocity\"}]}, \"BIND\": {\"HEIGHT\": [\"z\"], \"MASS\": [\"m\"], \"UP_VELOCITY\": [\"v_z\"]}, \"VALUES\": {\"h_max\": {\"VALUE\": \"1\", \"UNIT\": \"m\"}}, \"ANSWERS\": {\"FIXED:v_z\": \"YES\"}}]}",
"{\"ID\": \"MATH\", \"VERSION\": \"1.0.0\", \"TITLE\": \"The mathematical constant pi, as the CONSTANT pi_c\", \"SOURCE\": \"pi to 16 significant digits, 3.141592653589793, the nearest IEEE 754 binary64 value\", \"PREREQUISITES\": [], \"PARAMETERS\": [{\"NAME\": \"pi_c\", \"DIMENSION\": \"1\", \"SUPPLY\": \"DECLARED\", \"VALUE\": \"3.141592653589793\", \"UNIT\": \"1\", \"OVERRIDABLE\": \"NO\", \"LABEL\": \"pi, to 16 significant digits\"}], \"SUMS\": [], \"TERMS\": [], \"ASSUMPTIONS\": [], \"BOUNDARIES\": [], \"NOT_CHOSEN\": \"No mathematical constant: pi exists only if you declare it.\", \"NOT_INCLUDED\": [\"pi_c is pi rounded to 16 significant digits; no other mathematical constant is declared.\"], \"EXCLUDES\": [], \"INTERACTS_WITH\": [], \"TEST_BINDINGS\": [{\"NAME\": \"PROJECTILE_2D\", \"TPK\": {\"DOF\": [{\"NAME\": \"t\", \"DIMENSION\": \"T1\"}, {\"NAME\": \"x\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"z\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"v_x\", \"DIMENSION\": \"L1 T-1\"}, {\"NAME\": \"v_z\", \"DIMENSION\": \"L1 T-1\"}], \"CONSTANT\": [{\"NAME\": \"m\", \"DIMENSION\": \"M1\"}], \"LAW\": [{\"NAME\": \"KIN_X\", \"STATEMENT\": \"dx/dt = v_x\", \"REFS\": [\"t\", \"v_x\", \"x\"], \"ROLE\": \"EOM(x)\", \"EQUATION\": \"D(x,t)=v_x\"}, {\"NAME\": \"KIN_Z\", \"STATEMENT\": \"dz/dt = v_z\", \"REFS\": [\"t\", \"v_z\", \"z\"], \"ROLE\": \"EOM(z)\", \"EQUATION\": \"D(z,t)=v_z\"}, {\"NAME\": \"EOM_X\", \"STATEMENT\": \"m dv_x/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_x\"], \"ROLE\": \"EOM(v_x)\", \"EQUATION\": \"m*D(v_x,t)=0\"}, {\"NAME\": \"EOM_Z\", \"STATEMENT\": \"m dv_z/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_z\"], \"ROLE\": \"EOM(v_z)\", \"EQUATION\": \"m*D(v_z,t)=0\"}], \"ASSUMPTION\": [{\"NAME\": \"point_mass\", \"PROPOSITION\": \"the body is treated as a point mass\", \"REFS\": [\"m\"]}]}, \"BIND\": {}, \"VALUES\": {}, \"ANSWERS\": {}}]}"
]
},
"expected": "[\"REFUSED\",\"CLAIM 1: DIGEST is not a digest\"]",
"fn": "module_expand",
"hand_checked": true,
"name": "X41 a claim whose DIGEST is not a digest"
},
{
"args": {
"claims": [
{
"ANSWERS": {},
"BIND": {
"HEIGHT": [
"z"
],
"MASS": [
"m"
],
"UP_VELOCITY": [
"v_z"
]
},
"DIGEST": "24877ccb5c8ec300d29ed82ce6650592f35cf8899a3d878ccce9c08d4c72c025",
"ID": "GRAV-UNIFORM",
"VALUES": {
"h_max": {
"UNIT": "m",
"VALUE": "100"
}
},
"VERSION": "1.0.0"
}
],
"draft": [
{
"ASSUMPTION": [
{
"NAME": "point_mass",
"PROPOSITION": "the body is treated as a point mass",
"REFS": [
"m"
]
}
],
"CONSTANT": [
{
"DIMENSION": "M1",
"NAME": "m"
}
],
"DOF": [
{
"DIMENSION": "T1",
"NAME": "t"
},
{
"DIMENSION": "L1",
"NAME": "x"
},
{
"DIMENSION": "L1",
"NAME": "z"
},
{
"DIMENSION": "L1 T-1",
"NAME": "v_x"
},
{
"DIMENSION": "L1 T-1",
"NAME": "v_z"
}
],
"LAW": [
{
"EQUATION": "D(x,t)=v_x",
"NAME": "KIN_X",
"REFS": [
"t",
"v_x",
"x"
],
"ROLE": "EOM(x)",
"STATEMENT": "dx/dt = v_x"
},
{
"EQUATION": "D(z,t)=v_z",
"NAME": "KIN_Z",
"REFS": [
"t",
"v_z",
"z"
],
"ROLE": "EOM(z)",
"STATEMENT": "dz/dt = v_z"
},
{
"EQUATION": "m*D(v_x,t)=0",
"NAME": "EOM_X",
"REFS": [
"m",
"t",
"v_x"
],
"ROLE": "EOM(v_x)",
"STATEMENT": "m dv_x/dt = 0"
},
{
"EQUATION": "m*D(v_z,t)=0",
"NAME": "EOM_Z",
"REFS": [
"m",
"t",
"v_z"
],
"ROLE": "EOM(v_z)",
"STATEMENT": "m dv_z/dt = 0"
}
]
}
],
"modules": [
"{\"ID\": \"AIR-LINEAR\", \"VERSION\": \"1.0.0\", \"TITLE\": \"Air resistance at sea level, linear in the speed (Stokes drag on a sphere)\", \"SOURCE\": \"ISO 2533:1975, Standard Atmosphere, sea-level values: density 1.225 kg m-3, dynamic viscosity 1.7894e-5 Pa s\", \"PREREQUISITES\": [{\"SLOT\": \"VELOCITY\", \"KIND\": \"DOF\", \"DIMENSION\": \"L1 T-1\", \"MIN\": 1, \"MAX\": 3, \"LABEL\": \"the velocity components of the body, one per axis\"}], \"PARAMETERS\": [{\"NAME\": \"rho_air\", \"DIMENSION\": \"L-3 M1\", \"SUPPLY\": \"DECLARED\", \"VALUE\": \"1.225\", \"UNIT\": \"kg m-3\", \"OVERRIDABLE\": \"NO\", \"LABEL\": \"the density of air at sea level\"}, {\"NAME\": \"mu_air\", \"DIMENSION\": \"L-1 M1 T-1\", \"SUPPLY\": \"DECLARED\", \"VALUE\": \"1.7894e-5\", \"UNIT\": \"Pa s\", \"OVERRIDABLE\": \"NO\", \"LABEL\": \"the dynamic viscosity of air at sea level\"}, {\"NAME\": \"pi_c\", \"DIMENSION\": \"1\", \"SUPPLY\": \"DECLARED\", \"VALUE\": \"3.141592653589793\", \"UNIT\": \"1\", \"OVERRIDABLE\": \"NO\", \"LABEL\": \"pi, to 16 significant digits\"}, {\"NAME\": \"R_s\", \"DIMENSION\": \"L1\", \"SUPPLY\": \"AUTHOR\", \"LABEL\": \"the radius of the sphere\"}], \"SUMS\": [{\"NAME\": \"SPEED2\", \"OVER\": \"VELOCITY\", \"EACH\": \"VELOCITY^2\"}], \"TERMS\": [{\"TARGET\": \"VELOCITY\", \"SIGN\": \"-\", \"EXPR\": \"6*pi_c*mu_air*R_s*VELOCITY\", \"LABEL\": \"the linear (Stokes) drag\"}], \"ASSUMPTIONS\": [{\"NAME\": \"air_still\", \"PROPOSITION\": \"the air is at rest in the frame of the body's velocity\", \"REFS\": [\"VELOCITY\"]}, {\"NAME\": \"air_uniform\", \"PROPOSITION\": \"the air density is uniform over the region of motion\", \"REFS\": [\"rho_air\"]}, {\"NAME\": \"drag_sphere\", \"PROPOSITION\": \"the body is a rigid sphere of radius R_s\", \"REFS\": [\"R_s\"]}], \"BOUNDARIES\": [{\"NAME\": \"drag_linear_regime\", \"PREDICATE\": \"2 rho_air |v| R_s / mu_air < 1: the regime of the linear law\", \"CONDITION\": \"mu_air != 0 and SPEED2 >= 0 and 2*rho_air*sqrt(SPEED2)*R_s/mu_air < 1\"}], \"NOT_CHOSEN\": \"No linear (Stokes) air resistance.\", \"NOT_INCLUDED\": [\"No wind: the air is at rest.\", \"No change of air density or viscosity with altitude or temperature.\", \"No drag outside the regime of the linear law.\"], \"EXCLUDES\": [], \"INTERACTS_WITH\": [], \"TEST_BINDINGS\": [{\"NAME\": \"PROJECTILE_2D\", \"TPK\": {\"DOF\": [{\"NAME\": \"t\", \"DIMENSION\": \"T1\"}, {\"NAME\": \"x\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"z\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"v_x\", \"DIMENSION\": \"L1 T-1\"}, {\"NAME\": \"v_z\", \"DIMENSION\": \"L1 T-1\"}], \"CONSTANT\": [{\"NAME\": \"m\", \"DIMENSION\": \"M1\"}], \"LAW\": [{\"NAME\": \"KIN_X\", \"STATEMENT\": \"dx/dt = v_x\", \"REFS\": [\"t\", \"v_x\", \"x\"], \"ROLE\": \"EOM(x)\", \"EQUATION\": \"D(x,t)=v_x\"}, {\"NAME\": \"KIN_Z\", \"STATEMENT\": \"dz/dt = v_z\", \"REFS\": [\"t\", \"v_z\", \"z\"], \"ROLE\": \"EOM(z)\", \"EQUATION\": \"D(z,t)=v_z\"}, {\"NAME\": \"EOM_X\", \"STATEMENT\": \"m dv_x/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_x\"], \"ROLE\": \"EOM(v_x)\", \"EQUATION\": \"m*D(v_x,t)=0\"}, {\"NAME\": \"EOM_Z\", \"STATEMENT\": \"m dv_z/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_z\"], \"ROLE\": \"EOM(v_z)\", \"EQUATION\": \"m*D(v_z,t)=0\"}], \"ASSUMPTION\": [{\"NAME\": \"point_mass\", \"PROPOSITION\": \"the body is treated as a point mass\", \"REFS\": [\"m\"]}]}, \"BIND\": {\"VELOCITY\": [\"v_x\", \"v_z\"]}, \"VALUES\": {\"R_s\": {}}, \"ANSWERS\": {}}]}",
"{\"ID\": \"AIR-QUADRATIC\", \"VERSION\": \"1.0.0\", \"TITLE\": \"Air resistance at sea level, quadratic in the speed\", \"SOURCE\": \"ISO 2533:1975, Standard Atmosphere, sea-level values: density 1.225 kg m-3, dynamic viscosity 1.7894e-5 Pa s\", \"PREREQUISITES\": [{\"SLOT\": \"VELOCITY\", \"KIND\": \"DOF\", \"DIMENSION\": \"L1 T-1\", \"MIN\": 1, \"MAX\": 3, \"LABEL\": \"the velocity components of the body, one per axis\"}], \"PARAMETERS\": [{\"NAME\": \"rho_air\", \"DIMENSION\": \"L-3 M1\", \"SUPPLY\": \"DECLARED\", \"VALUE\": \"1.225\", \"UNIT\": \"kg m-3\", \"OVERRIDABLE\": \"NO\", \"LABEL\": \"the density of air at sea level\"}, {\"NAME\": \"mu_air\", \"DIMENSION\": \"L-1 M1 T-1\", \"SUPPLY\": \"DECLARED\", \"VALUE\": \"1.7894e-5\", \"UNIT\": \"Pa s\", \"OVERRIDABLE\": \"NO\", \"LABEL\": \"the dynamic viscosity of air at sea level\"}, {\"NAME\": \"C_d\", \"DIMENSION\": \"1\", \"SUPPLY\": \"AUTHOR\", \"LABEL\": \"the drag coefficient of the body\"}, {\"NAME\": \"A_ref\", \"DIMENSION\": \"L2\", \"SUPPLY\": \"AUTHOR\", \"LABEL\": \"the reference area of the drag coefficient\"}, {\"NAME\": \"L_ref\", \"DIMENSION\": \"L1\", \"SUPPLY\": \"AUTHOR\", \"LABEL\": \"the reference length of the Reynolds number\"}], \"SUMS\": [{\"NAME\": \"SPEED2\", \"OVER\": \"VELOCITY\", \"EACH\": \"VELOCITY^2\"}], \"TERMS\": [{\"TARGET\": \"VELOCITY\", \"SIGN\": \"-\", \"EXPR\": \"0.5*rho_air*C_d*A_ref*sqrt(SPEED2)*VELOCITY\", \"LABEL\": \"the quadratic drag\"}], \"ASSUMPTIONS\": [{\"NAME\": \"air_still\", \"PROPOSITION\": \"the air is at rest in the frame of the body's velocity\", \"REFS\": [\"VELOCITY\"]}, {\"NAME\": \"air_uniform\", \"PROPOSITION\": \"the air density is uniform over the region of motion\", \"REFS\": [\"rho_air\"]}, {\"NAME\": \"drag_cd_constant\", \"PROPOSITION\": \"the drag coefficient C_d is constant over the motion\", \"REFS\": [\"C_d\"]}, {\"NAME\": \"drag_no_lift\", \"PROPOSITION\": \"the body experiences no lift force\", \"REFS\": [\"VELOCITY\"]}, {\"NAME\": \"drag_no_magnus\", \"PROPOSITION\": \"the body experiences no Magnus force\", \"REFS\": [\"VELOCITY\"]}], \"BOUNDARIES\": [{\"NAME\": \"drag_quadratic_regime\", \"PREDICATE\": \"1e3 < rho_air |v| L_ref / mu_air < 2e5: the Reynolds window of the quadratic law\", \"CONDITION\": \"mu_air != 0 and SPEED2 >= 0 and rho_air*sqrt(SPEED2)*L_ref/mu_air > 1000 and rho_air*sqrt(SPEED2)*L_ref/mu_air < 200000\"}], \"NOT_CHOSEN\": \"No quadratic air resistance.\", \"NOT_INCLUDED\": [\"No wind: the air is at rest.\", \"No change of air density or viscosity with altitude or temperature.\", \"No lift, Magnus or added-mass force.\", \"No drag outside the Reynolds window of the quadratic law.\"], \"EXCLUDES\": [\"AIR-LINEAR\"], \"INTERACTS_WITH\": [], \"TEST_BINDINGS\": [{\"NAME\": \"PROJECTILE_2D\", \"TPK\": {\"DOF\": [{\"NAME\": \"t\", \"DIMENSION\": \"T1\"}, {\"NAME\": \"x\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"z\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"v_x\", \"DIMENSION\": \"L1 T-1\"}, {\"NAME\": \"v_z\", \"DIMENSION\": \"L1 T-1\"}], \"CONSTANT\": [{\"NAME\": \"m\", \"DIMENSION\": \"M1\"}], \"LAW\": [{\"NAME\": \"KIN_X\", \"STATEMENT\": \"dx/dt = v_x\", \"REFS\": [\"t\", \"v_x\", \"x\"], \"ROLE\": \"EOM(x)\", \"EQUATION\": \"D(x,t)=v_x\"}, {\"NAME\": \"KIN_Z\", \"STATEMENT\": \"dz/dt = v_z\", \"REFS\": [\"t\", \"v_z\", \"z\"], \"ROLE\": \"EOM(z)\", \"EQUATION\": \"D(z,t)=v_z\"}, {\"NAME\": \"EOM_X\", \"STATEMENT\": \"m dv_x/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_x\"], \"ROLE\": \"EOM(v_x)\", \"EQUATION\": \"m*D(v_x,t)=0\"}, {\"NAME\": \"EOM_Z\", \"STATEMENT\": \"m dv_z/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_z\"], \"ROLE\": \"EOM(v_z)\", \"EQUATION\": \"m*D(v_z,t)=0\"}], \"ASSUMPTION\": [{\"NAME\": \"point_mass\", \"PROPOSITION\": \"the body is treated as a point mass\", \"REFS\": [\"m\"]}]}, \"BIND\": {\"VELOCITY\": [\"v_x\", \"v_z\"]}, \"VALUES\": {\"A_ref\": {}, \"C_d\": {}, \"L_ref\": {}}, \"ANSWERS\": {}}]}",
"{\"ID\": \"GRAV-UNIFORM\", \"VERSION\": \"1.0.0\", \"TITLE\": \"Uniform gravity at the standard value g_n\", \"SOURCE\": \"g_n = 9.80665 m s-2, exact by definition: 3rd CGPM (1901), declaration on the unit of mass and on the definition of weight\", \"PREREQUISITES\": [{\"SLOT\": \"MASS\", \"KIND\": \"CONSTANT\", \"DIMENSION\": \"M1\", \"MIN\": 1, \"MAX\": 1, \"LABEL\": \"the mass of the body\"}, {\"SLOT\": \"UP_VELOCITY\", \"KIND\": \"DOF\", \"DIMENSION\": \"L1 T-1\", \"MIN\": 1, \"MAX\": 1, \"LABEL\": \"the velocity component pointing up; its equation of motion receives the weight\"}, {\"SLOT\": \"HEIGHT\", \"KIND\": \"DOF\", \"DIMENSION\": \"L1\", \"MIN\": 1, \"MAX\": 1, \"LABEL\": \"the position along the same upward axis\"}], \"PARAMETERS\": [{\"NAME\": \"g_n\", \"DIMENSION\": \"L1 T-2\", \"SUPPLY\": \"DECLARED\", \"VALUE\": \"9.80665\", \"UNIT\": \"m s-2\", \"OVERRIDABLE\": \"NO\", \"LABEL\": \"the standard acceleration of gravity\"}, {\"NAME\": \"h_max\", \"DIMENSION\": \"L1\", \"SUPPLY\": \"AUTHOR\", \"LABEL\": \"the largest height, above or below the origin, over which the field is taken as uniform\"}], \"SUMS\": [], \"TERMS\": [{\"TARGET\": \"UP_VELOCITY\", \"SIGN\": \"-\", \"EXPR\": \"MASS*g_n\", \"LABEL\": \"the weight\"}], \"ASSUMPTIONS\": [{\"NAME\": \"gravity_uniform\", \"PROPOSITION\": \"the gravitational field is uniform over the region abs({HEIGHT}) < h_max\", \"REFS\": [\"HEIGHT\", \"h_max\"]}, {\"NAME\": \"gravity_standard\", \"PROPOSITION\": \"the local gravitational acceleration equals the conventional standard value g_n\", \"REFS\": [\"g_n\"]}, {\"NAME\": \"frame_inertial\", \"PROPOSITION\": \"the frame in which {HEIGHT} is measured is treated as inertial\", \"REFS\": [\"HEIGHT\"]}], \"BOUNDARIES\": [{\"NAME\": \"gravity_region\", \"PREDICATE\": \"abs({HEIGHT}) < h_max\", \"CONDITION\": \"abs(HEIGHT) < h_max\"}], \"NOT_CHOSEN\": \"No gravity: no weight acts on any DOF.\", \"NOT_INCLUDED\": [\"No variation of gravity with height or latitude beyond what g_n contains.\", \"No Earth rotation (Coriolis or centrifugal force) beyond what g_n contains.\", \"No gravity of bodies other than the Earth.\"], \"EXCLUDES\": [], \"INTERACTS_WITH\": [{\"WITH\": \"AIR-*\", \"QUESTION_ID\": \"BUOYANCY\", \"QUESTION\": \"Does the air's buoyancy (upthrust) act on the body in the system you mean?\", \"YES_LINE\": \"Buoyancy acts (your answer): no module adds it; it acts in this kernel only where one of your own laws states it.\", \"NO_LINE\": \"No buoyancy: the air's upthrust on the body is not included.\"}], \"TEST_BINDINGS\": [{\"NAME\": \"PROJECTILE_2D\", \"TPK\": {\"DOF\": [{\"NAME\": \"t\", \"DIMENSION\": \"T1\"}, {\"NAME\": \"x\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"z\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"v_x\", \"DIMENSION\": \"L1 T-1\"}, {\"NAME\": \"v_z\", \"DIMENSION\": \"L1 T-1\"}], \"CONSTANT\": [{\"NAME\": \"m\", \"DIMENSION\": \"M1\"}], \"LAW\": [{\"NAME\": \"KIN_X\", \"STATEMENT\": \"dx/dt = v_x\", \"REFS\": [\"t\", \"v_x\", \"x\"], \"ROLE\": \"EOM(x)\", \"EQUATION\": \"D(x,t)=v_x\"}, {\"NAME\": \"KIN_Z\", \"STATEMENT\": \"dz/dt = v_z\", \"REFS\": [\"t\", \"v_z\", \"z\"], \"ROLE\": \"EOM(z)\", \"EQUATION\": \"D(z,t)=v_z\"}, {\"NAME\": \"EOM_X\", \"STATEMENT\": \"m dv_x/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_x\"], \"ROLE\": \"EOM(v_x)\", \"EQUATION\": \"m*D(v_x,t)=0\"}, {\"NAME\": \"EOM_Z\", \"STATEMENT\": \"m dv_z/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_z\"], \"ROLE\": \"EOM(v_z)\", \"EQUATION\": \"m*D(v_z,t)=0\"}], \"ASSUMPTION\": [{\"NAME\": \"point_mass\", \"PROPOSITION\": \"the body is treated as a point mass\", \"REFS\": [\"m\"]}]}, \"BIND\": {\"HEIGHT\": [\"z\"], \"MASS\": [\"m\"], \"UP_VELOCITY\": [\"v_z\"]}, \"VALUES\": {\"h_max\": {\"VALUE\": \"100\", \"UNIT\": \"m\"}}, \"ANSWERS\": {}}, {\"NAME\": \"TABLE\", \"TPK\": {\"DOF\": [{\"NAME\": \"t\", \"DIMENSION\": \"T1\"}, {\"NAME\": \"x\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"z\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"v_x\", \"DIMENSION\": \"L1 T-1\"}, {\"NAME\": \"v_z\", \"DIMENSION\": \"L1 T-1\"}], \"CONSTANT\": [{\"NAME\": \"m\", \"DIMENSION\": \"M1\"}], \"LAW\": [{\"NAME\": \"KIN_X\", \"STATEMENT\": \"dx/dt = v_x\", \"REFS\": [\"t\", \"v_x\", \"x\"], \"ROLE\": \"EOM(x)\", \"EQUATION\": \"D(x,t)=v_x\"}, {\"NAME\": \"KIN_Z\", \"STATEMENT\": \"dz/dt = v_z\", \"REFS\": [\"t\", \"v_z\", \"z\"], \"ROLE\": \"CONSTRAINT\", \"EQUATION\": \"D(z,t)=v_z\"}, {\"NAME\": \"EOM_X\", \"STATEMENT\": \"m dv_x/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_x\"], \"ROLE\": \"EOM(v_x)\", \"EQUATION\": \"m*D(v_x,t)=0\"}], \"CONSTRAINT\": [{\"NAME\": \"C_Z\", \"TARGET\": \"z\", \"ACTION\": \"FIX\", \"VALUE\": \"0\", \"UNIT\": \"m\", \"STATEMENT\": \"the puck stays on the table top, z = 0\"}, {\"NAME\": \"C_VZ\", \"TARGET\": \"v_z\", \"ACTION\": \"FIX\", \"VALUE\": \"0\", \"UNIT\": \"m s-1\", \"STATEMENT\": \"the puck has no vertical velocity\"}]}, \"BIND\": {\"HEIGHT\": [\"z\"], \"MASS\": [\"m\"], \"UP_VELOCITY\": [\"v_z\"]}, \"VALUES\": {\"h_max\": {\"VALUE\": \"1\", \"UNIT\": \"m\"}}, \"ANSWERS\": {\"FIXED:v_z\": \"YES\"}}]}",
"{\"ID\": \"MATH\", \"VERSION\": \"1.0.0\", \"TITLE\": \"The mathematical constant pi, as the CONSTANT pi_c\", \"SOURCE\": \"pi to 16 significant digits, 3.141592653589793, the nearest IEEE 754 binary64 value\", \"PREREQUISITES\": [], \"PARAMETERS\": [{\"NAME\": \"pi_c\", \"DIMENSION\": \"1\", \"SUPPLY\": \"DECLARED\", \"VALUE\": \"3.141592653589793\", \"UNIT\": \"1\", \"OVERRIDABLE\": \"NO\", \"LABEL\": \"pi, to 16 significant digits\"}], \"SUMS\": [], \"TERMS\": [], \"ASSUMPTIONS\": [], \"BOUNDARIES\": [], \"NOT_CHOSEN\": \"No mathematical constant: pi exists only if you declare it.\", \"NOT_INCLUDED\": [\"pi_c is pi rounded to 16 significant digits; no other mathematical constant is declared.\"], \"EXCLUDES\": [], \"INTERACTS_WITH\": [], \"TEST_BINDINGS\": [{\"NAME\": \"PROJECTILE_2D\", \"TPK\": {\"DOF\": [{\"NAME\": \"t\", \"DIMENSION\": \"T1\"}, {\"NAME\": \"x\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"z\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"v_x\", \"DIMENSION\": \"L1 T-1\"}, {\"NAME\": \"v_z\", \"DIMENSION\": \"L1 T-1\"}], \"CONSTANT\": [{\"NAME\": \"m\", \"DIMENSION\": \"M1\"}], \"LAW\": [{\"NAME\": \"KIN_X\", \"STATEMENT\": \"dx/dt = v_x\", \"REFS\": [\"t\", \"v_x\", \"x\"], \"ROLE\": \"EOM(x)\", \"EQUATION\": \"D(x,t)=v_x\"}, {\"NAME\": \"KIN_Z\", \"STATEMENT\": \"dz/dt = v_z\", \"REFS\": [\"t\", \"v_z\", \"z\"], \"ROLE\": \"EOM(z)\", \"EQUATION\": \"D(z,t)=v_z\"}, {\"NAME\": \"EOM_X\", \"STATEMENT\": \"m dv_x/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_x\"], \"ROLE\": \"EOM(v_x)\", \"EQUATION\": \"m*D(v_x,t)=0\"}, {\"NAME\": \"EOM_Z\", \"STATEMENT\": \"m dv_z/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_z\"], \"ROLE\": \"EOM(v_z)\", \"EQUATION\": \"m*D(v_z,t)=0\"}], \"ASSUMPTION\": [{\"NAME\": \"point_mass\", \"PROPOSITION\": \"the body is treated as a point mass\", \"REFS\": [\"m\"]}]}, \"BIND\": {}, \"VALUES\": {}, \"ANSWERS\": {}}]}"
]
},
"expected": "[\"REFUSED\",\"DRAFT: not an object\"]",
"fn": "module_expand",
"hand_checked": true,
"name": "X42 the draft not an object"
},
{
"args": {
"claims": [
{
"ANSWERS": {},
"BIND": {
"HEIGHT": [
"z"
],
"MASS": [
"m"
],
"UP_VELOCITY": [
"v_z"
]
},
"DIGEST": "24877ccb5c8ec300d29ed82ce6650592f35cf8899a3d878ccce9c08d4c72c025",
"ID": "GRAV-UNIFORM",
"VALUES": {
"h_max": {
"UNIT": "m",
"VALUE": "100"
}
},
"VERSION": "1.0.0"
}
],
"draft": {
"RR": {},
"TPK": {
"ASSUMPTION": [
{
"NAME": "point_mass",
"PROPOSITION": "the body is treated as a point mass",
"REFS": [
"m"
]
}
],
"CONSTANT": [
{
"DIMENSION": "M1",
"NAME": "m"
}
],
"DOF": [
{
"DIMENSION": "T1",
"NAME": "t"
},
{
"DIMENSION": "L1",
"NAME": "x"
},
{
"DIMENSION": "L1",
"NAME": "z"
},
{
"DIMENSION": "L1 T-1",
"NAME": "v_x"
},
{
"DIMENSION": "L1 T-1",
"NAME": "v_z"
}
],
"LAW": [
{
"EQUATION": "D(x,t)=v_x",
"NAME": "KIN_X",
"REFS": [
"t",
"v_x",
"x"
],
"ROLE": "EOM(x)",
"STATEMENT": "dx/dt = v_x"
},
{
"EQUATION": "D(z,t)=v_z",
"NAME": "KIN_Z",
"REFS": [
"t",
"v_z",
"z"
],
"ROLE": "EOM(z)",
"STATEMENT": "dz/dt = v_z"
},
{
"EQUATION": "m*D(v_x,t)=0",
"NAME": "EOM_X",
"REFS": [
"m",
"t",
"v_x"
],
"ROLE": "EOM(v_x)",
"STATEMENT": "m dv_x/dt = 0"
},
{
"EQUATION": "m*D(v_z,t)=0",
"NAME": "EOM_Z",
"REFS": [
"m",
"t",
"v_z"
],
"ROLE": "EOM(v_z)",
"STATEMENT": "m dv_z/dt = 0"
}
]
}
},
"modules": [
"{\"ID\": \"AIR-LINEAR\", \"VERSION\": \"1.0.0\", \"TITLE\": \"Air resistance at sea level, linear in the speed (Stokes drag on a sphere)\", \"SOURCE\": \"ISO 2533:1975, Standard Atmosphere, sea-level values: density 1.225 kg m-3, dynamic viscosity 1.7894e-5 Pa s\", \"PREREQUISITES\": [{\"SLOT\": \"VELOCITY\", \"KIND\": \"DOF\", \"DIMENSION\": \"L1 T-1\", \"MIN\": 1, \"MAX\": 3, \"LABEL\": \"the velocity components of the body, one per axis\"}], \"PARAMETERS\": [{\"NAME\": \"rho_air\", \"DIMENSION\": \"L-3 M1\", \"SUPPLY\": \"DECLARED\", \"VALUE\": \"1.225\", \"UNIT\": \"kg m-3\", \"OVERRIDABLE\": \"NO\", \"LABEL\": \"the density of air at sea level\"}, {\"NAME\": \"mu_air\", \"DIMENSION\": \"L-1 M1 T-1\", \"SUPPLY\": \"DECLARED\", \"VALUE\": \"1.7894e-5\", \"UNIT\": \"Pa s\", \"OVERRIDABLE\": \"NO\", \"LABEL\": \"the dynamic viscosity of air at sea level\"}, {\"NAME\": \"pi_c\", \"DIMENSION\": \"1\", \"SUPPLY\": \"DECLARED\", \"VALUE\": \"3.141592653589793\", \"UNIT\": \"1\", \"OVERRIDABLE\": \"NO\", \"LABEL\": \"pi, to 16 significant digits\"}, {\"NAME\": \"R_s\", \"DIMENSION\": \"L1\", \"SUPPLY\": \"AUTHOR\", \"LABEL\": \"the radius of the sphere\"}], \"SUMS\": [{\"NAME\": \"SPEED2\", \"OVER\": \"VELOCITY\", \"EACH\": \"VELOCITY^2\"}], \"TERMS\": [{\"TARGET\": \"VELOCITY\", \"SIGN\": \"-\", \"EXPR\": \"6*pi_c*mu_air*R_s*VELOCITY\", \"LABEL\": \"the linear (Stokes) drag\"}], \"ASSUMPTIONS\": [{\"NAME\": \"air_still\", \"PROPOSITION\": \"the air is at rest in the frame of the body's velocity\", \"REFS\": [\"VELOCITY\"]}, {\"NAME\": \"air_uniform\", \"PROPOSITION\": \"the air density is uniform over the region of motion\", \"REFS\": [\"rho_air\"]}, {\"NAME\": \"drag_sphere\", \"PROPOSITION\": \"the body is a rigid sphere of radius R_s\", \"REFS\": [\"R_s\"]}], \"BOUNDARIES\": [{\"NAME\": \"drag_linear_regime\", \"PREDICATE\": \"2 rho_air |v| R_s / mu_air < 1: the regime of the linear law\", \"CONDITION\": \"mu_air != 0 and SPEED2 >= 0 and 2*rho_air*sqrt(SPEED2)*R_s/mu_air < 1\"}], \"NOT_CHOSEN\": \"No linear (Stokes) air resistance.\", \"NOT_INCLUDED\": [\"No wind: the air is at rest.\", \"No change of air density or viscosity with altitude or temperature.\", \"No drag outside the regime of the linear law.\"], \"EXCLUDES\": [], \"INTERACTS_WITH\": [], \"TEST_BINDINGS\": [{\"NAME\": \"PROJECTILE_2D\", \"TPK\": {\"DOF\": [{\"NAME\": \"t\", \"DIMENSION\": \"T1\"}, {\"NAME\": \"x\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"z\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"v_x\", \"DIMENSION\": \"L1 T-1\"}, {\"NAME\": \"v_z\", \"DIMENSION\": \"L1 T-1\"}], \"CONSTANT\": [{\"NAME\": \"m\", \"DIMENSION\": \"M1\"}], \"LAW\": [{\"NAME\": \"KIN_X\", \"STATEMENT\": \"dx/dt = v_x\", \"REFS\": [\"t\", \"v_x\", \"x\"], \"ROLE\": \"EOM(x)\", \"EQUATION\": \"D(x,t)=v_x\"}, {\"NAME\": \"KIN_Z\", \"STATEMENT\": \"dz/dt = v_z\", \"REFS\": [\"t\", \"v_z\", \"z\"], \"ROLE\": \"EOM(z)\", \"EQUATION\": \"D(z,t)=v_z\"}, {\"NAME\": \"EOM_X\", \"STATEMENT\": \"m dv_x/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_x\"], \"ROLE\": \"EOM(v_x)\", \"EQUATION\": \"m*D(v_x,t)=0\"}, {\"NAME\": \"EOM_Z\", \"STATEMENT\": \"m dv_z/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_z\"], \"ROLE\": \"EOM(v_z)\", \"EQUATION\": \"m*D(v_z,t)=0\"}], \"ASSUMPTION\": [{\"NAME\": \"point_mass\", \"PROPOSITION\": \"the body is treated as a point mass\", \"REFS\": [\"m\"]}]}, \"BIND\": {\"VELOCITY\": [\"v_x\", \"v_z\"]}, \"VALUES\": {\"R_s\": {}}, \"ANSWERS\": {}}]}",
"{\"ID\": \"AIR-QUADRATIC\", \"VERSION\": \"1.0.0\", \"TITLE\": \"Air resistance at sea level, quadratic in the speed\", \"SOURCE\": \"ISO 2533:1975, Standard Atmosphere, sea-level values: density 1.225 kg m-3, dynamic viscosity 1.7894e-5 Pa s\", \"PREREQUISITES\": [{\"SLOT\": \"VELOCITY\", \"KIND\": \"DOF\", \"DIMENSION\": \"L1 T-1\", \"MIN\": 1, \"MAX\": 3, \"LABEL\": \"the velocity components of the body, one per axis\"}], \"PARAMETERS\": [{\"NAME\": \"rho_air\", \"DIMENSION\": \"L-3 M1\", \"SUPPLY\": \"DECLARED\", \"VALUE\": \"1.225\", \"UNIT\": \"kg m-3\", \"OVERRIDABLE\": \"NO\", \"LABEL\": \"the density of air at sea level\"}, {\"NAME\": \"mu_air\", \"DIMENSION\": \"L-1 M1 T-1\", \"SUPPLY\": \"DECLARED\", \"VALUE\": \"1.7894e-5\", \"UNIT\": \"Pa s\", \"OVERRIDABLE\": \"NO\", \"LABEL\": \"the dynamic viscosity of air at sea level\"}, {\"NAME\": \"C_d\", \"DIMENSION\": \"1\", \"SUPPLY\": \"AUTHOR\", \"LABEL\": \"the drag coefficient of the body\"}, {\"NAME\": \"A_ref\", \"DIMENSION\": \"L2\", \"SUPPLY\": \"AUTHOR\", \"LABEL\": \"the reference area of the drag coefficient\"}, {\"NAME\": \"L_ref\", \"DIMENSION\": \"L1\", \"SUPPLY\": \"AUTHOR\", \"LABEL\": \"the reference length of the Reynolds number\"}], \"SUMS\": [{\"NAME\": \"SPEED2\", \"OVER\": \"VELOCITY\", \"EACH\": \"VELOCITY^2\"}], \"TERMS\": [{\"TARGET\": \"VELOCITY\", \"SIGN\": \"-\", \"EXPR\": \"0.5*rho_air*C_d*A_ref*sqrt(SPEED2)*VELOCITY\", \"LABEL\": \"the quadratic drag\"}], \"ASSUMPTIONS\": [{\"NAME\": \"air_still\", \"PROPOSITION\": \"the air is at rest in the frame of the body's velocity\", \"REFS\": [\"VELOCITY\"]}, {\"NAME\": \"air_uniform\", \"PROPOSITION\": \"the air density is uniform over the region of motion\", \"REFS\": [\"rho_air\"]}, {\"NAME\": \"drag_cd_constant\", \"PROPOSITION\": \"the drag coefficient C_d is constant over the motion\", \"REFS\": [\"C_d\"]}, {\"NAME\": \"drag_no_lift\", \"PROPOSITION\": \"the body experiences no lift force\", \"REFS\": [\"VELOCITY\"]}, {\"NAME\": \"drag_no_magnus\", \"PROPOSITION\": \"the body experiences no Magnus force\", \"REFS\": [\"VELOCITY\"]}], \"BOUNDARIES\": [{\"NAME\": \"drag_quadratic_regime\", \"PREDICATE\": \"1e3 < rho_air |v| L_ref / mu_air < 2e5: the Reynolds window of the quadratic law\", \"CONDITION\": \"mu_air != 0 and SPEED2 >= 0 and rho_air*sqrt(SPEED2)*L_ref/mu_air > 1000 and rho_air*sqrt(SPEED2)*L_ref/mu_air < 200000\"}], \"NOT_CHOSEN\": \"No quadratic air resistance.\", \"NOT_INCLUDED\": [\"No wind: the air is at rest.\", \"No change of air density or viscosity with altitude or temperature.\", \"No lift, Magnus or added-mass force.\", \"No drag outside the Reynolds window of the quadratic law.\"], \"EXCLUDES\": [\"AIR-LINEAR\"], \"INTERACTS_WITH\": [], \"TEST_BINDINGS\": [{\"NAME\": \"PROJECTILE_2D\", \"TPK\": {\"DOF\": [{\"NAME\": \"t\", \"DIMENSION\": \"T1\"}, {\"NAME\": \"x\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"z\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"v_x\", \"DIMENSION\": \"L1 T-1\"}, {\"NAME\": \"v_z\", \"DIMENSION\": \"L1 T-1\"}], \"CONSTANT\": [{\"NAME\": \"m\", \"DIMENSION\": \"M1\"}], \"LAW\": [{\"NAME\": \"KIN_X\", \"STATEMENT\": \"dx/dt = v_x\", \"REFS\": [\"t\", \"v_x\", \"x\"], \"ROLE\": \"EOM(x)\", \"EQUATION\": \"D(x,t)=v_x\"}, {\"NAME\": \"KIN_Z\", \"STATEMENT\": \"dz/dt = v_z\", \"REFS\": [\"t\", \"v_z\", \"z\"], \"ROLE\": \"EOM(z)\", \"EQUATION\": \"D(z,t)=v_z\"}, {\"NAME\": \"EOM_X\", \"STATEMENT\": \"m dv_x/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_x\"], \"ROLE\": \"EOM(v_x)\", \"EQUATION\": \"m*D(v_x,t)=0\"}, {\"NAME\": \"EOM_Z\", \"STATEMENT\": \"m dv_z/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_z\"], \"ROLE\": \"EOM(v_z)\", \"EQUATION\": \"m*D(v_z,t)=0\"}], \"ASSUMPTION\": [{\"NAME\": \"point_mass\", \"PROPOSITION\": \"the body is treated as a point mass\", \"REFS\": [\"m\"]}]}, \"BIND\": {\"VELOCITY\": [\"v_x\", \"v_z\"]}, \"VALUES\": {\"A_ref\": {}, \"C_d\": {}, \"L_ref\": {}}, \"ANSWERS\": {}}]}",
"{\"ID\": \"GRAV-UNIFORM\", \"VERSION\": \"1.0.0\", \"TITLE\": \"Uniform gravity at the standard value g_n\", \"SOURCE\": \"g_n = 9.80665 m s-2, exact by definition: 3rd CGPM (1901), declaration on the unit of mass and on the definition of weight\", \"PREREQUISITES\": [{\"SLOT\": \"MASS\", \"KIND\": \"CONSTANT\", \"DIMENSION\": \"M1\", \"MIN\": 1, \"MAX\": 1, \"LABEL\": \"the mass of the body\"}, {\"SLOT\": \"UP_VELOCITY\", \"KIND\": \"DOF\", \"DIMENSION\": \"L1 T-1\", \"MIN\": 1, \"MAX\": 1, \"LABEL\": \"the velocity component pointing up; its equation of motion receives the weight\"}, {\"SLOT\": \"HEIGHT\", \"KIND\": \"DOF\", \"DIMENSION\": \"L1\", \"MIN\": 1, \"MAX\": 1, \"LABEL\": \"the position along the same upward axis\"}], \"PARAMETERS\": [{\"NAME\": \"g_n\", \"DIMENSION\": \"L1 T-2\", \"SUPPLY\": \"DECLARED\", \"VALUE\": \"9.80665\", \"UNIT\": \"m s-2\", \"OVERRIDABLE\": \"NO\", \"LABEL\": \"the standard acceleration of gravity\"}, {\"NAME\": \"h_max\", \"DIMENSION\": \"L1\", \"SUPPLY\": \"AUTHOR\", \"LABEL\": \"the largest height, above or below the origin, over which the field is taken as uniform\"}], \"SUMS\": [], \"TERMS\": [{\"TARGET\": \"UP_VELOCITY\", \"SIGN\": \"-\", \"EXPR\": \"MASS*g_n\", \"LABEL\": \"the weight\"}], \"ASSUMPTIONS\": [{\"NAME\": \"gravity_uniform\", \"PROPOSITION\": \"the gravitational field is uniform over the region abs({HEIGHT}) < h_max\", \"REFS\": [\"HEIGHT\", \"h_max\"]}, {\"NAME\": \"gravity_standard\", \"PROPOSITION\": \"the local gravitational acceleration equals the conventional standard value g_n\", \"REFS\": [\"g_n\"]}, {\"NAME\": \"frame_inertial\", \"PROPOSITION\": \"the frame in which {HEIGHT} is measured is treated as inertial\", \"REFS\": [\"HEIGHT\"]}], \"BOUNDARIES\": [{\"NAME\": \"gravity_region\", \"PREDICATE\": \"abs({HEIGHT}) < h_max\", \"CONDITION\": \"abs(HEIGHT) < h_max\"}], \"NOT_CHOSEN\": \"No gravity: no weight acts on any DOF.\", \"NOT_INCLUDED\": [\"No variation of gravity with height or latitude beyond what g_n contains.\", \"No Earth rotation (Coriolis or centrifugal force) beyond what g_n contains.\", \"No gravity of bodies other than the Earth.\"], \"EXCLUDES\": [], \"INTERACTS_WITH\": [{\"WITH\": \"AIR-*\", \"QUESTION_ID\": \"BUOYANCY\", \"QUESTION\": \"Does the air's buoyancy (upthrust) act on the body in the system you mean?\", \"YES_LINE\": \"Buoyancy acts (your answer): no module adds it; it acts in this kernel only where one of your own laws states it.\", \"NO_LINE\": \"No buoyancy: the air's upthrust on the body is not included.\"}], \"TEST_BINDINGS\": [{\"NAME\": \"PROJECTILE_2D\", \"TPK\": {\"DOF\": [{\"NAME\": \"t\", \"DIMENSION\": \"T1\"}, {\"NAME\": \"x\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"z\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"v_x\", \"DIMENSION\": \"L1 T-1\"}, {\"NAME\": \"v_z\", \"DIMENSION\": \"L1 T-1\"}], \"CONSTANT\": [{\"NAME\": \"m\", \"DIMENSION\": \"M1\"}], \"LAW\": [{\"NAME\": \"KIN_X\", \"STATEMENT\": \"dx/dt = v_x\", \"REFS\": [\"t\", \"v_x\", \"x\"], \"ROLE\": \"EOM(x)\", \"EQUATION\": \"D(x,t)=v_x\"}, {\"NAME\": \"KIN_Z\", \"STATEMENT\": \"dz/dt = v_z\", \"REFS\": [\"t\", \"v_z\", \"z\"], \"ROLE\": \"EOM(z)\", \"EQUATION\": \"D(z,t)=v_z\"}, {\"NAME\": \"EOM_X\", \"STATEMENT\": \"m dv_x/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_x\"], \"ROLE\": \"EOM(v_x)\", \"EQUATION\": \"m*D(v_x,t)=0\"}, {\"NAME\": \"EOM_Z\", \"STATEMENT\": \"m dv_z/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_z\"], \"ROLE\": \"EOM(v_z)\", \"EQUATION\": \"m*D(v_z,t)=0\"}], \"ASSUMPTION\": [{\"NAME\": \"point_mass\", \"PROPOSITION\": \"the body is treated as a point mass\", \"REFS\": [\"m\"]}]}, \"BIND\": {\"HEIGHT\": [\"z\"], \"MASS\": [\"m\"], \"UP_VELOCITY\": [\"v_z\"]}, \"VALUES\": {\"h_max\": {\"VALUE\": \"100\", \"UNIT\": \"m\"}}, \"ANSWERS\": {}}, {\"NAME\": \"TABLE\", \"TPK\": {\"DOF\": [{\"NAME\": \"t\", \"DIMENSION\": \"T1\"}, {\"NAME\": \"x\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"z\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"v_x\", \"DIMENSION\": \"L1 T-1\"}, {\"NAME\": \"v_z\", \"DIMENSION\": \"L1 T-1\"}], \"CONSTANT\": [{\"NAME\": \"m\", \"DIMENSION\": \"M1\"}], \"LAW\": [{\"NAME\": \"KIN_X\", \"STATEMENT\": \"dx/dt = v_x\", \"REFS\": [\"t\", \"v_x\", \"x\"], \"ROLE\": \"EOM(x)\", \"EQUATION\": \"D(x,t)=v_x\"}, {\"NAME\": \"KIN_Z\", \"STATEMENT\": \"dz/dt = v_z\", \"REFS\": [\"t\", \"v_z\", \"z\"], \"ROLE\": \"CONSTRAINT\", \"EQUATION\": \"D(z,t)=v_z\"}, {\"NAME\": \"EOM_X\", \"STATEMENT\": \"m dv_x/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_x\"], \"ROLE\": \"EOM(v_x)\", \"EQUATION\": \"m*D(v_x,t)=0\"}], \"CONSTRAINT\": [{\"NAME\": \"C_Z\", \"TARGET\": \"z\", \"ACTION\": \"FIX\", \"VALUE\": \"0\", \"UNIT\": \"m\", \"STATEMENT\": \"the puck stays on the table top, z = 0\"}, {\"NAME\": \"C_VZ\", \"TARGET\": \"v_z\", \"ACTION\": \"FIX\", \"VALUE\": \"0\", \"UNIT\": \"m s-1\", \"STATEMENT\": \"the puck has no vertical velocity\"}]}, \"BIND\": {\"HEIGHT\": [\"z\"], \"MASS\": [\"m\"], \"UP_VELOCITY\": [\"v_z\"]}, \"VALUES\": {\"h_max\": {\"VALUE\": \"1\", \"UNIT\": \"m\"}}, \"ANSWERS\": {\"FIXED:v_z\": \"YES\"}}]}",
"{\"ID\": \"MATH\", \"VERSION\": \"1.0.0\", \"TITLE\": \"The mathematical constant pi, as the CONSTANT pi_c\", \"SOURCE\": \"pi to 16 significant digits, 3.141592653589793, the nearest IEEE 754 binary64 value\", \"PREREQUISITES\": [], \"PARAMETERS\": [{\"NAME\": \"pi_c\", \"DIMENSION\": \"1\", \"SUPPLY\": \"DECLARED\", \"VALUE\": \"3.141592653589793\", \"UNIT\": \"1\", \"OVERRIDABLE\": \"NO\", \"LABEL\": \"pi, to 16 significant digits\"}], \"SUMS\": [], \"TERMS\": [], \"ASSUMPTIONS\": [], \"BOUNDARIES\": [], \"NOT_CHOSEN\": \"No mathematical constant: pi exists only if you declare it.\", \"NOT_INCLUDED\": [\"pi_c is pi rounded to 16 significant digits; no other mathematical constant is declared.\"], \"EXCLUDES\": [], \"INTERACTS_WITH\": [], \"TEST_BINDINGS\": [{\"NAME\": \"PROJECTILE_2D\", \"TPK\": {\"DOF\": [{\"NAME\": \"t\", \"DIMENSION\": \"T1\"}, {\"NAME\": \"x\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"z\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"v_x\", \"DIMENSION\": \"L1 T-1\"}, {\"NAME\": \"v_z\", \"DIMENSION\": \"L1 T-1\"}], \"CONSTANT\": [{\"NAME\": \"m\", \"DIMENSION\": \"M1\"}], \"LAW\": [{\"NAME\": \"KIN_X\", \"STATEMENT\": \"dx/dt = v_x\", \"REFS\": [\"t\", \"v_x\", \"x\"], \"ROLE\": \"EOM(x)\", \"EQUATION\": \"D(x,t)=v_x\"}, {\"NAME\": \"KIN_Z\", \"STATEMENT\": \"dz/dt = v_z\", \"REFS\": [\"t\", \"v_z\", \"z\"], \"ROLE\": \"EOM(z)\", \"EQUATION\": \"D(z,t)=v_z\"}, {\"NAME\": \"EOM_X\", \"STATEMENT\": \"m dv_x/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_x\"], \"ROLE\": \"EOM(v_x)\", \"EQUATION\": \"m*D(v_x,t)=0\"}, {\"NAME\": \"EOM_Z\", \"STATEMENT\": \"m dv_z/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_z\"], \"ROLE\": \"EOM(v_z)\", \"EQUATION\": \"m*D(v_z,t)=0\"}], \"ASSUMPTION\": [{\"NAME\": \"point_mass\", \"PROPOSITION\": \"the body is treated as a point mass\", \"REFS\": [\"m\"]}]}, \"BIND\": {}, \"VALUES\": {}, \"ANSWERS\": {}}]}"
]
},
"expected": "[\"REFUSED\",\"DRAFT: unknown zone RR\"]",
"fn": "module_expand",
"hand_checked": true,
"name": "X43 an unknown zone"
},
{
"args": {
"claims": [
{
"ANSWERS": {},
"BIND": {
"HEIGHT": [
"z"
],
"MASS": [
"m"
],
"UP_VELOCITY": [
"v_z"
]
},
"DIGEST": "24877ccb5c8ec300d29ed82ce6650592f35cf8899a3d878ccce9c08d4c72c025",
"ID": "GRAV-UNIFORM",
"VALUES": {
"h_max": {
"UNIT": "m",
"VALUE": "100"
}
},
"VERSION": "1.0.0"
}
],
"draft": {
"TMS": {}
},
"modules": [
"{\"ID\": \"AIR-LINEAR\", \"VERSION\": \"1.0.0\", \"TITLE\": \"Air resistance at sea level, linear in the speed (Stokes drag on a sphere)\", \"SOURCE\": \"ISO 2533:1975, Standard Atmosphere, sea-level values: density 1.225 kg m-3, dynamic viscosity 1.7894e-5 Pa s\", \"PREREQUISITES\": [{\"SLOT\": \"VELOCITY\", \"KIND\": \"DOF\", \"DIMENSION\": \"L1 T-1\", \"MIN\": 1, \"MAX\": 3, \"LABEL\": \"the velocity components of the body, one per axis\"}], \"PARAMETERS\": [{\"NAME\": \"rho_air\", \"DIMENSION\": \"L-3 M1\", \"SUPPLY\": \"DECLARED\", \"VALUE\": \"1.225\", \"UNIT\": \"kg m-3\", \"OVERRIDABLE\": \"NO\", \"LABEL\": \"the density of air at sea level\"}, {\"NAME\": \"mu_air\", \"DIMENSION\": \"L-1 M1 T-1\", \"SUPPLY\": \"DECLARED\", \"VALUE\": \"1.7894e-5\", \"UNIT\": \"Pa s\", \"OVERRIDABLE\": \"NO\", \"LABEL\": \"the dynamic viscosity of air at sea level\"}, {\"NAME\": \"pi_c\", \"DIMENSION\": \"1\", \"SUPPLY\": \"DECLARED\", \"VALUE\": \"3.141592653589793\", \"UNIT\": \"1\", \"OVERRIDABLE\": \"NO\", \"LABEL\": \"pi, to 16 significant digits\"}, {\"NAME\": \"R_s\", \"DIMENSION\": \"L1\", \"SUPPLY\": \"AUTHOR\", \"LABEL\": \"the radius of the sphere\"}], \"SUMS\": [{\"NAME\": \"SPEED2\", \"OVER\": \"VELOCITY\", \"EACH\": \"VELOCITY^2\"}], \"TERMS\": [{\"TARGET\": \"VELOCITY\", \"SIGN\": \"-\", \"EXPR\": \"6*pi_c*mu_air*R_s*VELOCITY\", \"LABEL\": \"the linear (Stokes) drag\"}], \"ASSUMPTIONS\": [{\"NAME\": \"air_still\", \"PROPOSITION\": \"the air is at rest in the frame of the body's velocity\", \"REFS\": [\"VELOCITY\"]}, {\"NAME\": \"air_uniform\", \"PROPOSITION\": \"the air density is uniform over the region of motion\", \"REFS\": [\"rho_air\"]}, {\"NAME\": \"drag_sphere\", \"PROPOSITION\": \"the body is a rigid sphere of radius R_s\", \"REFS\": [\"R_s\"]}], \"BOUNDARIES\": [{\"NAME\": \"drag_linear_regime\", \"PREDICATE\": \"2 rho_air |v| R_s / mu_air < 1: the regime of the linear law\", \"CONDITION\": \"mu_air != 0 and SPEED2 >= 0 and 2*rho_air*sqrt(SPEED2)*R_s/mu_air < 1\"}], \"NOT_CHOSEN\": \"No linear (Stokes) air resistance.\", \"NOT_INCLUDED\": [\"No wind: the air is at rest.\", \"No change of air density or viscosity with altitude or temperature.\", \"No drag outside the regime of the linear law.\"], \"EXCLUDES\": [], \"INTERACTS_WITH\": [], \"TEST_BINDINGS\": [{\"NAME\": \"PROJECTILE_2D\", \"TPK\": {\"DOF\": [{\"NAME\": \"t\", \"DIMENSION\": \"T1\"}, {\"NAME\": \"x\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"z\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"v_x\", \"DIMENSION\": \"L1 T-1\"}, {\"NAME\": \"v_z\", \"DIMENSION\": \"L1 T-1\"}], \"CONSTANT\": [{\"NAME\": \"m\", \"DIMENSION\": \"M1\"}], \"LAW\": [{\"NAME\": \"KIN_X\", \"STATEMENT\": \"dx/dt = v_x\", \"REFS\": [\"t\", \"v_x\", \"x\"], \"ROLE\": \"EOM(x)\", \"EQUATION\": \"D(x,t)=v_x\"}, {\"NAME\": \"KIN_Z\", \"STATEMENT\": \"dz/dt = v_z\", \"REFS\": [\"t\", \"v_z\", \"z\"], \"ROLE\": \"EOM(z)\", \"EQUATION\": \"D(z,t)=v_z\"}, {\"NAME\": \"EOM_X\", \"STATEMENT\": \"m dv_x/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_x\"], \"ROLE\": \"EOM(v_x)\", \"EQUATION\": \"m*D(v_x,t)=0\"}, {\"NAME\": \"EOM_Z\", \"STATEMENT\": \"m dv_z/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_z\"], \"ROLE\": \"EOM(v_z)\", \"EQUATION\": \"m*D(v_z,t)=0\"}], \"ASSUMPTION\": [{\"NAME\": \"point_mass\", \"PROPOSITION\": \"the body is treated as a point mass\", \"REFS\": [\"m\"]}]}, \"BIND\": {\"VELOCITY\": [\"v_x\", \"v_z\"]}, \"VALUES\": {\"R_s\": {}}, \"ANSWERS\": {}}]}",
"{\"ID\": \"AIR-QUADRATIC\", \"VERSION\": \"1.0.0\", \"TITLE\": \"Air resistance at sea level, quadratic in the speed\", \"SOURCE\": \"ISO 2533:1975, Standard Atmosphere, sea-level values: density 1.225 kg m-3, dynamic viscosity 1.7894e-5 Pa s\", \"PREREQUISITES\": [{\"SLOT\": \"VELOCITY\", \"KIND\": \"DOF\", \"DIMENSION\": \"L1 T-1\", \"MIN\": 1, \"MAX\": 3, \"LABEL\": \"the velocity components of the body, one per axis\"}], \"PARAMETERS\": [{\"NAME\": \"rho_air\", \"DIMENSION\": \"L-3 M1\", \"SUPPLY\": \"DECLARED\", \"VALUE\": \"1.225\", \"UNIT\": \"kg m-3\", \"OVERRIDABLE\": \"NO\", \"LABEL\": \"the density of air at sea level\"}, {\"NAME\": \"mu_air\", \"DIMENSION\": \"L-1 M1 T-1\", \"SUPPLY\": \"DECLARED\", \"VALUE\": \"1.7894e-5\", \"UNIT\": \"Pa s\", \"OVERRIDABLE\": \"NO\", \"LABEL\": \"the dynamic viscosity of air at sea level\"}, {\"NAME\": \"C_d\", \"DIMENSION\": \"1\", \"SUPPLY\": \"AUTHOR\", \"LABEL\": \"the drag coefficient of the body\"}, {\"NAME\": \"A_ref\", \"DIMENSION\": \"L2\", \"SUPPLY\": \"AUTHOR\", \"LABEL\": \"the reference area of the drag coefficient\"}, {\"NAME\": \"L_ref\", \"DIMENSION\": \"L1\", \"SUPPLY\": \"AUTHOR\", \"LABEL\": \"the reference length of the Reynolds number\"}], \"SUMS\": [{\"NAME\": \"SPEED2\", \"OVER\": \"VELOCITY\", \"EACH\": \"VELOCITY^2\"}], \"TERMS\": [{\"TARGET\": \"VELOCITY\", \"SIGN\": \"-\", \"EXPR\": \"0.5*rho_air*C_d*A_ref*sqrt(SPEED2)*VELOCITY\", \"LABEL\": \"the quadratic drag\"}], \"ASSUMPTIONS\": [{\"NAME\": \"air_still\", \"PROPOSITION\": \"the air is at rest in the frame of the body's velocity\", \"REFS\": [\"VELOCITY\"]}, {\"NAME\": \"air_uniform\", \"PROPOSITION\": \"the air density is uniform over the region of motion\", \"REFS\": [\"rho_air\"]}, {\"NAME\": \"drag_cd_constant\", \"PROPOSITION\": \"the drag coefficient C_d is constant over the motion\", \"REFS\": [\"C_d\"]}, {\"NAME\": \"drag_no_lift\", \"PROPOSITION\": \"the body experiences no lift force\", \"REFS\": [\"VELOCITY\"]}, {\"NAME\": \"drag_no_magnus\", \"PROPOSITION\": \"the body experiences no Magnus force\", \"REFS\": [\"VELOCITY\"]}], \"BOUNDARIES\": [{\"NAME\": \"drag_quadratic_regime\", \"PREDICATE\": \"1e3 < rho_air |v| L_ref / mu_air < 2e5: the Reynolds window of the quadratic law\", \"CONDITION\": \"mu_air != 0 and SPEED2 >= 0 and rho_air*sqrt(SPEED2)*L_ref/mu_air > 1000 and rho_air*sqrt(SPEED2)*L_ref/mu_air < 200000\"}], \"NOT_CHOSEN\": \"No quadratic air resistance.\", \"NOT_INCLUDED\": [\"No wind: the air is at rest.\", \"No change of air density or viscosity with altitude or temperature.\", \"No lift, Magnus or added-mass force.\", \"No drag outside the Reynolds window of the quadratic law.\"], \"EXCLUDES\": [\"AIR-LINEAR\"], \"INTERACTS_WITH\": [], \"TEST_BINDINGS\": [{\"NAME\": \"PROJECTILE_2D\", \"TPK\": {\"DOF\": [{\"NAME\": \"t\", \"DIMENSION\": \"T1\"}, {\"NAME\": \"x\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"z\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"v_x\", \"DIMENSION\": \"L1 T-1\"}, {\"NAME\": \"v_z\", \"DIMENSION\": \"L1 T-1\"}], \"CONSTANT\": [{\"NAME\": \"m\", \"DIMENSION\": \"M1\"}], \"LAW\": [{\"NAME\": \"KIN_X\", \"STATEMENT\": \"dx/dt = v_x\", \"REFS\": [\"t\", \"v_x\", \"x\"], \"ROLE\": \"EOM(x)\", \"EQUATION\": \"D(x,t)=v_x\"}, {\"NAME\": \"KIN_Z\", \"STATEMENT\": \"dz/dt = v_z\", \"REFS\": [\"t\", \"v_z\", \"z\"], \"ROLE\": \"EOM(z)\", \"EQUATION\": \"D(z,t)=v_z\"}, {\"NAME\": \"EOM_X\", \"STATEMENT\": \"m dv_x/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_x\"], \"ROLE\": \"EOM(v_x)\", \"EQUATION\": \"m*D(v_x,t)=0\"}, {\"NAME\": \"EOM_Z\", \"STATEMENT\": \"m dv_z/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_z\"], \"ROLE\": \"EOM(v_z)\", \"EQUATION\": \"m*D(v_z,t)=0\"}], \"ASSUMPTION\": [{\"NAME\": \"point_mass\", \"PROPOSITION\": \"the body is treated as a point mass\", \"REFS\": [\"m\"]}]}, \"BIND\": {\"VELOCITY\": [\"v_x\", \"v_z\"]}, \"VALUES\": {\"A_ref\": {}, \"C_d\": {}, \"L_ref\": {}}, \"ANSWERS\": {}}]}",
"{\"ID\": \"GRAV-UNIFORM\", \"VERSION\": \"1.0.0\", \"TITLE\": \"Uniform gravity at the standard value g_n\", \"SOURCE\": \"g_n = 9.80665 m s-2, exact by definition: 3rd CGPM (1901), declaration on the unit of mass and on the definition of weight\", \"PREREQUISITES\": [{\"SLOT\": \"MASS\", \"KIND\": \"CONSTANT\", \"DIMENSION\": \"M1\", \"MIN\": 1, \"MAX\": 1, \"LABEL\": \"the mass of the body\"}, {\"SLOT\": \"UP_VELOCITY\", \"KIND\": \"DOF\", \"DIMENSION\": \"L1 T-1\", \"MIN\": 1, \"MAX\": 1, \"LABEL\": \"the velocity component pointing up; its equation of motion receives the weight\"}, {\"SLOT\": \"HEIGHT\", \"KIND\": \"DOF\", \"DIMENSION\": \"L1\", \"MIN\": 1, \"MAX\": 1, \"LABEL\": \"the position along the same upward axis\"}], \"PARAMETERS\": [{\"NAME\": \"g_n\", \"DIMENSION\": \"L1 T-2\", \"SUPPLY\": \"DECLARED\", \"VALUE\": \"9.80665\", \"UNIT\": \"m s-2\", \"OVERRIDABLE\": \"NO\", \"LABEL\": \"the standard acceleration of gravity\"}, {\"NAME\": \"h_max\", \"DIMENSION\": \"L1\", \"SUPPLY\": \"AUTHOR\", \"LABEL\": \"the largest height, above or below the origin, over which the field is taken as uniform\"}], \"SUMS\": [], \"TERMS\": [{\"TARGET\": \"UP_VELOCITY\", \"SIGN\": \"-\", \"EXPR\": \"MASS*g_n\", \"LABEL\": \"the weight\"}], \"ASSUMPTIONS\": [{\"NAME\": \"gravity_uniform\", \"PROPOSITION\": \"the gravitational field is uniform over the region abs({HEIGHT}) < h_max\", \"REFS\": [\"HEIGHT\", \"h_max\"]}, {\"NAME\": \"gravity_standard\", \"PROPOSITION\": \"the local gravitational acceleration equals the conventional standard value g_n\", \"REFS\": [\"g_n\"]}, {\"NAME\": \"frame_inertial\", \"PROPOSITION\": \"the frame in which {HEIGHT} is measured is treated as inertial\", \"REFS\": [\"HEIGHT\"]}], \"BOUNDARIES\": [{\"NAME\": \"gravity_region\", \"PREDICATE\": \"abs({HEIGHT}) < h_max\", \"CONDITION\": \"abs(HEIGHT) < h_max\"}], \"NOT_CHOSEN\": \"No gravity: no weight acts on any DOF.\", \"NOT_INCLUDED\": [\"No variation of gravity with height or latitude beyond what g_n contains.\", \"No Earth rotation (Coriolis or centrifugal force) beyond what g_n contains.\", \"No gravity of bodies other than the Earth.\"], \"EXCLUDES\": [], \"INTERACTS_WITH\": [{\"WITH\": \"AIR-*\", \"QUESTION_ID\": \"BUOYANCY\", \"QUESTION\": \"Does the air's buoyancy (upthrust) act on the body in the system you mean?\", \"YES_LINE\": \"Buoyancy acts (your answer): no module adds it; it acts in this kernel only where one of your own laws states it.\", \"NO_LINE\": \"No buoyancy: the air's upthrust on the body is not included.\"}], \"TEST_BINDINGS\": [{\"NAME\": \"PROJECTILE_2D\", \"TPK\": {\"DOF\": [{\"NAME\": \"t\", \"DIMENSION\": \"T1\"}, {\"NAME\": \"x\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"z\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"v_x\", \"DIMENSION\": \"L1 T-1\"}, {\"NAME\": \"v_z\", \"DIMENSION\": \"L1 T-1\"}], \"CONSTANT\": [{\"NAME\": \"m\", \"DIMENSION\": \"M1\"}], \"LAW\": [{\"NAME\": \"KIN_X\", \"STATEMENT\": \"dx/dt = v_x\", \"REFS\": [\"t\", \"v_x\", \"x\"], \"ROLE\": \"EOM(x)\", \"EQUATION\": \"D(x,t)=v_x\"}, {\"NAME\": \"KIN_Z\", \"STATEMENT\": \"dz/dt = v_z\", \"REFS\": [\"t\", \"v_z\", \"z\"], \"ROLE\": \"EOM(z)\", \"EQUATION\": \"D(z,t)=v_z\"}, {\"NAME\": \"EOM_X\", \"STATEMENT\": \"m dv_x/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_x\"], \"ROLE\": \"EOM(v_x)\", \"EQUATION\": \"m*D(v_x,t)=0\"}, {\"NAME\": \"EOM_Z\", \"STATEMENT\": \"m dv_z/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_z\"], \"ROLE\": \"EOM(v_z)\", \"EQUATION\": \"m*D(v_z,t)=0\"}], \"ASSUMPTION\": [{\"NAME\": \"point_mass\", \"PROPOSITION\": \"the body is treated as a point mass\", \"REFS\": [\"m\"]}]}, \"BIND\": {\"HEIGHT\": [\"z\"], \"MASS\": [\"m\"], \"UP_VELOCITY\": [\"v_z\"]}, \"VALUES\": {\"h_max\": {\"VALUE\": \"100\", \"UNIT\": \"m\"}}, \"ANSWERS\": {}}, {\"NAME\": \"TABLE\", \"TPK\": {\"DOF\": [{\"NAME\": \"t\", \"DIMENSION\": \"T1\"}, {\"NAME\": \"x\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"z\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"v_x\", \"DIMENSION\": \"L1 T-1\"}, {\"NAME\": \"v_z\", \"DIMENSION\": \"L1 T-1\"}], \"CONSTANT\": [{\"NAME\": \"m\", \"DIMENSION\": \"M1\"}], \"LAW\": [{\"NAME\": \"KIN_X\", \"STATEMENT\": \"dx/dt = v_x\", \"REFS\": [\"t\", \"v_x\", \"x\"], \"ROLE\": \"EOM(x)\", \"EQUATION\": \"D(x,t)=v_x\"}, {\"NAME\": \"KIN_Z\", \"STATEMENT\": \"dz/dt = v_z\", \"REFS\": [\"t\", \"v_z\", \"z\"], \"ROLE\": \"CONSTRAINT\", \"EQUATION\": \"D(z,t)=v_z\"}, {\"NAME\": \"EOM_X\", \"STATEMENT\": \"m dv_x/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_x\"], \"ROLE\": \"EOM(v_x)\", \"EQUATION\": \"m*D(v_x,t)=0\"}], \"CONSTRAINT\": [{\"NAME\": \"C_Z\", \"TARGET\": \"z\", \"ACTION\": \"FIX\", \"VALUE\": \"0\", \"UNIT\": \"m\", \"STATEMENT\": \"the puck stays on the table top, z = 0\"}, {\"NAME\": \"C_VZ\", \"TARGET\": \"v_z\", \"ACTION\": \"FIX\", \"VALUE\": \"0\", \"UNIT\": \"m s-1\", \"STATEMENT\": \"the puck has no vertical velocity\"}]}, \"BIND\": {\"HEIGHT\": [\"z\"], \"MASS\": [\"m\"], \"UP_VELOCITY\": [\"v_z\"]}, \"VALUES\": {\"h_max\": {\"VALUE\": \"1\", \"UNIT\": \"m\"}}, \"ANSWERS\": {\"FIXED:v_z\": \"YES\"}}]}",
"{\"ID\": \"MATH\", \"VERSION\": \"1.0.0\", \"TITLE\": \"The mathematical constant pi, as the CONSTANT pi_c\", \"SOURCE\": \"pi to 16 significant digits, 3.141592653589793, the nearest IEEE 754 binary64 value\", \"PREREQUISITES\": [], \"PARAMETERS\": [{\"NAME\": \"pi_c\", \"DIMENSION\": \"1\", \"SUPPLY\": \"DECLARED\", \"VALUE\": \"3.141592653589793\", \"UNIT\": \"1\", \"OVERRIDABLE\": \"NO\", \"LABEL\": \"pi, to 16 significant digits\"}], \"SUMS\": [], \"TERMS\": [], \"ASSUMPTIONS\": [], \"BOUNDARIES\": [], \"NOT_CHOSEN\": \"No mathematical constant: pi exists only if you declare it.\", \"NOT_INCLUDED\": [\"pi_c is pi rounded to 16 significant digits; no other mathematical constant is declared.\"], \"EXCLUDES\": [], \"INTERACTS_WITH\": [], \"TEST_BINDINGS\": [{\"NAME\": \"PROJECTILE_2D\", \"TPK\": {\"DOF\": [{\"NAME\": \"t\", \"DIMENSION\": \"T1\"}, {\"NAME\": \"x\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"z\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"v_x\", \"DIMENSION\": \"L1 T-1\"}, {\"NAME\": \"v_z\", \"DIMENSION\": \"L1 T-1\"}], \"CONSTANT\": [{\"NAME\": \"m\", \"DIMENSION\": \"M1\"}], \"LAW\": [{\"NAME\": \"KIN_X\", \"STATEMENT\": \"dx/dt = v_x\", \"REFS\": [\"t\", \"v_x\", \"x\"], \"ROLE\": \"EOM(x)\", \"EQUATION\": \"D(x,t)=v_x\"}, {\"NAME\": \"KIN_Z\", \"STATEMENT\": \"dz/dt = v_z\", \"REFS\": [\"t\", \"v_z\", \"z\"], \"ROLE\": \"EOM(z)\", \"EQUATION\": \"D(z,t)=v_z\"}, {\"NAME\": \"EOM_X\", \"STATEMENT\": \"m dv_x/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_x\"], \"ROLE\": \"EOM(v_x)\", \"EQUATION\": \"m*D(v_x,t)=0\"}, {\"NAME\": \"EOM_Z\", \"STATEMENT\": \"m dv_z/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_z\"], \"ROLE\": \"EOM(v_z)\", \"EQUATION\": \"m*D(v_z,t)=0\"}], \"ASSUMPTION\": [{\"NAME\": \"point_mass\", \"PROPOSITION\": \"the body is treated as a point mass\", \"REFS\": [\"m\"]}]}, \"BIND\": {}, \"VALUES\": {}, \"ANSWERS\": {}}]}"
]
},
"expected": "[\"REFUSED\",\"DRAFT: missing zone TPK\"]",
"fn": "module_expand",
"hand_checked": true,
"name": "X44 no TPK"
},
{
"args": {
"claims": [
{
"ANSWERS": {},
"BIND": {
"HEIGHT": [
"z"
],
"MASS": [
"m"
],
"UP_VELOCITY": [
"v_z"
]
},
"DIGEST": "24877ccb5c8ec300d29ed82ce6650592f35cf8899a3d878ccce9c08d4c72c025",
"ID": "GRAV-UNIFORM",
"VALUES": {
"h_max": {
"UNIT": "m",
"VALUE": "100"
}
},
"VERSION": "1.0.0"
}
],
"draft": {
"TPK": {
"ASSUMPTION": [
{
"NAME": "point_mass",
"PROPOSITION": "the body is treated as a point mass",
"REFS": [
"m"
]
}
],
"CONSTANT": [
{
"DIMENSION": "M1",
"NAME": "m"
}
],
"DOF": [
{
"DIMENSION": "T1",
"NAME": "t"
},
{
"DIMENSION": "L1",
"NAME": "x"
},
{
"DIMENSION": "L1",
"NAME": "z"
},
{
"DIMENSION": "L1 T-1",
"NAME": "v_x"
},
{
"DIMENSION": "L1 T-1",
"NAME": "v_z"
}
],
"LAW": [
{
"EQUATION": "D(x,t)=v_x",
"NAME": "KIN_X",
"REFS": [
"t",
"v_x",
"x"
],
"ROLE": "EOM(x)",
"STATEMENT": "dx/dt = v_x"
},
{
"EQUATION": "D(z,t)=v_z",
"NAME": "KIN_Z",
"REFS": [
"t",
"v_z",
"z"
],
"ROLE": "EOM(z)",
"STATEMENT": "dz/dt = v_z"
},
{
"EQUATION": "m*D(v_x,t)=0",
"NAME": "EOM_X",
"REFS": [
"m",
"t",
"v_x"
],
"ROLE": "EOM(v_x)",
"STATEMENT": "m dv_x/dt = 0"
},
{
"EQUATION": "m*D(v_z,t)=-m*g_n",
"NAME": "EOM_Z",
"REFS": [
"g_n",
"m",
"t",
"v_z"
],
"ROLE": "EOM(v_z)",
"STATEMENT": "x"
}
]
}
},
"modules": [
"{\"ID\": \"AIR-LINEAR\", \"VERSION\": \"1.0.0\", \"TITLE\": \"Air resistance at sea level, linear in the speed (Stokes drag on a sphere)\", \"SOURCE\": \"ISO 2533:1975, Standard Atmosphere, sea-level values: density 1.225 kg m-3, dynamic viscosity 1.7894e-5 Pa s\", \"PREREQUISITES\": [{\"SLOT\": \"VELOCITY\", \"KIND\": \"DOF\", \"DIMENSION\": \"L1 T-1\", \"MIN\": 1, \"MAX\": 3, \"LABEL\": \"the velocity components of the body, one per axis\"}], \"PARAMETERS\": [{\"NAME\": \"rho_air\", \"DIMENSION\": \"L-3 M1\", \"SUPPLY\": \"DECLARED\", \"VALUE\": \"1.225\", \"UNIT\": \"kg m-3\", \"OVERRIDABLE\": \"NO\", \"LABEL\": \"the density of air at sea level\"}, {\"NAME\": \"mu_air\", \"DIMENSION\": \"L-1 M1 T-1\", \"SUPPLY\": \"DECLARED\", \"VALUE\": \"1.7894e-5\", \"UNIT\": \"Pa s\", \"OVERRIDABLE\": \"NO\", \"LABEL\": \"the dynamic viscosity of air at sea level\"}, {\"NAME\": \"pi_c\", \"DIMENSION\": \"1\", \"SUPPLY\": \"DECLARED\", \"VALUE\": \"3.141592653589793\", \"UNIT\": \"1\", \"OVERRIDABLE\": \"NO\", \"LABEL\": \"pi, to 16 significant digits\"}, {\"NAME\": \"R_s\", \"DIMENSION\": \"L1\", \"SUPPLY\": \"AUTHOR\", \"LABEL\": \"the radius of the sphere\"}], \"SUMS\": [{\"NAME\": \"SPEED2\", \"OVER\": \"VELOCITY\", \"EACH\": \"VELOCITY^2\"}], \"TERMS\": [{\"TARGET\": \"VELOCITY\", \"SIGN\": \"-\", \"EXPR\": \"6*pi_c*mu_air*R_s*VELOCITY\", \"LABEL\": \"the linear (Stokes) drag\"}], \"ASSUMPTIONS\": [{\"NAME\": \"air_still\", \"PROPOSITION\": \"the air is at rest in the frame of the body's velocity\", \"REFS\": [\"VELOCITY\"]}, {\"NAME\": \"air_uniform\", \"PROPOSITION\": \"the air density is uniform over the region of motion\", \"REFS\": [\"rho_air\"]}, {\"NAME\": \"drag_sphere\", \"PROPOSITION\": \"the body is a rigid sphere of radius R_s\", \"REFS\": [\"R_s\"]}], \"BOUNDARIES\": [{\"NAME\": \"drag_linear_regime\", \"PREDICATE\": \"2 rho_air |v| R_s / mu_air < 1: the regime of the linear law\", \"CONDITION\": \"mu_air != 0 and SPEED2 >= 0 and 2*rho_air*sqrt(SPEED2)*R_s/mu_air < 1\"}], \"NOT_CHOSEN\": \"No linear (Stokes) air resistance.\", \"NOT_INCLUDED\": [\"No wind: the air is at rest.\", \"No change of air density or viscosity with altitude or temperature.\", \"No drag outside the regime of the linear law.\"], \"EXCLUDES\": [], \"INTERACTS_WITH\": [], \"TEST_BINDINGS\": [{\"NAME\": \"PROJECTILE_2D\", \"TPK\": {\"DOF\": [{\"NAME\": \"t\", \"DIMENSION\": \"T1\"}, {\"NAME\": \"x\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"z\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"v_x\", \"DIMENSION\": \"L1 T-1\"}, {\"NAME\": \"v_z\", \"DIMENSION\": \"L1 T-1\"}], \"CONSTANT\": [{\"NAME\": \"m\", \"DIMENSION\": \"M1\"}], \"LAW\": [{\"NAME\": \"KIN_X\", \"STATEMENT\": \"dx/dt = v_x\", \"REFS\": [\"t\", \"v_x\", \"x\"], \"ROLE\": \"EOM(x)\", \"EQUATION\": \"D(x,t)=v_x\"}, {\"NAME\": \"KIN_Z\", \"STATEMENT\": \"dz/dt = v_z\", \"REFS\": [\"t\", \"v_z\", \"z\"], \"ROLE\": \"EOM(z)\", \"EQUATION\": \"D(z,t)=v_z\"}, {\"NAME\": \"EOM_X\", \"STATEMENT\": \"m dv_x/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_x\"], \"ROLE\": \"EOM(v_x)\", \"EQUATION\": \"m*D(v_x,t)=0\"}, {\"NAME\": \"EOM_Z\", \"STATEMENT\": \"m dv_z/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_z\"], \"ROLE\": \"EOM(v_z)\", \"EQUATION\": \"m*D(v_z,t)=0\"}], \"ASSUMPTION\": [{\"NAME\": \"point_mass\", \"PROPOSITION\": \"the body is treated as a point mass\", \"REFS\": [\"m\"]}]}, \"BIND\": {\"VELOCITY\": [\"v_x\", \"v_z\"]}, \"VALUES\": {\"R_s\": {}}, \"ANSWERS\": {}}]}",
"{\"ID\": \"AIR-QUADRATIC\", \"VERSION\": \"1.0.0\", \"TITLE\": \"Air resistance at sea level, quadratic in the speed\", \"SOURCE\": \"ISO 2533:1975, Standard Atmosphere, sea-level values: density 1.225 kg m-3, dynamic viscosity 1.7894e-5 Pa s\", \"PREREQUISITES\": [{\"SLOT\": \"VELOCITY\", \"KIND\": \"DOF\", \"DIMENSION\": \"L1 T-1\", \"MIN\": 1, \"MAX\": 3, \"LABEL\": \"the velocity components of the body, one per axis\"}], \"PARAMETERS\": [{\"NAME\": \"rho_air\", \"DIMENSION\": \"L-3 M1\", \"SUPPLY\": \"DECLARED\", \"VALUE\": \"1.225\", \"UNIT\": \"kg m-3\", \"OVERRIDABLE\": \"NO\", \"LABEL\": \"the density of air at sea level\"}, {\"NAME\": \"mu_air\", \"DIMENSION\": \"L-1 M1 T-1\", \"SUPPLY\": \"DECLARED\", \"VALUE\": \"1.7894e-5\", \"UNIT\": \"Pa s\", \"OVERRIDABLE\": \"NO\", \"LABEL\": \"the dynamic viscosity of air at sea level\"}, {\"NAME\": \"C_d\", \"DIMENSION\": \"1\", \"SUPPLY\": \"AUTHOR\", \"LABEL\": \"the drag coefficient of the body\"}, {\"NAME\": \"A_ref\", \"DIMENSION\": \"L2\", \"SUPPLY\": \"AUTHOR\", \"LABEL\": \"the reference area of the drag coefficient\"}, {\"NAME\": \"L_ref\", \"DIMENSION\": \"L1\", \"SUPPLY\": \"AUTHOR\", \"LABEL\": \"the reference length of the Reynolds number\"}], \"SUMS\": [{\"NAME\": \"SPEED2\", \"OVER\": \"VELOCITY\", \"EACH\": \"VELOCITY^2\"}], \"TERMS\": [{\"TARGET\": \"VELOCITY\", \"SIGN\": \"-\", \"EXPR\": \"0.5*rho_air*C_d*A_ref*sqrt(SPEED2)*VELOCITY\", \"LABEL\": \"the quadratic drag\"}], \"ASSUMPTIONS\": [{\"NAME\": \"air_still\", \"PROPOSITION\": \"the air is at rest in the frame of the body's velocity\", \"REFS\": [\"VELOCITY\"]}, {\"NAME\": \"air_uniform\", \"PROPOSITION\": \"the air density is uniform over the region of motion\", \"REFS\": [\"rho_air\"]}, {\"NAME\": \"drag_cd_constant\", \"PROPOSITION\": \"the drag coefficient C_d is constant over the motion\", \"REFS\": [\"C_d\"]}, {\"NAME\": \"drag_no_lift\", \"PROPOSITION\": \"the body experiences no lift force\", \"REFS\": [\"VELOCITY\"]}, {\"NAME\": \"drag_no_magnus\", \"PROPOSITION\": \"the body experiences no Magnus force\", \"REFS\": [\"VELOCITY\"]}], \"BOUNDARIES\": [{\"NAME\": \"drag_quadratic_regime\", \"PREDICATE\": \"1e3 < rho_air |v| L_ref / mu_air < 2e5: the Reynolds window of the quadratic law\", \"CONDITION\": \"mu_air != 0 and SPEED2 >= 0 and rho_air*sqrt(SPEED2)*L_ref/mu_air > 1000 and rho_air*sqrt(SPEED2)*L_ref/mu_air < 200000\"}], \"NOT_CHOSEN\": \"No quadratic air resistance.\", \"NOT_INCLUDED\": [\"No wind: the air is at rest.\", \"No change of air density or viscosity with altitude or temperature.\", \"No lift, Magnus or added-mass force.\", \"No drag outside the Reynolds window of the quadratic law.\"], \"EXCLUDES\": [\"AIR-LINEAR\"], \"INTERACTS_WITH\": [], \"TEST_BINDINGS\": [{\"NAME\": \"PROJECTILE_2D\", \"TPK\": {\"DOF\": [{\"NAME\": \"t\", \"DIMENSION\": \"T1\"}, {\"NAME\": \"x\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"z\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"v_x\", \"DIMENSION\": \"L1 T-1\"}, {\"NAME\": \"v_z\", \"DIMENSION\": \"L1 T-1\"}], \"CONSTANT\": [{\"NAME\": \"m\", \"DIMENSION\": \"M1\"}], \"LAW\": [{\"NAME\": \"KIN_X\", \"STATEMENT\": \"dx/dt = v_x\", \"REFS\": [\"t\", \"v_x\", \"x\"], \"ROLE\": \"EOM(x)\", \"EQUATION\": \"D(x,t)=v_x\"}, {\"NAME\": \"KIN_Z\", \"STATEMENT\": \"dz/dt = v_z\", \"REFS\": [\"t\", \"v_z\", \"z\"], \"ROLE\": \"EOM(z)\", \"EQUATION\": \"D(z,t)=v_z\"}, {\"NAME\": \"EOM_X\", \"STATEMENT\": \"m dv_x/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_x\"], \"ROLE\": \"EOM(v_x)\", \"EQUATION\": \"m*D(v_x,t)=0\"}, {\"NAME\": \"EOM_Z\", \"STATEMENT\": \"m dv_z/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_z\"], \"ROLE\": \"EOM(v_z)\", \"EQUATION\": \"m*D(v_z,t)=0\"}], \"ASSUMPTION\": [{\"NAME\": \"point_mass\", \"PROPOSITION\": \"the body is treated as a point mass\", \"REFS\": [\"m\"]}]}, \"BIND\": {\"VELOCITY\": [\"v_x\", \"v_z\"]}, \"VALUES\": {\"A_ref\": {}, \"C_d\": {}, \"L_ref\": {}}, \"ANSWERS\": {}}]}",
"{\"ID\": \"GRAV-UNIFORM\", \"VERSION\": \"1.0.0\", \"TITLE\": \"Uniform gravity at the standard value g_n\", \"SOURCE\": \"g_n = 9.80665 m s-2, exact by definition: 3rd CGPM (1901), declaration on the unit of mass and on the definition of weight\", \"PREREQUISITES\": [{\"SLOT\": \"MASS\", \"KIND\": \"CONSTANT\", \"DIMENSION\": \"M1\", \"MIN\": 1, \"MAX\": 1, \"LABEL\": \"the mass of the body\"}, {\"SLOT\": \"UP_VELOCITY\", \"KIND\": \"DOF\", \"DIMENSION\": \"L1 T-1\", \"MIN\": 1, \"MAX\": 1, \"LABEL\": \"the velocity component pointing up; its equation of motion receives the weight\"}, {\"SLOT\": \"HEIGHT\", \"KIND\": \"DOF\", \"DIMENSION\": \"L1\", \"MIN\": 1, \"MAX\": 1, \"LABEL\": \"the position along the same upward axis\"}], \"PARAMETERS\": [{\"NAME\": \"g_n\", \"DIMENSION\": \"L1 T-2\", \"SUPPLY\": \"DECLARED\", \"VALUE\": \"9.80665\", \"UNIT\": \"m s-2\", \"OVERRIDABLE\": \"NO\", \"LABEL\": \"the standard acceleration of gravity\"}, {\"NAME\": \"h_max\", \"DIMENSION\": \"L1\", \"SUPPLY\": \"AUTHOR\", \"LABEL\": \"the largest height, above or below the origin, over which the field is taken as uniform\"}], \"SUMS\": [], \"TERMS\": [{\"TARGET\": \"UP_VELOCITY\", \"SIGN\": \"-\", \"EXPR\": \"MASS*g_n\", \"LABEL\": \"the weight\"}], \"ASSUMPTIONS\": [{\"NAME\": \"gravity_uniform\", \"PROPOSITION\": \"the gravitational field is uniform over the region abs({HEIGHT}) < h_max\", \"REFS\": [\"HEIGHT\", \"h_max\"]}, {\"NAME\": \"gravity_standard\", \"PROPOSITION\": \"the local gravitational acceleration equals the conventional standard value g_n\", \"REFS\": [\"g_n\"]}, {\"NAME\": \"frame_inertial\", \"PROPOSITION\": \"the frame in which {HEIGHT} is measured is treated as inertial\", \"REFS\": [\"HEIGHT\"]}], \"BOUNDARIES\": [{\"NAME\": \"gravity_region\", \"PREDICATE\": \"abs({HEIGHT}) < h_max\", \"CONDITION\": \"abs(HEIGHT) < h_max\"}], \"NOT_CHOSEN\": \"No gravity: no weight acts on any DOF.\", \"NOT_INCLUDED\": [\"No variation of gravity with height or latitude beyond what g_n contains.\", \"No Earth rotation (Coriolis or centrifugal force) beyond what g_n contains.\", \"No gravity of bodies other than the Earth.\"], \"EXCLUDES\": [], \"INTERACTS_WITH\": [{\"WITH\": \"AIR-*\", \"QUESTION_ID\": \"BUOYANCY\", \"QUESTION\": \"Does the air's buoyancy (upthrust) act on the body in the system you mean?\", \"YES_LINE\": \"Buoyancy acts (your answer): no module adds it; it acts in this kernel only where one of your own laws states it.\", \"NO_LINE\": \"No buoyancy: the air's upthrust on the body is not included.\"}], \"TEST_BINDINGS\": [{\"NAME\": \"PROJECTILE_2D\", \"TPK\": {\"DOF\": [{\"NAME\": \"t\", \"DIMENSION\": \"T1\"}, {\"NAME\": \"x\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"z\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"v_x\", \"DIMENSION\": \"L1 T-1\"}, {\"NAME\": \"v_z\", \"DIMENSION\": \"L1 T-1\"}], \"CONSTANT\": [{\"NAME\": \"m\", \"DIMENSION\": \"M1\"}], \"LAW\": [{\"NAME\": \"KIN_X\", \"STATEMENT\": \"dx/dt = v_x\", \"REFS\": [\"t\", \"v_x\", \"x\"], \"ROLE\": \"EOM(x)\", \"EQUATION\": \"D(x,t)=v_x\"}, {\"NAME\": \"KIN_Z\", \"STATEMENT\": \"dz/dt = v_z\", \"REFS\": [\"t\", \"v_z\", \"z\"], \"ROLE\": \"EOM(z)\", \"EQUATION\": \"D(z,t)=v_z\"}, {\"NAME\": \"EOM_X\", \"STATEMENT\": \"m dv_x/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_x\"], \"ROLE\": \"EOM(v_x)\", \"EQUATION\": \"m*D(v_x,t)=0\"}, {\"NAME\": \"EOM_Z\", \"STATEMENT\": \"m dv_z/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_z\"], \"ROLE\": \"EOM(v_z)\", \"EQUATION\": \"m*D(v_z,t)=0\"}], \"ASSUMPTION\": [{\"NAME\": \"point_mass\", \"PROPOSITION\": \"the body is treated as a point mass\", \"REFS\": [\"m\"]}]}, \"BIND\": {\"HEIGHT\": [\"z\"], \"MASS\": [\"m\"], \"UP_VELOCITY\": [\"v_z\"]}, \"VALUES\": {\"h_max\": {\"VALUE\": \"100\", \"UNIT\": \"m\"}}, \"ANSWERS\": {}}, {\"NAME\": \"TABLE\", \"TPK\": {\"DOF\": [{\"NAME\": \"t\", \"DIMENSION\": \"T1\"}, {\"NAME\": \"x\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"z\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"v_x\", \"DIMENSION\": \"L1 T-1\"}, {\"NAME\": \"v_z\", \"DIMENSION\": \"L1 T-1\"}], \"CONSTANT\": [{\"NAME\": \"m\", \"DIMENSION\": \"M1\"}], \"LAW\": [{\"NAME\": \"KIN_X\", \"STATEMENT\": \"dx/dt = v_x\", \"REFS\": [\"t\", \"v_x\", \"x\"], \"ROLE\": \"EOM(x)\", \"EQUATION\": \"D(x,t)=v_x\"}, {\"NAME\": \"KIN_Z\", \"STATEMENT\": \"dz/dt = v_z\", \"REFS\": [\"t\", \"v_z\", \"z\"], \"ROLE\": \"CONSTRAINT\", \"EQUATION\": \"D(z,t)=v_z\"}, {\"NAME\": \"EOM_X\", \"STATEMENT\": \"m dv_x/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_x\"], \"ROLE\": \"EOM(v_x)\", \"EQUATION\": \"m*D(v_x,t)=0\"}], \"CONSTRAINT\": [{\"NAME\": \"C_Z\", \"TARGET\": \"z\", \"ACTION\": \"FIX\", \"VALUE\": \"0\", \"UNIT\": \"m\", \"STATEMENT\": \"the puck stays on the table top, z = 0\"}, {\"NAME\": \"C_VZ\", \"TARGET\": \"v_z\", \"ACTION\": \"FIX\", \"VALUE\": \"0\", \"UNIT\": \"m s-1\", \"STATEMENT\": \"the puck has no vertical velocity\"}]}, \"BIND\": {\"HEIGHT\": [\"z\"], \"MASS\": [\"m\"], \"UP_VELOCITY\": [\"v_z\"]}, \"VALUES\": {\"h_max\": {\"VALUE\": \"1\", \"UNIT\": \"m\"}}, \"ANSWERS\": {\"FIXED:v_z\": \"YES\"}}]}",
"{\"ID\": \"MATH\", \"VERSION\": \"1.0.0\", \"TITLE\": \"The mathematical constant pi, as the CONSTANT pi_c\", \"SOURCE\": \"pi to 16 significant digits, 3.141592653589793, the nearest IEEE 754 binary64 value\", \"PREREQUISITES\": [], \"PARAMETERS\": [{\"NAME\": \"pi_c\", \"DIMENSION\": \"1\", \"SUPPLY\": \"DECLARED\", \"VALUE\": \"3.141592653589793\", \"UNIT\": \"1\", \"OVERRIDABLE\": \"NO\", \"LABEL\": \"pi, to 16 significant digits\"}], \"SUMS\": [], \"TERMS\": [], \"ASSUMPTIONS\": [], \"BOUNDARIES\": [], \"NOT_CHOSEN\": \"No mathematical constant: pi exists only if you declare it.\", \"NOT_INCLUDED\": [\"pi_c is pi rounded to 16 significant digits; no other mathematical constant is declared.\"], \"EXCLUDES\": [], \"INTERACTS_WITH\": [], \"TEST_BINDINGS\": [{\"NAME\": \"PROJECTILE_2D\", \"TPK\": {\"DOF\": [{\"NAME\": \"t\", \"DIMENSION\": \"T1\"}, {\"NAME\": \"x\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"z\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"v_x\", \"DIMENSION\": \"L1 T-1\"}, {\"NAME\": \"v_z\", \"DIMENSION\": \"L1 T-1\"}], \"CONSTANT\": [{\"NAME\": \"m\", \"DIMENSION\": \"M1\"}], \"LAW\": [{\"NAME\": \"KIN_X\", \"STATEMENT\": \"dx/dt = v_x\", \"REFS\": [\"t\", \"v_x\", \"x\"], \"ROLE\": \"EOM(x)\", \"EQUATION\": \"D(x,t)=v_x\"}, {\"NAME\": \"KIN_Z\", \"STATEMENT\": \"dz/dt = v_z\", \"REFS\": [\"t\", \"v_z\", \"z\"], \"ROLE\": \"EOM(z)\", \"EQUATION\": \"D(z,t)=v_z\"}, {\"NAME\": \"EOM_X\", \"STATEMENT\": \"m dv_x/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_x\"], \"ROLE\": \"EOM(v_x)\", \"EQUATION\": \"m*D(v_x,t)=0\"}, {\"NAME\": \"EOM_Z\", \"STATEMENT\": \"m dv_z/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_z\"], \"ROLE\": \"EOM(v_z)\", \"EQUATION\": \"m*D(v_z,t)=0\"}], \"ASSUMPTION\": [{\"NAME\": \"point_mass\", \"PROPOSITION\": \"the body is treated as a point mass\", \"REFS\": [\"m\"]}]}, \"BIND\": {}, \"VALUES\": {}, \"ANSWERS\": {}}]}"
]
},
"expected": "[\"REFUSED\",\"BASE: the TPK fails T1: LAW:EOM_Z: REFS g_n does not resolve\"]",
"fn": "module_expand",
"hand_checked": true,
"name": "X45 a base TPK failing T1"
},
{
"args": {
"claims": [
{
"ANSWERS": {},
"BIND": {
"HEIGHT": [
"z"
],
"MASS": [
"m"
],
"UP_VELOCITY": [
"v_z"
]
},
"DIGEST": "24877ccb5c8ec300d29ed82ce6650592f35cf8899a3d878ccce9c08d4c72c025",
"ID": "GRAV-UNIFORM",
"VALUES": {
"h_max": {
"UNIT": "m",
"VALUE": "100"
}
},
"VERSION": "1.0.0"
}
],
"draft": {
"TPK": {
"ASSUMPTION": [
{
"NAME": "point_mass",
"PROPOSITION": "the body is treated as a point mass",
"REFS": [
"m"
]
}
],
"CONSTANT": [
{
"DIMENSION": "M1",
"NAME": "m"
}
],
"DOF": [
{
"DIMENSION": "T1",
"NAME": "t"
},
{
"DIMENSION": "L1",
"NAME": "x"
},
{
"DIMENSION": "L1",
"NAME": "z"
},
{
"DIMENSION": "L1 T-1",
"NAME": "v_x"
},
{
"DIMENSION": "L1 T-1",
"NAME": "v_z"
}
],
"LAW": [
{
"EQUATION": "D(x,t)=v_x",
"NAME": "KIN_X",
"REFS": [
"t",
"v_x",
"x"
],
"ROLE": "EOM(x)",
"STATEMENT": "dx/dt = v_x"
},
{
"EQUATION": "D(z,t)=v_z",
"NAME": "KIN_Z",
"REFS": [
"t",
"v_z",
"z"
],
"ROLE": "EOM(z)",
"STATEMENT": "dz/dt = v_z"
},
{
"EQUATION": "m*D(v_x,t)=0",
"NAME": "EOM_X",
"REFS": [
"m",
"t",
"v_x"
],
"ROLE": "EOM(v_x)",
"STATEMENT": "m dv_x/dt = 0"
},
{
"EQUATION": "m*D(v_z,t)=0",
"NAME": "EOM_Z",
"REFS": [
"m",
"t",
"v_z"
],
"ROLE": "EOM(v_z)",
"STATEMENT": "m dv_z/dt = 0"
}
]
}
},
"modules": "{\"ID\": \"GRAV-UNIFORM\", \"VERSION\": \"1.0.0\", \"TITLE\": \"Uniform gravity at the standard value g_n\", \"SOURCE\": \"g_n = 9.80665 m s-2, exact by definition: 3rd CGPM (1901), declaration on the unit of mass and on the definition of weight\", \"PREREQUISITES\": [{\"SLOT\": \"MASS\", \"KIND\": \"CONSTANT\", \"DIMENSION\": \"M1\", \"MIN\": 1, \"MAX\": 1, \"LABEL\": \"the mass of the body\"}, {\"SLOT\": \"UP_VELOCITY\", \"KIND\": \"DOF\", \"DIMENSION\": \"L1 T-1\", \"MIN\": 1, \"MAX\": 1, \"LABEL\": \"the velocity component pointing up; its equation of motion receives the weight\"}, {\"SLOT\": \"HEIGHT\", \"KIND\": \"DOF\", \"DIMENSION\": \"L1\", \"MIN\": 1, \"MAX\": 1, \"LABEL\": \"the position along the same upward axis\"}], \"PARAMETERS\": [{\"NAME\": \"g_n\", \"DIMENSION\": \"L1 T-2\", \"SUPPLY\": \"DECLARED\", \"VALUE\": \"9.80665\", \"UNIT\": \"m s-2\", \"OVERRIDABLE\": \"NO\", \"LABEL\": \"the standard acceleration of gravity\"}, {\"NAME\": \"h_max\", \"DIMENSION\": \"L1\", \"SUPPLY\": \"AUTHOR\", \"LABEL\": \"the largest height, above or below the origin, over which the field is taken as uniform\"}], \"SUMS\": [], \"TERMS\": [{\"TARGET\": \"UP_VELOCITY\", \"SIGN\": \"-\", \"EXPR\": \"MASS*g_n\", \"LABEL\": \"the weight\"}], \"ASSUMPTIONS\": [{\"NAME\": \"gravity_uniform\", \"PROPOSITION\": \"the gravitational field is uniform over the region abs({HEIGHT}) < h_max\", \"REFS\": [\"HEIGHT\", \"h_max\"]}, {\"NAME\": \"gravity_standard\", \"PROPOSITION\": \"the local gravitational acceleration equals the conventional standard value g_n\", \"REFS\": [\"g_n\"]}, {\"NAME\": \"frame_inertial\", \"PROPOSITION\": \"the frame in which {HEIGHT} is measured is treated as inertial\", \"REFS\": [\"HEIGHT\"]}], \"BOUNDARIES\": [{\"NAME\": \"gravity_region\", \"PREDICATE\": \"abs({HEIGHT}) < h_max\", \"CONDITION\": \"abs(HEIGHT) < h_max\"}], \"NOT_CHOSEN\": \"No gravity: no weight acts on any DOF.\", \"NOT_INCLUDED\": [\"No variation of gravity with height or latitude beyond what g_n contains.\", \"No Earth rotation (Coriolis or centrifugal force) beyond what g_n contains.\", \"No gravity of bodies other than the Earth.\"], \"EXCLUDES\": [], \"INTERACTS_WITH\": [{\"WITH\": \"AIR-*\", \"QUESTION_ID\": \"BUOYANCY\", \"QUESTION\": \"Does the air's buoyancy (upthrust) act on the body in the system you mean?\", \"YES_LINE\": \"Buoyancy acts (your answer): no module adds it; 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"{\"ID\": \"GRAV-UNIFORM\", \"VERSION\": \"1.0.0\", \"TITLE\": \"Uniform gravity at the standard value g_n\", \"SOURCE\": \"g_n = 9.80665 m s-2, exact by definition: 3rd CGPM (1901), declaration on the unit of mass and on the definition of weight\", \"PREREQUISITES\": [{\"SLOT\": \"MASS\", \"KIND\": \"CONSTANT\", \"DIMENSION\": \"M1\", \"MIN\": 1, \"MAX\": 1, \"LABEL\": \"the mass of the body\"}, {\"SLOT\": \"UP_VELOCITY\", \"KIND\": \"DOF\", \"DIMENSION\": \"L1 T-1\", \"MIN\": 1, \"MAX\": 1, \"LABEL\": \"the velocity component pointing up; its equation of motion receives the weight\"}, {\"SLOT\": \"HEIGHT\", \"KIND\": \"DOF\", \"DIMENSION\": \"L1\", \"MIN\": 1, \"MAX\": 1, \"LABEL\": \"the position along the same upward axis\"}], \"PARAMETERS\": [{\"NAME\": \"g_n\", \"DIMENSION\": \"L1 T-2\", \"SUPPLY\": \"DECLARED\", \"VALUE\": \"9.80665\", \"UNIT\": \"m s-2\", \"OVERRIDABLE\": \"NO\", \"LABEL\": \"the standard acceleration of gravity\"}, {\"NAME\": \"h_max\", \"DIMENSION\": \"L1\", \"SUPPLY\": \"AUTHOR\", \"LABEL\": \"the largest height, above or below the origin, over which the field is taken as uniform\"}], \"SUMS\": [], \"TERMS\": [{\"TARGET\": \"UP_VELOCITY\", \"SIGN\": \"-\", \"EXPR\": \"MASS*g_n\", \"LABEL\": \"the weight\"}], \"ASSUMPTIONS\": [{\"NAME\": \"gravity_uniform\", \"PROPOSITION\": \"the gravitational field is uniform over the region abs({HEIGHT}) < h_max\", \"REFS\": [\"HEIGHT\", \"h_max\"]}, {\"NAME\": \"gravity_standard\", \"PROPOSITION\": \"the local gravitational acceleration equals the conventional standard value g_n\", \"REFS\": [\"g_n\"]}, {\"NAME\": \"frame_inertial\", \"PROPOSITION\": \"the frame in which {HEIGHT} is measured is treated as inertial\", \"REFS\": [\"HEIGHT\"]}], \"BOUNDARIES\": [{\"NAME\": \"gravity_region\", \"PREDICATE\": \"abs({HEIGHT}) < h_max\", \"CONDITION\": \"abs(HEIGHT) < h_max\"}], \"NOT_CHOSEN\": \"No gravity: no weight acts on any DOF.\", \"NOT_INCLUDED\": [\"No variation of gravity with height or latitude beyond what g_n contains.\", \"No Earth rotation (Coriolis or centrifugal force) beyond what g_n contains.\", \"No gravity of bodies other than the Earth.\"], \"EXCLUDES\": [], \"INTERACTS_WITH\": [{\"WITH\": \"AIR-*\", \"QUESTION_ID\": \"BUOYANCY\", \"QUESTION\": \"Does the air's buoyancy (upthrust) act on the body in the system you mean?\", \"YES_LINE\": \"Buoyancy acts (your answer): no module adds it; 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it acts in this kernel only where one of your own laws states it.\",\n \"NO_LINE\": \"No buoyancy: the air's upthrust on the body is not included.\"\n }\n ],\n \"TEST_BINDINGS\": [\n {\n \"NAME\": \"PROJECTILE_2D\",\n \"TPK\": {\n \"DOF\": [\n {\n \"NAME\": \"t\",\n \"DIMENSION\": \"T1\"\n },\n {\n \"NAME\": \"x\",\n \"DIMENSION\": \"L1\"\n },\n {\n \"NAME\": \"z\",\n \"DIMENSION\": \"L1\"\n },\n {\n \"NAME\": \"v_x\",\n \"DIMENSION\": \"L1 T-1\"\n },\n {\n \"NAME\": \"v_z\",\n \"DIMENSION\": \"L1 T-1\"\n }\n ],\n \"CONSTANT\": [\n {\n \"NAME\": \"m\",\n \"DIMENSION\": \"M1\"\n }\n ],\n \"LAW\": [\n {\n \"NAME\": \"KIN_X\",\n \"STATEMENT\": \"dx/dt = v_x\",\n \"REFS\": [\n \"t\",\n \"v_x\",\n \"x\"\n ],\n \"ROLE\": \"EOM(x)\",\n \"EQUATION\": \"D(x,t)=v_x\"\n },\n {\n \"NAME\": \"KIN_Z\",\n \"STATEMENT\": \"dz/dt = v_z\",\n \"REFS\": [\n \"t\",\n \"v_z\",\n \"z\"\n ],\n \"ROLE\": \"EOM(z)\",\n \"EQUATION\": \"D(z,t)=v_z\"\n },\n {\n \"NAME\": \"EOM_X\",\n \"STATEMENT\": \"m dv_x/dt = 0\",\n \"REFS\": [\n \"m\",\n \"t\",\n \"v_x\"\n ],\n \"ROLE\": \"EOM(v_x)\",\n \"EQUATION\": \"m*D(v_x,t)=0\"\n },\n {\n \"NAME\": \"EOM_Z\",\n \"STATEMENT\": \"m dv_z/dt = 0\",\n \"REFS\": [\n \"m\",\n \"t\",\n \"v_z\"\n ],\n \"ROLE\": \"EOM(v_z)\",\n \"EQUATION\": \"m*D(v_z,t)=0\"\n }\n ],\n \"ASSUMPTION\": [\n {\n \"NAME\": \"point_mass\",\n \"PROPOSITION\": \"the body is treated as a point mass\",\n \"REFS\": [\n \"m\"\n ]\n }\n ]\n },\n \"BIND\": {\n \"HEIGHT\": [\n \"z\"\n ],\n \"MASS\": [\n \"m\"\n ],\n \"UP_VELOCITY\": [\n \"v_z\"\n ]\n },\n \"VALUES\": {\n \"h_max\": {\n \"VALUE\": \"100\",\n \"UNIT\": \"m\"\n }\n },\n \"ANSWERS\": {}\n },\n {\n \"NAME\": \"TABLE\",\n \"TPK\": {\n \"DOF\": [\n {\n \"NAME\": \"t\",\n \"DIMENSION\": \"T1\"\n },\n {\n \"NAME\": \"x\",\n \"DIMENSION\": \"L1\"\n },\n {\n \"NAME\": \"z\",\n \"DIMENSION\": \"L1\"\n },\n {\n \"NAME\": \"v_x\",\n \"DIMENSION\": \"L1 T-1\"\n },\n {\n \"NAME\": \"v_z\",\n \"DIMENSION\": \"L1 T-1\"\n }\n ],\n \"CONSTANT\": [\n {\n \"NAME\": \"m\",\n \"DIMENSION\": \"M1\"\n }\n ],\n \"LAW\": [\n {\n \"NAME\": \"KIN_X\",\n \"STATEMENT\": \"dx/dt = v_x\",\n \"REFS\": [\n \"t\",\n \"v_x\",\n \"x\"\n ],\n \"ROLE\": \"EOM(x)\",\n \"EQUATION\": \"D(x,t)=v_x\"\n },\n {\n \"NAME\": \"KIN_Z\",\n \"STATEMENT\": \"dz/dt = v_z\",\n \"REFS\": [\n \"t\",\n \"v_z\",\n \"z\"\n ],\n \"ROLE\": \"CONSTRAINT\",\n \"EQUATION\": \"D(z,t)=v_z\"\n },\n {\n \"NAME\": \"EOM_X\",\n \"STATEMENT\": \"m dv_x/dt = 0\",\n \"REFS\": [\n \"m\",\n \"t\",\n \"v_x\"\n ],\n \"ROLE\": \"EOM(v_x)\",\n \"EQUATION\": \"m*D(v_x,t)=0\"\n }\n ],\n \"CONSTRAINT\": [\n {\n \"NAME\": \"C_Z\",\n \"TARGET\": \"z\",\n \"ACTION\": \"FIX\",\n \"VALUE\": \"0\",\n \"UNIT\": \"m\",\n \"STATEMENT\": \"the puck stays on the table top, z = 0\"\n },\n {\n \"NAME\": \"C_VZ\",\n \"TARGET\": \"v_z\",\n \"ACTION\": \"FIX\",\n \"VALUE\": \"0\",\n \"UNIT\": \"m s-1\",\n \"STATEMENT\": \"the puck has no vertical velocity\"\n }\n ]\n },\n \"BIND\": {\n \"HEIGHT\": [\n \"z\"\n ],\n \"MASS\": [\n \"m\"\n ],\n \"UP_VELOCITY\": [\n \"v_z\"\n ]\n },\n \"VALUES\": {\n \"h_max\": {\n \"VALUE\": \"1\",\n \"UNIT\": \"m\"\n }\n },\n \"ANSWERS\": {\n \"FIXED:v_z\": \"YES\"\n }\n }\n ]\n}"
]
},
"expected": "[\"REFUSED\",\"MODULES: duplicate text of GRAV-UNIFORM 1.0.0\"]",
"fn": "module_expand",
"hand_checked": true,
"name": "X48 one text twice"
},
{
"args": {
"claims": [],
"draft": {
"TPK": {
"ASSUMPTION": [
{
"NAME": "point_mass",
"PROPOSITION": "the body is treated as a point mass",
"REFS": [
"m"
]
}
],
"CONSTANT": [
{
"DIMENSION": "M1",
"NAME": "m"
}
],
"DOF": [
{
"DIMENSION": "T1",
"NAME": "t"
},
{
"DIMENSION": "L1",
"NAME": "x"
},
{
"DIMENSION": "L1",
"NAME": "z"
},
{
"DIMENSION": "L1 T-1",
"NAME": "v_x"
},
{
"DIMENSION": "L1 T-1",
"NAME": "v_z"
}
],
"LAW": [
{
"EQUATION": "D(x,t)=v_x",
"NAME": "KIN_X",
"REFS": [
"t",
"v_x",
"x"
],
"ROLE": "EOM(x)",
"STATEMENT": "dx/dt = v_x"
},
{
"EQUATION": "D(z,t)=v_z",
"NAME": "KIN_Z",
"REFS": [
"t",
"v_z",
"z"
],
"ROLE": "EOM(z)",
"STATEMENT": "dz/dt = v_z"
},
{
"EQUATION": "m*D(v_x,t)=0",
"NAME": "EOM_X",
"REFS": [
"m",
"t",
"v_x"
],
"ROLE": "EOM(v_x)",
"STATEMENT": "m dv_x/dt = 0"
},
{
"EQUATION": "m*D(v_z,t)=0",
"NAME": "EOM_Z",
"REFS": [
"m",
"t",
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],
"ROLE": "EOM(v_z)",
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]
}
},
"modules": [
"{\"ID\": \"AIR-LINEAR\", \"VERSION\": \"1.0.0\", \"TITLE\": \"Air resistance at sea level, linear in the speed (Stokes drag on a sphere)\", \"SOURCE\": \"ISO 2533:1975, Standard Atmosphere, sea-level values: density 1.225 kg m-3, dynamic viscosity 1.7894e-5 Pa s\", \"PREREQUISITES\": [{\"SLOT\": \"VELOCITY\", \"KIND\": \"DOF\", \"DIMENSION\": \"L1 T-1\", \"MIN\": 1, \"MAX\": 3, \"LABEL\": \"the velocity components of the body, one per axis\"}], \"PARAMETERS\": [{\"NAME\": \"rho_air\", \"DIMENSION\": \"L-3 M1\", \"SUPPLY\": \"DECLARED\", \"VALUE\": \"1.225\", \"UNIT\": \"kg m-3\", \"OVERRIDABLE\": \"NO\", \"LABEL\": \"the density of air at sea level\"}, {\"NAME\": \"mu_air\", \"DIMENSION\": \"L-1 M1 T-1\", \"SUPPLY\": \"DECLARED\", \"VALUE\": \"1.7894e-5\", \"UNIT\": \"Pa s\", \"OVERRIDABLE\": \"NO\", \"LABEL\": \"the dynamic viscosity of air at sea level\"}, {\"NAME\": \"pi_c\", \"DIMENSION\": \"1\", \"SUPPLY\": \"DECLARED\", \"VALUE\": \"3.141592653589793\", \"UNIT\": \"1\", \"OVERRIDABLE\": \"NO\", \"LABEL\": \"pi, to 16 significant digits\"}, {\"NAME\": \"R_s\", \"DIMENSION\": \"L1\", \"SUPPLY\": \"AUTHOR\", \"LABEL\": \"the radius of the sphere\"}], \"SUMS\": [{\"NAME\": \"SPEED2\", \"OVER\": \"VELOCITY\", \"EACH\": \"VELOCITY^2\"}], \"TERMS\": [{\"TARGET\": \"VELOCITY\", \"SIGN\": \"-\", \"EXPR\": \"6*pi_c*mu_air*R_s*VELOCITY\", \"LABEL\": \"the linear (Stokes) drag\"}], \"ASSUMPTIONS\": [{\"NAME\": \"air_still\", \"PROPOSITION\": \"the air is at rest in the frame of the body's velocity\", \"REFS\": [\"VELOCITY\"]}, {\"NAME\": \"air_uniform\", \"PROPOSITION\": \"the air density is uniform over the region of motion\", \"REFS\": [\"rho_air\"]}, {\"NAME\": \"drag_sphere\", \"PROPOSITION\": \"the body is a rigid sphere of radius R_s\", \"REFS\": [\"R_s\"]}], \"BOUNDARIES\": [{\"NAME\": \"drag_linear_regime\", \"PREDICATE\": \"2 rho_air |v| R_s / mu_air < 1: the regime of the linear law\", \"CONDITION\": \"mu_air != 0 and SPEED2 >= 0 and 2*rho_air*sqrt(SPEED2)*R_s/mu_air < 1\"}], \"NOT_CHOSEN\": \"No linear (Stokes) air resistance.\", \"NOT_INCLUDED\": [\"No wind: the air is at rest.\", \"No change of air density or viscosity with altitude or temperature.\", \"No drag outside the regime of the linear law.\"], \"EXCLUDES\": [], \"INTERACTS_WITH\": [], \"TEST_BINDINGS\": [{\"NAME\": \"PROJECTILE_2D\", \"TPK\": {\"DOF\": [{\"NAME\": \"t\", \"DIMENSION\": \"T1\"}, {\"NAME\": \"x\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"z\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"v_x\", \"DIMENSION\": \"L1 T-1\"}, {\"NAME\": \"v_z\", \"DIMENSION\": \"L1 T-1\"}], \"CONSTANT\": [{\"NAME\": \"m\", \"DIMENSION\": \"M1\"}], \"LAW\": [{\"NAME\": \"KIN_X\", \"STATEMENT\": \"dx/dt = v_x\", \"REFS\": [\"t\", \"v_x\", \"x\"], \"ROLE\": \"EOM(x)\", \"EQUATION\": \"D(x,t)=v_x\"}, {\"NAME\": \"KIN_Z\", \"STATEMENT\": \"dz/dt = v_z\", \"REFS\": [\"t\", \"v_z\", \"z\"], \"ROLE\": \"EOM(z)\", \"EQUATION\": \"D(z,t)=v_z\"}, {\"NAME\": \"EOM_X\", \"STATEMENT\": \"m dv_x/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_x\"], \"ROLE\": \"EOM(v_x)\", \"EQUATION\": \"m*D(v_x,t)=0\"}, {\"NAME\": \"EOM_Z\", \"STATEMENT\": \"m dv_z/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_z\"], \"ROLE\": \"EOM(v_z)\", \"EQUATION\": \"m*D(v_z,t)=0\"}], \"ASSUMPTION\": [{\"NAME\": \"point_mass\", \"PROPOSITION\": \"the body is treated as a point mass\", \"REFS\": [\"m\"]}]}, \"BIND\": {\"VELOCITY\": [\"v_x\", \"v_z\"]}, \"VALUES\": {\"R_s\": {}}, \"ANSWERS\": {}}]}",
"{\"ID\": \"AIR-QUADRATIC\", \"VERSION\": \"1.0.0\", \"TITLE\": \"Air resistance at sea level, quadratic in the speed\", \"SOURCE\": \"ISO 2533:1975, Standard Atmosphere, sea-level values: density 1.225 kg m-3, dynamic viscosity 1.7894e-5 Pa s\", \"PREREQUISITES\": [{\"SLOT\": \"VELOCITY\", \"KIND\": \"DOF\", \"DIMENSION\": \"L1 T-1\", \"MIN\": 1, \"MAX\": 3, \"LABEL\": \"the velocity components of the body, one per axis\"}], \"PARAMETERS\": [{\"NAME\": \"rho_air\", \"DIMENSION\": \"L-3 M1\", \"SUPPLY\": \"DECLARED\", \"VALUE\": \"1.225\", \"UNIT\": \"kg m-3\", \"OVERRIDABLE\": \"NO\", \"LABEL\": \"the density of air at sea level\"}, {\"NAME\": \"mu_air\", \"DIMENSION\": \"L-1 M1 T-1\", \"SUPPLY\": \"DECLARED\", \"VALUE\": \"1.7894e-5\", \"UNIT\": \"Pa s\", \"OVERRIDABLE\": \"NO\", \"LABEL\": \"the dynamic viscosity of air at sea level\"}, {\"NAME\": \"C_d\", \"DIMENSION\": \"1\", \"SUPPLY\": \"AUTHOR\", \"LABEL\": \"the drag coefficient of the body\"}, {\"NAME\": \"A_ref\", \"DIMENSION\": \"L2\", \"SUPPLY\": \"AUTHOR\", \"LABEL\": \"the reference area of the drag coefficient\"}, {\"NAME\": \"L_ref\", \"DIMENSION\": \"L1\", \"SUPPLY\": \"AUTHOR\", \"LABEL\": \"the reference length of the Reynolds number\"}], \"SUMS\": [{\"NAME\": \"SPEED2\", \"OVER\": \"VELOCITY\", \"EACH\": \"VELOCITY^2\"}], \"TERMS\": [{\"TARGET\": \"VELOCITY\", \"SIGN\": \"-\", \"EXPR\": \"0.5*rho_air*C_d*A_ref*sqrt(SPEED2)*VELOCITY\", \"LABEL\": \"the quadratic drag\"}], \"ASSUMPTIONS\": [{\"NAME\": \"air_still\", \"PROPOSITION\": \"the air is at rest in the frame of the body's velocity\", \"REFS\": [\"VELOCITY\"]}, {\"NAME\": \"air_uniform\", \"PROPOSITION\": \"the air density is uniform over the region of motion\", \"REFS\": [\"rho_air\"]}, {\"NAME\": \"drag_cd_constant\", \"PROPOSITION\": \"the drag coefficient C_d is constant over the motion\", \"REFS\": [\"C_d\"]}, {\"NAME\": \"drag_no_lift\", \"PROPOSITION\": \"the body experiences no lift force\", \"REFS\": [\"VELOCITY\"]}, {\"NAME\": \"drag_no_magnus\", \"PROPOSITION\": \"the body experiences no Magnus force\", \"REFS\": [\"VELOCITY\"]}], \"BOUNDARIES\": [{\"NAME\": \"drag_quadratic_regime\", \"PREDICATE\": \"1e3 < rho_air |v| L_ref / mu_air < 2e5: the Reynolds window of the quadratic law\", \"CONDITION\": \"mu_air != 0 and SPEED2 >= 0 and rho_air*sqrt(SPEED2)*L_ref/mu_air > 1000 and rho_air*sqrt(SPEED2)*L_ref/mu_air < 200000\"}], \"NOT_CHOSEN\": \"No quadratic air resistance.\", \"NOT_INCLUDED\": [\"No wind: the air is at rest.\", \"No change of air density or viscosity with altitude or temperature.\", \"No lift, Magnus or added-mass force.\", \"No drag outside the Reynolds window of the quadratic law.\"], \"EXCLUDES\": [\"AIR-LINEAR\"], \"INTERACTS_WITH\": [], \"TEST_BINDINGS\": [{\"NAME\": \"PROJECTILE_2D\", \"TPK\": {\"DOF\": [{\"NAME\": \"t\", \"DIMENSION\": \"T1\"}, {\"NAME\": \"x\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"z\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"v_x\", \"DIMENSION\": \"L1 T-1\"}, {\"NAME\": \"v_z\", \"DIMENSION\": \"L1 T-1\"}], \"CONSTANT\": [{\"NAME\": \"m\", \"DIMENSION\": \"M1\"}], \"LAW\": [{\"NAME\": \"KIN_X\", \"STATEMENT\": \"dx/dt = v_x\", \"REFS\": [\"t\", \"v_x\", \"x\"], \"ROLE\": \"EOM(x)\", \"EQUATION\": \"D(x,t)=v_x\"}, {\"NAME\": \"KIN_Z\", \"STATEMENT\": \"dz/dt = v_z\", \"REFS\": [\"t\", \"v_z\", \"z\"], \"ROLE\": \"EOM(z)\", \"EQUATION\": \"D(z,t)=v_z\"}, {\"NAME\": \"EOM_X\", \"STATEMENT\": \"m dv_x/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_x\"], \"ROLE\": \"EOM(v_x)\", \"EQUATION\": \"m*D(v_x,t)=0\"}, {\"NAME\": \"EOM_Z\", \"STATEMENT\": \"m dv_z/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_z\"], \"ROLE\": \"EOM(v_z)\", \"EQUATION\": \"m*D(v_z,t)=0\"}], \"ASSUMPTION\": [{\"NAME\": \"point_mass\", \"PROPOSITION\": \"the body is treated as a point mass\", \"REFS\": [\"m\"]}]}, \"BIND\": {\"VELOCITY\": [\"v_x\", \"v_z\"]}, \"VALUES\": {\"A_ref\": {}, \"C_d\": {}, \"L_ref\": {}}, \"ANSWERS\": {}}]}",
"{\"ID\": \"GRAV-UNIFORM\", \"VERSION\": \"1.0.0\", \"TITLE\": \"Uniform gravity at the standard value g_n\", \"SOURCE\": \"g_n = 9.80665 m s-2, exact by definition: 3rd CGPM (1901), declaration on the unit of mass and on the definition of weight\", \"PREREQUISITES\": [{\"SLOT\": \"MASS\", \"KIND\": \"CONSTANT\", \"DIMENSION\": \"M1\", \"MIN\": 1, \"MAX\": 1, \"LABEL\": \"the mass of the body\"}, {\"SLOT\": \"UP_VELOCITY\", \"KIND\": \"DOF\", \"DIMENSION\": \"L1 T-1\", \"MIN\": 1, \"MAX\": 1, \"LABEL\": \"the velocity component pointing up; its equation of motion receives the weight\"}, {\"SLOT\": \"HEIGHT\", \"KIND\": \"DOF\", \"DIMENSION\": \"L1\", \"MIN\": 1, \"MAX\": 1, \"LABEL\": \"the position along the same upward axis\"}], \"PARAMETERS\": [{\"NAME\": \"g_n\", \"DIMENSION\": \"L1 T-2\", \"SUPPLY\": \"DECLARED\", \"VALUE\": \"9.80665\", \"UNIT\": \"m s-2\", \"OVERRIDABLE\": \"NO\", \"LABEL\": \"the standard acceleration of gravity\"}, {\"NAME\": \"h_max\", \"DIMENSION\": \"L1\", \"SUPPLY\": \"AUTHOR\", \"LABEL\": \"the largest height, above or below the origin, over which the field is taken as uniform\"}], \"SUMS\": [], \"TERMS\": [{\"TARGET\": \"UP_VELOCITY\", \"SIGN\": \"-\", \"EXPR\": \"MASS*g_n\", \"LABEL\": \"the weight\"}], \"ASSUMPTIONS\": [{\"NAME\": \"gravity_uniform\", \"PROPOSITION\": \"the gravitational field is uniform over the region abs({HEIGHT}) < h_max\", \"REFS\": [\"HEIGHT\", \"h_max\"]}, {\"NAME\": \"gravity_standard\", \"PROPOSITION\": \"the local gravitational acceleration equals the conventional standard value g_n\", \"REFS\": [\"g_n\"]}, {\"NAME\": \"frame_inertial\", \"PROPOSITION\": \"the frame in which {HEIGHT} is measured is treated as inertial\", \"REFS\": [\"HEIGHT\"]}], \"BOUNDARIES\": [{\"NAME\": \"gravity_region\", \"PREDICATE\": \"abs({HEIGHT}) < h_max\", \"CONDITION\": \"abs(HEIGHT) < h_max\"}], \"NOT_CHOSEN\": \"No gravity: no weight acts on any DOF.\", \"NOT_INCLUDED\": [\"No variation of gravity with height or latitude beyond what g_n contains.\", \"No Earth rotation (Coriolis or centrifugal force) beyond what g_n contains.\", \"No gravity of bodies other than the Earth.\"], \"EXCLUDES\": [], \"INTERACTS_WITH\": [{\"WITH\": \"AIR-*\", \"QUESTION_ID\": \"BUOYANCY\", \"QUESTION\": \"Does the air's buoyancy (upthrust) act on the body in the system you mean?\", \"YES_LINE\": \"Buoyancy acts (your answer): no module adds it; it acts in this kernel only where one of your own laws states it.\", \"NO_LINE\": \"No buoyancy: the air's upthrust on the body is not included.\"}], \"TEST_BINDINGS\": [{\"NAME\": \"PROJECTILE_2D\", \"TPK\": {\"DOF\": [{\"NAME\": \"t\", \"DIMENSION\": \"T1\"}, {\"NAME\": \"x\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"z\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"v_x\", \"DIMENSION\": \"L1 T-1\"}, {\"NAME\": \"v_z\", \"DIMENSION\": \"L1 T-1\"}], \"CONSTANT\": [{\"NAME\": \"m\", \"DIMENSION\": \"M1\"}], \"LAW\": [{\"NAME\": \"KIN_X\", \"STATEMENT\": \"dx/dt = v_x\", \"REFS\": [\"t\", \"v_x\", \"x\"], \"ROLE\": \"EOM(x)\", \"EQUATION\": \"D(x,t)=v_x\"}, {\"NAME\": \"KIN_Z\", \"STATEMENT\": \"dz/dt = v_z\", \"REFS\": [\"t\", \"v_z\", \"z\"], \"ROLE\": \"EOM(z)\", \"EQUATION\": \"D(z,t)=v_z\"}, {\"NAME\": \"EOM_X\", \"STATEMENT\": \"m dv_x/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_x\"], \"ROLE\": \"EOM(v_x)\", \"EQUATION\": \"m*D(v_x,t)=0\"}, {\"NAME\": \"EOM_Z\", \"STATEMENT\": \"m dv_z/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_z\"], \"ROLE\": \"EOM(v_z)\", \"EQUATION\": \"m*D(v_z,t)=0\"}], \"ASSUMPTION\": [{\"NAME\": \"point_mass\", \"PROPOSITION\": \"the body is treated as a point mass\", \"REFS\": [\"m\"]}]}, \"BIND\": {\"HEIGHT\": [\"z\"], \"MASS\": [\"m\"], \"UP_VELOCITY\": [\"v_z\"]}, \"VALUES\": {\"h_max\": {\"VALUE\": \"100\", \"UNIT\": \"m\"}}, \"ANSWERS\": {}}, {\"NAME\": \"TABLE\", \"TPK\": {\"DOF\": [{\"NAME\": \"t\", \"DIMENSION\": \"T1\"}, {\"NAME\": \"x\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"z\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"v_x\", \"DIMENSION\": \"L1 T-1\"}, {\"NAME\": \"v_z\", \"DIMENSION\": \"L1 T-1\"}], \"CONSTANT\": [{\"NAME\": \"m\", \"DIMENSION\": \"M1\"}], \"LAW\": [{\"NAME\": \"KIN_X\", \"STATEMENT\": \"dx/dt = v_x\", \"REFS\": [\"t\", \"v_x\", \"x\"], \"ROLE\": \"EOM(x)\", \"EQUATION\": \"D(x,t)=v_x\"}, {\"NAME\": \"KIN_Z\", \"STATEMENT\": \"dz/dt = v_z\", \"REFS\": [\"t\", \"v_z\", \"z\"], \"ROLE\": \"CONSTRAINT\", \"EQUATION\": \"D(z,t)=v_z\"}, {\"NAME\": \"EOM_X\", \"STATEMENT\": \"m dv_x/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_x\"], \"ROLE\": \"EOM(v_x)\", \"EQUATION\": \"m*D(v_x,t)=0\"}], \"CONSTRAINT\": [{\"NAME\": \"C_Z\", \"TARGET\": \"z\", \"ACTION\": \"FIX\", \"VALUE\": \"0\", \"UNIT\": \"m\", \"STATEMENT\": \"the puck stays on the table top, z = 0\"}, {\"NAME\": \"C_VZ\", \"TARGET\": \"v_z\", \"ACTION\": \"FIX\", \"VALUE\": \"0\", \"UNIT\": \"m s-1\", \"STATEMENT\": \"the puck has no vertical velocity\"}]}, \"BIND\": {\"HEIGHT\": [\"z\"], \"MASS\": [\"m\"], \"UP_VELOCITY\": [\"v_z\"]}, \"VALUES\": {\"h_max\": {\"VALUE\": \"1\", \"UNIT\": \"m\"}}, \"ANSWERS\": {\"FIXED:v_z\": \"YES\"}}]}",
"{\"ID\": \"MATH\", \"VERSION\": \"1.0.0\", \"TITLE\": \"The mathematical constant pi, as the CONSTANT pi_c\", \"SOURCE\": \"pi to 16 significant digits, 3.141592653589793, the nearest IEEE 754 binary64 value\", \"PREREQUISITES\": [], \"PARAMETERS\": [{\"NAME\": \"pi_c\", \"DIMENSION\": \"1\", \"SUPPLY\": \"DECLARED\", \"VALUE\": \"3.141592653589793\", \"UNIT\": \"1\", \"OVERRIDABLE\": \"NO\", \"LABEL\": \"pi, to 16 significant digits\"}], \"SUMS\": [], \"TERMS\": [], \"ASSUMPTIONS\": [], \"BOUNDARIES\": [], \"NOT_CHOSEN\": \"No mathematical constant: pi exists only if you declare it.\", \"NOT_INCLUDED\": [\"pi_c is pi rounded to 16 significant digits; no other mathematical constant is declared.\"], \"EXCLUDES\": [], \"INTERACTS_WITH\": [], \"TEST_BINDINGS\": [{\"NAME\": \"PROJECTILE_2D\", \"TPK\": {\"DOF\": [{\"NAME\": \"t\", \"DIMENSION\": \"T1\"}, {\"NAME\": \"x\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"z\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"v_x\", \"DIMENSION\": \"L1 T-1\"}, {\"NAME\": \"v_z\", \"DIMENSION\": \"L1 T-1\"}], \"CONSTANT\": [{\"NAME\": \"m\", \"DIMENSION\": \"M1\"}], \"LAW\": [{\"NAME\": \"KIN_X\", \"STATEMENT\": \"dx/dt = v_x\", \"REFS\": [\"t\", \"v_x\", \"x\"], \"ROLE\": \"EOM(x)\", \"EQUATION\": \"D(x,t)=v_x\"}, {\"NAME\": \"KIN_Z\", \"STATEMENT\": \"dz/dt = v_z\", \"REFS\": [\"t\", \"v_z\", \"z\"], \"ROLE\": \"EOM(z)\", \"EQUATION\": \"D(z,t)=v_z\"}, {\"NAME\": \"EOM_X\", \"STATEMENT\": \"m dv_x/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_x\"], \"ROLE\": \"EOM(v_x)\", \"EQUATION\": \"m*D(v_x,t)=0\"}, {\"NAME\": \"EOM_Z\", \"STATEMENT\": \"m dv_z/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_z\"], \"ROLE\": \"EOM(v_z)\", \"EQUATION\": \"m*D(v_z,t)=0\"}], \"ASSUMPTION\": [{\"NAME\": \"point_mass\", \"PROPOSITION\": \"the body is treated as a point mass\", \"REFS\": [\"m\"]}]}, \"BIND\": {}, \"VALUES\": {}, \"ANSWERS\": {}}]}"
]
},
"computed": "digests by existing TPC-PY functions over literal data",
"expected": "[\"OK\",[\"D(TPK)\",\"ef4a82ce6243cb179ef41037a1590dd707e66eb967d0f92f5a4214d5379bb9e2\"],[\"COMPOSED\",[]],[\"EMITTED\",[]],[\"DROPPED\",[]]]",
"fn": "module_expand",
"hand_checked": false,
"name": "X49 no claim: the base unchanged (the NONE answer)"
},
{
"args": {
"claims": [
{
"ANSWERS": {},
"BIND": {
"HEIGHT": [
"z"
],
"MASS": [
"m"
],
"UP_VELOCITY": [
"z"
]
},
"DIGEST": "24877ccb5c8ec300d29ed82ce6650592f35cf8899a3d878ccce9c08d4c72c025",
"ID": "GRAV-UNIFORM",
"VALUES": {
"h_max": {
"UNIT": "m",
"VALUE": "100"
}
},
"VERSION": "1.0.0"
}
],
"draft": {
"TPK": {
"ASSUMPTION": [
{
"NAME": "point_mass",
"PROPOSITION": "the body is treated as a point mass",
"REFS": [
"m"
]
}
],
"CONSTANT": [
{
"DIMENSION": "M1",
"NAME": "m"
}
],
"DOF": [
{
"DIMENSION": "T1",
"NAME": "t"
},
{
"DIMENSION": "L1",
"NAME": "x"
},
{
"DIMENSION": "L1",
"NAME": "z"
},
{
"DIMENSION": "L1 T-1",
"NAME": "v_x"
},
{
"DIMENSION": "L1 T-1",
"NAME": "v_z"
}
],
"LAW": [
{
"EQUATION": "D(x,t)=v_x",
"NAME": "KIN_X",
"REFS": [
"t",
"v_x",
"x"
],
"ROLE": "EOM(x)",
"STATEMENT": "dx/dt = v_x"
},
{
"EQUATION": "D(z,t)=v_z",
"NAME": "KIN_Z",
"REFS": [
"t",
"v_z",
"z"
],
"ROLE": "EOM(z)",
"STATEMENT": "dz/dt = v_z"
},
{
"EQUATION": "m*D(v_x,t)=0",
"NAME": "EOM_X",
"REFS": [
"m",
"t",
"v_x"
],
"ROLE": "EOM(v_x)",
"STATEMENT": "m dv_x/dt = 0"
},
{
"EQUATION": "m*D(v_z,t)=0",
"NAME": "EOM_Z",
"REFS": [
"m",
"t",
"v_z"
],
"ROLE": "EOM(v_z)",
"STATEMENT": "m dv_z/dt = 0"
}
]
}
},
"modules": [
"{\"ID\": \"AIR-LINEAR\", \"VERSION\": \"1.0.0\", \"TITLE\": \"Air resistance at sea level, linear in the speed (Stokes drag on a sphere)\", \"SOURCE\": \"ISO 2533:1975, Standard Atmosphere, sea-level values: density 1.225 kg m-3, dynamic viscosity 1.7894e-5 Pa s\", \"PREREQUISITES\": [{\"SLOT\": \"VELOCITY\", \"KIND\": \"DOF\", \"DIMENSION\": \"L1 T-1\", \"MIN\": 1, \"MAX\": 3, \"LABEL\": \"the velocity components of the body, one per axis\"}], \"PARAMETERS\": [{\"NAME\": \"rho_air\", \"DIMENSION\": \"L-3 M1\", \"SUPPLY\": \"DECLARED\", \"VALUE\": \"1.225\", \"UNIT\": \"kg m-3\", \"OVERRIDABLE\": \"NO\", \"LABEL\": \"the density of air at sea level\"}, {\"NAME\": \"mu_air\", \"DIMENSION\": \"L-1 M1 T-1\", \"SUPPLY\": \"DECLARED\", \"VALUE\": \"1.7894e-5\", \"UNIT\": \"Pa s\", \"OVERRIDABLE\": \"NO\", \"LABEL\": \"the dynamic viscosity of air at sea level\"}, {\"NAME\": \"pi_c\", \"DIMENSION\": \"1\", \"SUPPLY\": \"DECLARED\", \"VALUE\": \"3.141592653589793\", \"UNIT\": \"1\", \"OVERRIDABLE\": \"NO\", \"LABEL\": \"pi, to 16 significant digits\"}, {\"NAME\": \"R_s\", \"DIMENSION\": \"L1\", \"SUPPLY\": \"AUTHOR\", \"LABEL\": \"the radius of the sphere\"}], \"SUMS\": [{\"NAME\": \"SPEED2\", \"OVER\": \"VELOCITY\", \"EACH\": \"VELOCITY^2\"}], \"TERMS\": [{\"TARGET\": \"VELOCITY\", \"SIGN\": \"-\", \"EXPR\": \"6*pi_c*mu_air*R_s*VELOCITY\", \"LABEL\": \"the linear (Stokes) drag\"}], \"ASSUMPTIONS\": [{\"NAME\": \"air_still\", \"PROPOSITION\": \"the air is at rest in the frame of the body's velocity\", \"REFS\": [\"VELOCITY\"]}, {\"NAME\": \"air_uniform\", \"PROPOSITION\": \"the air density is uniform over the region of motion\", \"REFS\": [\"rho_air\"]}, {\"NAME\": \"drag_sphere\", \"PROPOSITION\": \"the body is a rigid sphere of radius R_s\", \"REFS\": [\"R_s\"]}], \"BOUNDARIES\": [{\"NAME\": \"drag_linear_regime\", \"PREDICATE\": \"2 rho_air |v| R_s / mu_air < 1: the regime of the linear law\", \"CONDITION\": \"mu_air != 0 and SPEED2 >= 0 and 2*rho_air*sqrt(SPEED2)*R_s/mu_air < 1\"}], \"NOT_CHOSEN\": \"No linear (Stokes) air resistance.\", \"NOT_INCLUDED\": [\"No wind: the air is at rest.\", \"No change of air density or viscosity with altitude or temperature.\", \"No drag outside the regime of the linear law.\"], \"EXCLUDES\": [], \"INTERACTS_WITH\": [], \"TEST_BINDINGS\": [{\"NAME\": \"PROJECTILE_2D\", \"TPK\": {\"DOF\": [{\"NAME\": \"t\", \"DIMENSION\": \"T1\"}, {\"NAME\": \"x\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"z\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"v_x\", \"DIMENSION\": \"L1 T-1\"}, {\"NAME\": \"v_z\", \"DIMENSION\": \"L1 T-1\"}], \"CONSTANT\": [{\"NAME\": \"m\", \"DIMENSION\": \"M1\"}], \"LAW\": [{\"NAME\": \"KIN_X\", \"STATEMENT\": \"dx/dt = v_x\", \"REFS\": [\"t\", \"v_x\", \"x\"], \"ROLE\": \"EOM(x)\", \"EQUATION\": \"D(x,t)=v_x\"}, {\"NAME\": \"KIN_Z\", \"STATEMENT\": \"dz/dt = v_z\", \"REFS\": [\"t\", \"v_z\", \"z\"], \"ROLE\": \"EOM(z)\", \"EQUATION\": \"D(z,t)=v_z\"}, {\"NAME\": \"EOM_X\", \"STATEMENT\": \"m dv_x/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_x\"], \"ROLE\": \"EOM(v_x)\", \"EQUATION\": \"m*D(v_x,t)=0\"}, {\"NAME\": \"EOM_Z\", \"STATEMENT\": \"m dv_z/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_z\"], \"ROLE\": \"EOM(v_z)\", \"EQUATION\": \"m*D(v_z,t)=0\"}], \"ASSUMPTION\": [{\"NAME\": \"point_mass\", \"PROPOSITION\": \"the body is treated as a point mass\", \"REFS\": [\"m\"]}]}, \"BIND\": {\"VELOCITY\": [\"v_x\", \"v_z\"]}, \"VALUES\": {\"R_s\": {}}, \"ANSWERS\": {}}]}",
"{\"ID\": \"AIR-QUADRATIC\", \"VERSION\": \"1.0.0\", \"TITLE\": \"Air resistance at sea level, quadratic in the speed\", \"SOURCE\": \"ISO 2533:1975, Standard Atmosphere, sea-level values: density 1.225 kg m-3, dynamic viscosity 1.7894e-5 Pa s\", \"PREREQUISITES\": [{\"SLOT\": \"VELOCITY\", \"KIND\": \"DOF\", \"DIMENSION\": \"L1 T-1\", \"MIN\": 1, \"MAX\": 3, \"LABEL\": \"the velocity components of the body, one per axis\"}], \"PARAMETERS\": [{\"NAME\": \"rho_air\", \"DIMENSION\": \"L-3 M1\", \"SUPPLY\": \"DECLARED\", \"VALUE\": \"1.225\", \"UNIT\": \"kg m-3\", \"OVERRIDABLE\": \"NO\", \"LABEL\": \"the density of air at sea level\"}, {\"NAME\": \"mu_air\", \"DIMENSION\": \"L-1 M1 T-1\", \"SUPPLY\": \"DECLARED\", \"VALUE\": \"1.7894e-5\", \"UNIT\": \"Pa s\", \"OVERRIDABLE\": \"NO\", \"LABEL\": \"the dynamic viscosity of air at sea level\"}, {\"NAME\": \"C_d\", \"DIMENSION\": \"1\", \"SUPPLY\": \"AUTHOR\", \"LABEL\": \"the drag coefficient of the body\"}, {\"NAME\": \"A_ref\", \"DIMENSION\": \"L2\", \"SUPPLY\": \"AUTHOR\", \"LABEL\": \"the reference area of the drag coefficient\"}, {\"NAME\": \"L_ref\", \"DIMENSION\": \"L1\", \"SUPPLY\": \"AUTHOR\", \"LABEL\": \"the reference length of the Reynolds number\"}], \"SUMS\": [{\"NAME\": \"SPEED2\", \"OVER\": \"VELOCITY\", \"EACH\": \"VELOCITY^2\"}], \"TERMS\": [{\"TARGET\": \"VELOCITY\", \"SIGN\": \"-\", \"EXPR\": \"0.5*rho_air*C_d*A_ref*sqrt(SPEED2)*VELOCITY\", \"LABEL\": \"the quadratic drag\"}], \"ASSUMPTIONS\": [{\"NAME\": \"air_still\", \"PROPOSITION\": \"the air is at rest in the frame of the body's velocity\", \"REFS\": [\"VELOCITY\"]}, {\"NAME\": \"air_uniform\", \"PROPOSITION\": \"the air density is uniform over the region of motion\", \"REFS\": [\"rho_air\"]}, {\"NAME\": \"drag_cd_constant\", \"PROPOSITION\": \"the drag coefficient C_d is constant over the motion\", \"REFS\": [\"C_d\"]}, {\"NAME\": \"drag_no_lift\", \"PROPOSITION\": \"the body experiences no lift force\", \"REFS\": [\"VELOCITY\"]}, {\"NAME\": \"drag_no_magnus\", \"PROPOSITION\": \"the body experiences no Magnus force\", \"REFS\": [\"VELOCITY\"]}], \"BOUNDARIES\": [{\"NAME\": \"drag_quadratic_regime\", \"PREDICATE\": \"1e3 < rho_air |v| L_ref / mu_air < 2e5: the Reynolds window of the quadratic law\", \"CONDITION\": \"mu_air != 0 and SPEED2 >= 0 and rho_air*sqrt(SPEED2)*L_ref/mu_air > 1000 and rho_air*sqrt(SPEED2)*L_ref/mu_air < 200000\"}], \"NOT_CHOSEN\": \"No quadratic air resistance.\", \"NOT_INCLUDED\": [\"No wind: the air is at rest.\", \"No change of air density or viscosity with altitude or temperature.\", \"No lift, Magnus or added-mass force.\", \"No drag outside the Reynolds window of the quadratic law.\"], \"EXCLUDES\": [\"AIR-LINEAR\"], \"INTERACTS_WITH\": [], \"TEST_BINDINGS\": [{\"NAME\": \"PROJECTILE_2D\", \"TPK\": {\"DOF\": [{\"NAME\": \"t\", \"DIMENSION\": \"T1\"}, {\"NAME\": \"x\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"z\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"v_x\", \"DIMENSION\": \"L1 T-1\"}, {\"NAME\": \"v_z\", \"DIMENSION\": \"L1 T-1\"}], \"CONSTANT\": [{\"NAME\": \"m\", \"DIMENSION\": \"M1\"}], \"LAW\": [{\"NAME\": \"KIN_X\", \"STATEMENT\": \"dx/dt = v_x\", \"REFS\": [\"t\", \"v_x\", \"x\"], \"ROLE\": \"EOM(x)\", \"EQUATION\": \"D(x,t)=v_x\"}, {\"NAME\": \"KIN_Z\", \"STATEMENT\": \"dz/dt = v_z\", \"REFS\": [\"t\", \"v_z\", \"z\"], \"ROLE\": \"EOM(z)\", \"EQUATION\": \"D(z,t)=v_z\"}, {\"NAME\": \"EOM_X\", \"STATEMENT\": \"m dv_x/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_x\"], \"ROLE\": \"EOM(v_x)\", \"EQUATION\": \"m*D(v_x,t)=0\"}, {\"NAME\": \"EOM_Z\", \"STATEMENT\": \"m dv_z/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_z\"], \"ROLE\": \"EOM(v_z)\", \"EQUATION\": \"m*D(v_z,t)=0\"}], \"ASSUMPTION\": [{\"NAME\": \"point_mass\", \"PROPOSITION\": \"the body is treated as a point mass\", \"REFS\": [\"m\"]}]}, \"BIND\": {\"VELOCITY\": [\"v_x\", \"v_z\"]}, \"VALUES\": {\"A_ref\": {}, \"C_d\": {}, \"L_ref\": {}}, \"ANSWERS\": {}}]}",
"{\"ID\": \"GRAV-UNIFORM\", \"VERSION\": \"1.0.0\", \"TITLE\": \"Uniform gravity at the standard value g_n\", \"SOURCE\": \"g_n = 9.80665 m s-2, exact by definition: 3rd CGPM (1901), declaration on the unit of mass and on the definition of weight\", \"PREREQUISITES\": [{\"SLOT\": \"MASS\", \"KIND\": \"CONSTANT\", \"DIMENSION\": \"M1\", \"MIN\": 1, \"MAX\": 1, \"LABEL\": \"the mass of the body\"}, {\"SLOT\": \"UP_VELOCITY\", \"KIND\": \"DOF\", \"DIMENSION\": \"L1 T-1\", \"MIN\": 1, \"MAX\": 1, \"LABEL\": \"the velocity component pointing up; its equation of motion receives the weight\"}, {\"SLOT\": \"HEIGHT\", \"KIND\": \"DOF\", \"DIMENSION\": \"L1\", \"MIN\": 1, \"MAX\": 1, \"LABEL\": \"the position along the same upward axis\"}], \"PARAMETERS\": [{\"NAME\": \"g_n\", \"DIMENSION\": \"L1 T-2\", \"SUPPLY\": \"DECLARED\", \"VALUE\": \"9.80665\", \"UNIT\": \"m s-2\", \"OVERRIDABLE\": \"NO\", \"LABEL\": \"the standard acceleration of gravity\"}, {\"NAME\": \"h_max\", \"DIMENSION\": \"L1\", \"SUPPLY\": \"AUTHOR\", \"LABEL\": \"the largest height, above or below the origin, over which the field is taken as uniform\"}], \"SUMS\": [], \"TERMS\": [{\"TARGET\": \"UP_VELOCITY\", \"SIGN\": \"-\", \"EXPR\": \"MASS*g_n\", \"LABEL\": \"the weight\"}], \"ASSUMPTIONS\": [{\"NAME\": \"gravity_uniform\", \"PROPOSITION\": \"the gravitational field is uniform over the region abs({HEIGHT}) < h_max\", \"REFS\": [\"HEIGHT\", \"h_max\"]}, {\"NAME\": \"gravity_standard\", \"PROPOSITION\": \"the local gravitational acceleration equals the conventional standard value g_n\", \"REFS\": [\"g_n\"]}, {\"NAME\": \"frame_inertial\", \"PROPOSITION\": \"the frame in which {HEIGHT} is measured is treated as inertial\", \"REFS\": [\"HEIGHT\"]}], \"BOUNDARIES\": [{\"NAME\": \"gravity_region\", \"PREDICATE\": \"abs({HEIGHT}) < h_max\", \"CONDITION\": \"abs(HEIGHT) < h_max\"}], \"NOT_CHOSEN\": \"No gravity: no weight acts on any DOF.\", \"NOT_INCLUDED\": [\"No variation of gravity with height or latitude beyond what g_n contains.\", \"No Earth rotation (Coriolis or centrifugal force) beyond what g_n contains.\", \"No gravity of bodies other than the Earth.\"], \"EXCLUDES\": [], \"INTERACTS_WITH\": [{\"WITH\": \"AIR-*\", \"QUESTION_ID\": \"BUOYANCY\", \"QUESTION\": \"Does the air's buoyancy (upthrust) act on the body in the system you mean?\", \"YES_LINE\": \"Buoyancy acts (your answer): no module adds it; it acts in this kernel only where one of your own laws states it.\", \"NO_LINE\": \"No buoyancy: the air's upthrust on the body is not included.\"}], \"TEST_BINDINGS\": [{\"NAME\": \"PROJECTILE_2D\", \"TPK\": {\"DOF\": [{\"NAME\": \"t\", \"DIMENSION\": \"T1\"}, {\"NAME\": \"x\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"z\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"v_x\", \"DIMENSION\": \"L1 T-1\"}, {\"NAME\": \"v_z\", \"DIMENSION\": \"L1 T-1\"}], \"CONSTANT\": [{\"NAME\": \"m\", \"DIMENSION\": \"M1\"}], \"LAW\": [{\"NAME\": \"KIN_X\", \"STATEMENT\": \"dx/dt = v_x\", \"REFS\": [\"t\", \"v_x\", \"x\"], \"ROLE\": \"EOM(x)\", \"EQUATION\": \"D(x,t)=v_x\"}, {\"NAME\": \"KIN_Z\", \"STATEMENT\": \"dz/dt = v_z\", \"REFS\": [\"t\", \"v_z\", \"z\"], \"ROLE\": \"EOM(z)\", \"EQUATION\": \"D(z,t)=v_z\"}, {\"NAME\": \"EOM_X\", \"STATEMENT\": \"m dv_x/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_x\"], \"ROLE\": \"EOM(v_x)\", \"EQUATION\": \"m*D(v_x,t)=0\"}, {\"NAME\": \"EOM_Z\", \"STATEMENT\": \"m dv_z/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_z\"], \"ROLE\": \"EOM(v_z)\", \"EQUATION\": \"m*D(v_z,t)=0\"}], \"ASSUMPTION\": [{\"NAME\": \"point_mass\", \"PROPOSITION\": \"the body is treated as a point mass\", \"REFS\": [\"m\"]}]}, \"BIND\": {\"HEIGHT\": [\"z\"], \"MASS\": [\"m\"], \"UP_VELOCITY\": [\"v_z\"]}, \"VALUES\": {\"h_max\": {\"VALUE\": \"100\", \"UNIT\": \"m\"}}, \"ANSWERS\": {}}, {\"NAME\": \"TABLE\", \"TPK\": {\"DOF\": [{\"NAME\": \"t\", \"DIMENSION\": \"T1\"}, {\"NAME\": \"x\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"z\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"v_x\", \"DIMENSION\": \"L1 T-1\"}, {\"NAME\": \"v_z\", \"DIMENSION\": \"L1 T-1\"}], \"CONSTANT\": [{\"NAME\": \"m\", \"DIMENSION\": \"M1\"}], \"LAW\": [{\"NAME\": \"KIN_X\", \"STATEMENT\": \"dx/dt = v_x\", \"REFS\": [\"t\", \"v_x\", \"x\"], \"ROLE\": \"EOM(x)\", \"EQUATION\": \"D(x,t)=v_x\"}, {\"NAME\": \"KIN_Z\", \"STATEMENT\": \"dz/dt = v_z\", \"REFS\": [\"t\", \"v_z\", \"z\"], \"ROLE\": \"CONSTRAINT\", \"EQUATION\": \"D(z,t)=v_z\"}, {\"NAME\": \"EOM_X\", \"STATEMENT\": \"m dv_x/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_x\"], \"ROLE\": \"EOM(v_x)\", \"EQUATION\": \"m*D(v_x,t)=0\"}], \"CONSTRAINT\": [{\"NAME\": \"C_Z\", \"TARGET\": \"z\", \"ACTION\": \"FIX\", \"VALUE\": \"0\", \"UNIT\": \"m\", \"STATEMENT\": \"the puck stays on the table top, z = 0\"}, {\"NAME\": \"C_VZ\", \"TARGET\": \"v_z\", \"ACTION\": \"FIX\", \"VALUE\": \"0\", \"UNIT\": \"m s-1\", \"STATEMENT\": \"the puck has no vertical velocity\"}]}, \"BIND\": {\"HEIGHT\": [\"z\"], \"MASS\": [\"m\"], \"UP_VELOCITY\": [\"v_z\"]}, \"VALUES\": {\"h_max\": {\"VALUE\": \"1\", \"UNIT\": \"m\"}}, \"ANSWERS\": {\"FIXED:v_z\": \"YES\"}}]}",
"{\"ID\": \"MATH\", \"VERSION\": \"1.0.0\", \"TITLE\": \"The mathematical constant pi, as the CONSTANT pi_c\", \"SOURCE\": \"pi to 16 significant digits, 3.141592653589793, the nearest IEEE 754 binary64 value\", \"PREREQUISITES\": [], \"PARAMETERS\": [{\"NAME\": \"pi_c\", \"DIMENSION\": \"1\", \"SUPPLY\": \"DECLARED\", \"VALUE\": \"3.141592653589793\", \"UNIT\": \"1\", \"OVERRIDABLE\": \"NO\", \"LABEL\": \"pi, to 16 significant digits\"}], \"SUMS\": [], \"TERMS\": [], \"ASSUMPTIONS\": [], \"BOUNDARIES\": [], \"NOT_CHOSEN\": \"No mathematical constant: pi exists only if you declare it.\", \"NOT_INCLUDED\": [\"pi_c is pi rounded to 16 significant digits; no other mathematical constant is declared.\"], \"EXCLUDES\": [], \"INTERACTS_WITH\": [], \"TEST_BINDINGS\": [{\"NAME\": \"PROJECTILE_2D\", \"TPK\": {\"DOF\": [{\"NAME\": \"t\", \"DIMENSION\": \"T1\"}, {\"NAME\": \"x\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"z\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"v_x\", \"DIMENSION\": \"L1 T-1\"}, {\"NAME\": \"v_z\", \"DIMENSION\": \"L1 T-1\"}], \"CONSTANT\": [{\"NAME\": \"m\", \"DIMENSION\": \"M1\"}], \"LAW\": [{\"NAME\": \"KIN_X\", \"STATEMENT\": \"dx/dt = v_x\", \"REFS\": [\"t\", \"v_x\", \"x\"], \"ROLE\": \"EOM(x)\", \"EQUATION\": \"D(x,t)=v_x\"}, {\"NAME\": \"KIN_Z\", \"STATEMENT\": \"dz/dt = v_z\", \"REFS\": [\"t\", \"v_z\", \"z\"], \"ROLE\": \"EOM(z)\", \"EQUATION\": \"D(z,t)=v_z\"}, {\"NAME\": \"EOM_X\", \"STATEMENT\": \"m dv_x/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_x\"], \"ROLE\": \"EOM(v_x)\", \"EQUATION\": \"m*D(v_x,t)=0\"}, {\"NAME\": \"EOM_Z\", \"STATEMENT\": \"m dv_z/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_z\"], \"ROLE\": \"EOM(v_z)\", \"EQUATION\": \"m*D(v_z,t)=0\"}], \"ASSUMPTION\": [{\"NAME\": \"point_mass\", \"PROPOSITION\": \"the body is treated as a point mass\", \"REFS\": [\"m\"]}]}, \"BIND\": {}, \"VALUES\": {}, \"ANSWERS\": {}}]}"
]
},
"expected": "[\"REFUSED\",\"CLAIM GRAV-UNIFORM 1.0.0: BIND: slot UP_VELOCITY: z has dimension L1, not L1 T-1\"]",
"fn": "module_expand",
"hand_checked": true,
"name": "X50 a binding refused inside the expansion"
},
{
"args": {
"claims": [
{
"ANSWERS": {},
"BIND": {
"HEIGHT": [
"z"
],
"MASS": [
"m"
],
"UP_VELOCITY": [
"v_z"
]
},
"DIGEST": "24877ccb5c8ec300d29ed82ce6650592f35cf8899a3d878ccce9c08d4c72c025",
"ID": "GRAV-UNIFORM",
"VALUES": {
"h_max": {
"UNIT": "m",
"VALUE": "100"
}
},
"VERSION": "1.0.0"
}
],
"draft": {
"TPK": {
"ASSUMPTION": [
{
"NAME": "point_mass",
"PROPOSITION": "the body is treated as a point mass",
"REFS": [
"m"
]
}
],
"CONSTANT": [
{
"DIMENSION": "M1",
"NAME": "m"
},
{
"DIMENSION": "M1 T-1",
"NAME": "c_1"
}
],
"DOF": [
{
"DIMENSION": "T1",
"NAME": "t"
},
{
"DIMENSION": "L1",
"NAME": "x"
},
{
"DIMENSION": "L1",
"NAME": "z"
},
{
"DIMENSION": "L1 T-1",
"NAME": "v_x"
},
{
"DIMENSION": "L1 T-1",
"NAME": "v_z"
}
],
"LAW": [
{
"EQUATION": "D(x,t)=v_x",
"NAME": "KIN_X",
"REFS": [
"t",
"v_x",
"x"
],
"ROLE": "EOM(x)",
"STATEMENT": "dx/dt = v_x"
},
{
"EQUATION": "D(z,t)=v_z",
"NAME": "KIN_Z",
"REFS": [
"t",
"v_z",
"z"
],
"ROLE": "EOM(z)",
"STATEMENT": "dz/dt = v_z"
},
{
"EQUATION": "m*D(v_x,t)=0",
"NAME": "EOM_X",
"REFS": [
"m",
"t",
"v_x"
],
"ROLE": "EOM(v_x)",
"STATEMENT": "m dv_x/dt = 0"
},
{
"EQUATION": "m*D(v_z,t)=-c_1*v_z-c_1*v_z-c_1*v_z-c_1*v_z-c_1*v_z-c_1*v_z-c_1*v_z-c_1*v_z-c_1*v_z-c_1*v_z-c_1*v_z-c_1*v_z-c_1*v_z-c_1*v_z-c_1*v_z-c_1*v_z-c_1*v_z-c_1*v_z-c_1*v_z-c_1*v_z-c_1*v_z-c_1*v_z-c_1*v_z-c_1*v_z-c_1*v_z-c_1*v_z-c_1*v_z-c_1*v_z-c_1*v_z-c_1*v_z-c_1*v_z-c_1*v_z-c_1*v_z-c_1*v_z-c_1*v_z-c_1*v_z-c_1*v_z-c_1*v_z-c_1*v_z-c_1*v_z-c_1*v_z-c_1*v_z-c_1*v_z-c_1*v_z-c_1*v_z-c_1*v_z-c_1*v_z-c_1*v_z-c_1*v_z-c_1*v_z-c_1*v_z-c_1*v_z-c_1*v_z-c_1*v_z-c_1*v_z-c_1*v_z-c_1*v_z-c_1*v_z-c_1*v_z-c_1*v_z-c_1*v_z-c_1*v_z-c_1*v_z-c_1*v_z-c_1*v_z-c_1*v_z-c_1*v_z-c_1*v_z-c_1*v_z-c_1*v_z-c_1*v_z-c_1*v_z-c_1*v_z-c_1*v_z-c_1*v_z-c_1*v_z-c_1*v_z-c_1*v_z-c_1*v_z-c_1*v_z-c_1*v_z-c_1*v_z-c_1*v_z-c_1*v_z-c_1*v_z-c_1*v_z-c_1*v_z-c_1*v_z-c_1*v_z-c_1*v_z-c_1*v_z-c_1*v_z-c_1*v_z-c_1*v_z-c_1*v_z-c_1*v_z-c_1*v_z-c_1*v_z-c_1*v_z-c_1*v_z-c_1*v_z-c_1*v_z-c_1*v_z-c_1*v_z-c_1*v_z-c_1*v_z-c_1*v_z-c_1*v_z-c_1*v_z-c_1*v_z-c_1*v_z-c_1*v_z-c_1*v_z-c_1*v_z-c_1*v_z-c_1*v_z-c_1*v_z-c_1*v_z-c_1*v_z-c_1*v_z-c_1*v_z-c_1*v_z-c_1*v_z-c_1*v_z-c_1*v_z-c_1*v_z-c_1*v_z-c_1*v_z-c_1*v_z-c_1*v_z-c_1*v_z-c_1*v_z-c_1*v_z-c_1*v_z-c_1*v_z-c_1*v_z-c_1*v_z-c_1*v_z-c_1*v_z-c_1*v_z-c_1*v_z-c_1*v_z-c_1*v_z-c_1*v_z-c_1*v_z-c_1*v_z-c_1*v_z-c_1*v_z-c_1*v_z-c_1*v_z-c_1*v_z-c_1*v_z-c_1*v_z-c_1*v_z-c_1*v_z-c_1*v_z-c_1*v_z-c_1*v_z-c_1*v_z-c_1*v_z-c_1*v_z-c_1*v_z-c_1*v_z-c_1*v_z-c_1*v_z-c_1*v_z-c_1*v_z-c_1*v_z-c_1*v_z-c_1*v_z-c_1*v_z-c_1*v_z-c_1*v_z-c_1*v_z-c_1*v_z-c_1*v_z-c_1*v_z-c_1*v_z-c_1*v_z-c_1*v_z-c_1*v_z-c_1*v_z-c_1*v_z-c_1*v_z-c_1*v_z-c_1*v_z-c_1*v_z-c_1*v_z-c_1*v_z-c_1*v_z-c_1*v_z-c_1*v_z-c_1*v_z-c_1*v_z-c_1*v_z-c_1*v_z-c_1*v_z-c_1*v_z-c_1*v_z-c_1*v_z-c_1*v_z-c_1*v_z-c_1*v_z-c_1*v_z-c_1*v_z-c_1*v_z-c_1*v_z-c_1*v_z-c_1*v_z-c_1*v_z-c_1*v_z-c_1*v_z-c_1*v_z-c_1*v_z-c_1*v_z-c_1*v_z-c_1*v_z-c_1*v_z-c_1*v_z-c_1*v_z-c_1*v_z-c_1*v_z-c_1*v_z-c_1*v_z-c_1*v_z-c_1*v_z-c_1*v_z-c_1*v_z-c_1*v_z-c_1*v_z-c_1*v_z-c_1*v_z-c_1*v_z-c_1*v_z-c_1*v_z-c_1*v_z-c_1*v_z-c_1*v_z-c_1*v_z-c_1*v_z-c_1*v_z-c_1*v_z-c_1*v_z-c_1*v_z-c_1*v_z-c_1*v_z-c_1*v_z-c_1*v_z-c_1*v_z-c_1*v_z-c_1*v_z-c_1*v_z-c_1*v_z-c_1*v_z-c_1*v_z-c_1*v_z-c_1*v_z-c_1*v_z-c_1*v_z-c_1*v_z-c_1*v_z-c_1*v_z-c_1*v_z-c_1*v_z-c_1*v_z-c_1*v_z-c_1*v_z-c_1*v_z-c_1*v_z-c_1*v_z-c_1*v_z-c_1*v_z-c_1*v_z-c_1*v_z-c_1*v_z-c_1*v_z-c_1*v_z-c_1*v_z-c_1*v_z-c_1*v_z-c_1*v_z-c_1*v_z-c_1*v_z-c_1*v_z-c_1*v_z-c_1*v_z-c_1*v_z-c_1*v_z-c_1*v_z-c_1*v_z-c_1*v_z-c_1*v_z-c_1*v_z-c_1*v_z-c_1*v_z-c_1*v_z-c_1*v_z-c_1*v_z-c_1*v_z-c_1*v_z-c_1*v_z-c_1*v_z-c_1*v_z-c_1*v_z-c_1*v_z-c_1*v_z-c_1*v_z-c_1*v_z-c_1*v_z-c_1*v_z-c_1*v_z-c_1*v_z-c_1*v_z-c_1*v_z-c_1*v_z-c_1*v_z-c_1*v_z-c_1*v_z-c_1*v_z-c_1*v_z-c_1*v_z-c_1*v_z-c_1*v_z-c_1*v_z-c_1*v_z-c_1*v_z-c_1*v_z-c_1*v_z-c_1*v_z-c_1*v_z-c_1*v_z-c_1*v_z-c_1*v_z-c_1*v_z-c_1*v_z-c_1*v_z-c_1*v_z-c_1*v_z-c_1*v_z-c_1*v_z-c_1*v_z-c_1*v_z-c_1*v_z-c_1*v_z-c_1*v_z-c_1*v_z-c_1*v_z-c_1*v_z-c_1*v_z-c_1*v_z-c_1*v_z-c_1*v_z-c_1*v_z-c_1*v_z-c_1*v_z-c_1*v_z-c_1*v_z-c_1*v_z-c_1*v_z-c_1*v_z-c_1*v_z-c_1*v_z-c_1*v_z-c_1*v_z-c_1*v_z-c_1*v_z-c_1*v_z-c_1*v_z-c_1*v_z-c_1*v_z-c_1*v_z-c_1*v_z-c_1*v_z-c_1*v_z-c_1*v_z-c_1*v_z-c_1*v_z-c_1*v_z-c_1*v_z-c_1*v_z-c_1*v_z-c_1*v_z-c_1*v_z-c_1*v_z-c_1*v_z-c_1*v_z-c_1*v_z-c_1*v_z-c_1*v_z-c_1*v_z-c_1*v_z-c_1*v_z-c_1*v_z-c_1*v_z-c_1*v_z-c_1*v_z-c_1*v_z-c_1*v_z-c_1*v_z-c_1*v_z-c_1*v_z-c_1*v_z-c_1*v_z-c_1*v_z-c_1*v_z-c_1*v_z-c_1*v_z-c_1*v_z-c_1*v_z-c_1*v_z-c_1*v_z-c_1*v_z-c_1*v_z-c_1*v_z-c_1*v_z-c_1*v_z-c_1*v_z-c_1*v_z-c_1*v_z-c_1*v_z-c_1*v_z-c_1*v_z-c_1*v_z-c_1*v_z-c_1*v_z-c_1*v_z-c_1*v_z-c_1*v_z-c_1*v_z-c_1*v_z-c_1*v_z-c_1*v_z-c_1*v_z-c_1*v_z-c_1*v_z-c_1*v_z-c_1*v_z-c_1*v_z-c_1*v_z-c_1*v_z-c_1*v_z-c_1*v_z-c_1*v_z-c_1*v_z-c_1*v_z-c_1*v_z-c_1*v_z-c_1*v_z-c_1*v_z-c_1*v_z-c_1*v_z-c_1*v_z-c_1*v_z-c_1*v_z-c_1*v_z-c_1*v_z-c_1*v_z-c_1*v_z-c_1*v_z-c_1*v_z-c_1*v_z-c_1*v_z-c_1*v_z-c_1*v_z-c_1*v_z-c_1*v_z-c_1*v_z-c_1*v_z-c_1*v_z-c_1*v_z-c_1*v_z-c_1*v_z-c_1*v_z-c_1*v_z-c_1*v_z-c_1*v_z-c_1*v_z-c_1*v_z-c_1*v_z-c_1*v_z-c_1*v_z-c_1*v_z-c_1*v_z-c_1*v_z-c_1*v_z-c_1*v_z-c_1*v_z-c_1*v_z-c_1*v_z-c_1*v_z-c_1*v_z-c_1*v_z-c_1*v_z-c_1*v_z-c_1*v_z-c_1*v_z-c_1*v_z-c_1*v_z-c_1*v_z-c_1*v_z-c_1*v_z-c_1*v_z-c_1*v_z-c_1*v_z-c_1*v_z-c_1*v_z-c_1*v_z-c_1*v_z-c_1*v_z-c_1*v_z",
"NAME": "EOM_Z",
"REFS": [
"c_1",
"m",
"t",
"v_z"
],
"ROLE": "EOM(v_z)",
"STATEMENT": "a long force side"
}
]
}
},
"modules": [
"{\"ID\": \"AIR-LINEAR\", \"VERSION\": \"1.0.0\", \"TITLE\": \"Air resistance at sea level, linear in the speed (Stokes drag on a sphere)\", \"SOURCE\": \"ISO 2533:1975, Standard Atmosphere, sea-level values: density 1.225 kg m-3, dynamic viscosity 1.7894e-5 Pa s\", \"PREREQUISITES\": [{\"SLOT\": \"VELOCITY\", \"KIND\": \"DOF\", \"DIMENSION\": \"L1 T-1\", \"MIN\": 1, \"MAX\": 3, \"LABEL\": \"the velocity components of the body, one per axis\"}], \"PARAMETERS\": [{\"NAME\": \"rho_air\", \"DIMENSION\": \"L-3 M1\", \"SUPPLY\": \"DECLARED\", \"VALUE\": \"1.225\", \"UNIT\": \"kg m-3\", \"OVERRIDABLE\": \"NO\", \"LABEL\": \"the density of air at sea level\"}, {\"NAME\": \"mu_air\", \"DIMENSION\": \"L-1 M1 T-1\", \"SUPPLY\": \"DECLARED\", \"VALUE\": \"1.7894e-5\", \"UNIT\": \"Pa s\", \"OVERRIDABLE\": \"NO\", \"LABEL\": \"the dynamic viscosity of air at sea level\"}, {\"NAME\": \"pi_c\", \"DIMENSION\": \"1\", \"SUPPLY\": \"DECLARED\", \"VALUE\": \"3.141592653589793\", \"UNIT\": \"1\", \"OVERRIDABLE\": \"NO\", \"LABEL\": \"pi, to 16 significant digits\"}, {\"NAME\": \"R_s\", \"DIMENSION\": \"L1\", \"SUPPLY\": \"AUTHOR\", \"LABEL\": \"the radius of the sphere\"}], \"SUMS\": [{\"NAME\": \"SPEED2\", \"OVER\": \"VELOCITY\", \"EACH\": \"VELOCITY^2\"}], \"TERMS\": [{\"TARGET\": \"VELOCITY\", \"SIGN\": \"-\", \"EXPR\": \"6*pi_c*mu_air*R_s*VELOCITY\", \"LABEL\": \"the linear (Stokes) drag\"}], \"ASSUMPTIONS\": [{\"NAME\": \"air_still\", \"PROPOSITION\": \"the air is at rest in the frame of the body's velocity\", \"REFS\": [\"VELOCITY\"]}, {\"NAME\": \"air_uniform\", \"PROPOSITION\": \"the air density is uniform over the region of motion\", \"REFS\": [\"rho_air\"]}, {\"NAME\": \"drag_sphere\", \"PROPOSITION\": \"the body is a rigid sphere of radius R_s\", \"REFS\": [\"R_s\"]}], \"BOUNDARIES\": [{\"NAME\": \"drag_linear_regime\", \"PREDICATE\": \"2 rho_air |v| R_s / mu_air < 1: the regime of the linear law\", \"CONDITION\": \"mu_air != 0 and SPEED2 >= 0 and 2*rho_air*sqrt(SPEED2)*R_s/mu_air < 1\"}], \"NOT_CHOSEN\": \"No linear (Stokes) air resistance.\", \"NOT_INCLUDED\": [\"No wind: the air is at rest.\", \"No change of air density or viscosity with altitude or temperature.\", \"No drag outside the regime of the linear law.\"], \"EXCLUDES\": [], \"INTERACTS_WITH\": [], \"TEST_BINDINGS\": [{\"NAME\": \"PROJECTILE_2D\", \"TPK\": {\"DOF\": [{\"NAME\": \"t\", \"DIMENSION\": \"T1\"}, {\"NAME\": \"x\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"z\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"v_x\", \"DIMENSION\": \"L1 T-1\"}, {\"NAME\": \"v_z\", \"DIMENSION\": \"L1 T-1\"}], \"CONSTANT\": [{\"NAME\": \"m\", \"DIMENSION\": \"M1\"}], \"LAW\": [{\"NAME\": \"KIN_X\", \"STATEMENT\": \"dx/dt = v_x\", \"REFS\": [\"t\", \"v_x\", \"x\"], \"ROLE\": \"EOM(x)\", \"EQUATION\": \"D(x,t)=v_x\"}, {\"NAME\": \"KIN_Z\", \"STATEMENT\": \"dz/dt = v_z\", \"REFS\": [\"t\", \"v_z\", \"z\"], \"ROLE\": \"EOM(z)\", \"EQUATION\": \"D(z,t)=v_z\"}, {\"NAME\": \"EOM_X\", \"STATEMENT\": \"m dv_x/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_x\"], \"ROLE\": \"EOM(v_x)\", \"EQUATION\": \"m*D(v_x,t)=0\"}, {\"NAME\": \"EOM_Z\", \"STATEMENT\": \"m dv_z/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_z\"], \"ROLE\": \"EOM(v_z)\", \"EQUATION\": \"m*D(v_z,t)=0\"}], \"ASSUMPTION\": [{\"NAME\": \"point_mass\", \"PROPOSITION\": \"the body is treated as a point mass\", \"REFS\": [\"m\"]}]}, \"BIND\": {\"VELOCITY\": [\"v_x\", \"v_z\"]}, \"VALUES\": {\"R_s\": {}}, \"ANSWERS\": {}}]}",
"{\"ID\": \"AIR-QUADRATIC\", \"VERSION\": \"1.0.0\", \"TITLE\": \"Air resistance at sea level, quadratic in the speed\", \"SOURCE\": \"ISO 2533:1975, Standard Atmosphere, sea-level values: density 1.225 kg m-3, dynamic viscosity 1.7894e-5 Pa s\", \"PREREQUISITES\": [{\"SLOT\": \"VELOCITY\", \"KIND\": \"DOF\", \"DIMENSION\": \"L1 T-1\", \"MIN\": 1, \"MAX\": 3, \"LABEL\": \"the velocity components of the body, one per axis\"}], \"PARAMETERS\": [{\"NAME\": \"rho_air\", \"DIMENSION\": \"L-3 M1\", \"SUPPLY\": \"DECLARED\", \"VALUE\": \"1.225\", \"UNIT\": \"kg m-3\", \"OVERRIDABLE\": \"NO\", \"LABEL\": \"the density of air at sea level\"}, {\"NAME\": \"mu_air\", \"DIMENSION\": \"L-1 M1 T-1\", \"SUPPLY\": \"DECLARED\", \"VALUE\": \"1.7894e-5\", \"UNIT\": \"Pa s\", \"OVERRIDABLE\": \"NO\", \"LABEL\": \"the dynamic viscosity of air at sea level\"}, {\"NAME\": \"C_d\", \"DIMENSION\": \"1\", \"SUPPLY\": \"AUTHOR\", \"LABEL\": \"the drag coefficient of the body\"}, {\"NAME\": \"A_ref\", \"DIMENSION\": \"L2\", \"SUPPLY\": \"AUTHOR\", \"LABEL\": \"the reference area of the drag coefficient\"}, {\"NAME\": \"L_ref\", \"DIMENSION\": \"L1\", \"SUPPLY\": \"AUTHOR\", \"LABEL\": \"the reference length of the Reynolds number\"}], \"SUMS\": [{\"NAME\": \"SPEED2\", \"OVER\": \"VELOCITY\", \"EACH\": \"VELOCITY^2\"}], \"TERMS\": [{\"TARGET\": \"VELOCITY\", \"SIGN\": \"-\", \"EXPR\": \"0.5*rho_air*C_d*A_ref*sqrt(SPEED2)*VELOCITY\", \"LABEL\": \"the quadratic drag\"}], \"ASSUMPTIONS\": [{\"NAME\": \"air_still\", \"PROPOSITION\": \"the air is at rest in the frame of the body's velocity\", \"REFS\": [\"VELOCITY\"]}, {\"NAME\": \"air_uniform\", \"PROPOSITION\": \"the air density is uniform over the region of motion\", \"REFS\": [\"rho_air\"]}, {\"NAME\": \"drag_cd_constant\", \"PROPOSITION\": \"the drag coefficient C_d is constant over the motion\", \"REFS\": [\"C_d\"]}, {\"NAME\": \"drag_no_lift\", \"PROPOSITION\": \"the body experiences no lift force\", \"REFS\": [\"VELOCITY\"]}, {\"NAME\": \"drag_no_magnus\", \"PROPOSITION\": \"the body experiences no Magnus force\", \"REFS\": [\"VELOCITY\"]}], \"BOUNDARIES\": [{\"NAME\": \"drag_quadratic_regime\", \"PREDICATE\": \"1e3 < rho_air |v| L_ref / mu_air < 2e5: the Reynolds window of the quadratic law\", \"CONDITION\": \"mu_air != 0 and SPEED2 >= 0 and rho_air*sqrt(SPEED2)*L_ref/mu_air > 1000 and rho_air*sqrt(SPEED2)*L_ref/mu_air < 200000\"}], \"NOT_CHOSEN\": \"No quadratic air resistance.\", \"NOT_INCLUDED\": [\"No wind: the air is at rest.\", \"No change of air density or viscosity with altitude or temperature.\", \"No lift, Magnus or added-mass force.\", \"No drag outside the Reynolds window of the quadratic law.\"], \"EXCLUDES\": [\"AIR-LINEAR\"], \"INTERACTS_WITH\": [], \"TEST_BINDINGS\": [{\"NAME\": \"PROJECTILE_2D\", \"TPK\": {\"DOF\": [{\"NAME\": \"t\", \"DIMENSION\": \"T1\"}, {\"NAME\": \"x\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"z\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"v_x\", \"DIMENSION\": \"L1 T-1\"}, {\"NAME\": \"v_z\", \"DIMENSION\": \"L1 T-1\"}], \"CONSTANT\": [{\"NAME\": \"m\", \"DIMENSION\": \"M1\"}], \"LAW\": [{\"NAME\": \"KIN_X\", \"STATEMENT\": \"dx/dt = v_x\", \"REFS\": [\"t\", \"v_x\", \"x\"], \"ROLE\": \"EOM(x)\", \"EQUATION\": \"D(x,t)=v_x\"}, {\"NAME\": \"KIN_Z\", \"STATEMENT\": \"dz/dt = v_z\", \"REFS\": [\"t\", \"v_z\", \"z\"], \"ROLE\": \"EOM(z)\", \"EQUATION\": \"D(z,t)=v_z\"}, {\"NAME\": \"EOM_X\", \"STATEMENT\": \"m dv_x/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_x\"], \"ROLE\": \"EOM(v_x)\", \"EQUATION\": \"m*D(v_x,t)=0\"}, {\"NAME\": \"EOM_Z\", \"STATEMENT\": \"m dv_z/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_z\"], \"ROLE\": \"EOM(v_z)\", \"EQUATION\": \"m*D(v_z,t)=0\"}], \"ASSUMPTION\": [{\"NAME\": \"point_mass\", \"PROPOSITION\": \"the body is treated as a point mass\", \"REFS\": [\"m\"]}]}, \"BIND\": {\"VELOCITY\": [\"v_x\", \"v_z\"]}, \"VALUES\": {\"A_ref\": {}, \"C_d\": {}, \"L_ref\": {}}, \"ANSWERS\": {}}]}",
"{\"ID\": \"GRAV-UNIFORM\", \"VERSION\": \"1.0.0\", \"TITLE\": \"Uniform gravity at the standard value g_n\", \"SOURCE\": \"g_n = 9.80665 m s-2, exact by definition: 3rd CGPM (1901), declaration on the unit of mass and on the definition of weight\", \"PREREQUISITES\": [{\"SLOT\": \"MASS\", \"KIND\": \"CONSTANT\", \"DIMENSION\": \"M1\", \"MIN\": 1, \"MAX\": 1, \"LABEL\": \"the mass of the body\"}, {\"SLOT\": \"UP_VELOCITY\", \"KIND\": \"DOF\", \"DIMENSION\": \"L1 T-1\", \"MIN\": 1, \"MAX\": 1, \"LABEL\": \"the velocity component pointing up; its equation of motion receives the weight\"}, {\"SLOT\": \"HEIGHT\", \"KIND\": \"DOF\", \"DIMENSION\": \"L1\", \"MIN\": 1, \"MAX\": 1, \"LABEL\": \"the position along the same upward axis\"}], \"PARAMETERS\": [{\"NAME\": \"g_n\", \"DIMENSION\": \"L1 T-2\", \"SUPPLY\": \"DECLARED\", \"VALUE\": \"9.80665\", \"UNIT\": \"m s-2\", \"OVERRIDABLE\": \"NO\", \"LABEL\": \"the standard acceleration of gravity\"}, {\"NAME\": \"h_max\", \"DIMENSION\": \"L1\", \"SUPPLY\": \"AUTHOR\", \"LABEL\": \"the largest height, above or below the origin, over which the field is taken as uniform\"}], \"SUMS\": [], \"TERMS\": [{\"TARGET\": \"UP_VELOCITY\", \"SIGN\": \"-\", \"EXPR\": \"MASS*g_n\", \"LABEL\": \"the weight\"}], \"ASSUMPTIONS\": [{\"NAME\": \"gravity_uniform\", \"PROPOSITION\": \"the gravitational field is uniform over the region abs({HEIGHT}) < h_max\", \"REFS\": [\"HEIGHT\", \"h_max\"]}, {\"NAME\": \"gravity_standard\", \"PROPOSITION\": \"the local gravitational acceleration equals the conventional standard value g_n\", \"REFS\": [\"g_n\"]}, {\"NAME\": \"frame_inertial\", \"PROPOSITION\": \"the frame in which {HEIGHT} is measured is treated as inertial\", \"REFS\": [\"HEIGHT\"]}], \"BOUNDARIES\": [{\"NAME\": \"gravity_region\", \"PREDICATE\": \"abs({HEIGHT}) < h_max\", \"CONDITION\": \"abs(HEIGHT) < h_max\"}], \"NOT_CHOSEN\": \"No gravity: no weight acts on any DOF.\", \"NOT_INCLUDED\": [\"No variation of gravity with height or latitude beyond what g_n contains.\", \"No Earth rotation (Coriolis or centrifugal force) beyond what g_n contains.\", \"No gravity of bodies other than the Earth.\"], \"EXCLUDES\": [], \"INTERACTS_WITH\": [{\"WITH\": \"AIR-*\", \"QUESTION_ID\": \"BUOYANCY\", \"QUESTION\": \"Does the air's buoyancy (upthrust) act on the body in the system you mean?\", \"YES_LINE\": \"Buoyancy acts (your answer): no module adds it; it acts in this kernel only where one of your own laws states it.\", \"NO_LINE\": \"No buoyancy: the air's upthrust on the body is not included.\"}], \"TEST_BINDINGS\": [{\"NAME\": \"PROJECTILE_2D\", \"TPK\": {\"DOF\": [{\"NAME\": \"t\", \"DIMENSION\": \"T1\"}, {\"NAME\": \"x\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"z\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"v_x\", \"DIMENSION\": \"L1 T-1\"}, {\"NAME\": \"v_z\", \"DIMENSION\": \"L1 T-1\"}], \"CONSTANT\": [{\"NAME\": \"m\", \"DIMENSION\": \"M1\"}], \"LAW\": [{\"NAME\": \"KIN_X\", \"STATEMENT\": \"dx/dt = v_x\", \"REFS\": [\"t\", \"v_x\", \"x\"], \"ROLE\": \"EOM(x)\", \"EQUATION\": \"D(x,t)=v_x\"}, {\"NAME\": \"KIN_Z\", \"STATEMENT\": \"dz/dt = v_z\", \"REFS\": [\"t\", \"v_z\", \"z\"], \"ROLE\": \"EOM(z)\", \"EQUATION\": \"D(z,t)=v_z\"}, {\"NAME\": \"EOM_X\", \"STATEMENT\": \"m dv_x/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_x\"], \"ROLE\": \"EOM(v_x)\", \"EQUATION\": \"m*D(v_x,t)=0\"}, {\"NAME\": \"EOM_Z\", \"STATEMENT\": \"m dv_z/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_z\"], \"ROLE\": \"EOM(v_z)\", \"EQUATION\": \"m*D(v_z,t)=0\"}], \"ASSUMPTION\": [{\"NAME\": \"point_mass\", \"PROPOSITION\": \"the body is treated as a point mass\", \"REFS\": [\"m\"]}]}, \"BIND\": {\"HEIGHT\": [\"z\"], \"MASS\": [\"m\"], \"UP_VELOCITY\": [\"v_z\"]}, \"VALUES\": {\"h_max\": {\"VALUE\": \"100\", \"UNIT\": \"m\"}}, \"ANSWERS\": {}}, {\"NAME\": \"TABLE\", \"TPK\": {\"DOF\": [{\"NAME\": \"t\", \"DIMENSION\": \"T1\"}, {\"NAME\": \"x\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"z\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"v_x\", \"DIMENSION\": \"L1 T-1\"}, {\"NAME\": \"v_z\", \"DIMENSION\": \"L1 T-1\"}], \"CONSTANT\": [{\"NAME\": \"m\", \"DIMENSION\": \"M1\"}], \"LAW\": [{\"NAME\": \"KIN_X\", \"STATEMENT\": \"dx/dt = v_x\", \"REFS\": [\"t\", \"v_x\", \"x\"], \"ROLE\": \"EOM(x)\", \"EQUATION\": \"D(x,t)=v_x\"}, {\"NAME\": \"KIN_Z\", \"STATEMENT\": \"dz/dt = v_z\", \"REFS\": [\"t\", \"v_z\", \"z\"], \"ROLE\": \"CONSTRAINT\", \"EQUATION\": \"D(z,t)=v_z\"}, {\"NAME\": \"EOM_X\", \"STATEMENT\": \"m dv_x/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_x\"], \"ROLE\": \"EOM(v_x)\", \"EQUATION\": \"m*D(v_x,t)=0\"}], \"CONSTRAINT\": [{\"NAME\": \"C_Z\", \"TARGET\": \"z\", \"ACTION\": \"FIX\", \"VALUE\": \"0\", \"UNIT\": \"m\", \"STATEMENT\": \"the puck stays on the table top, z = 0\"}, {\"NAME\": \"C_VZ\", \"TARGET\": \"v_z\", \"ACTION\": \"FIX\", \"VALUE\": \"0\", \"UNIT\": \"m s-1\", \"STATEMENT\": \"the puck has no vertical velocity\"}]}, \"BIND\": {\"HEIGHT\": [\"z\"], \"MASS\": [\"m\"], \"UP_VELOCITY\": [\"v_z\"]}, \"VALUES\": {\"h_max\": {\"VALUE\": \"1\", \"UNIT\": \"m\"}}, \"ANSWERS\": {\"FIXED:v_z\": \"YES\"}}]}",
"{\"ID\": \"MATH\", \"VERSION\": \"1.0.0\", \"TITLE\": \"The mathematical constant pi, as the CONSTANT pi_c\", \"SOURCE\": \"pi to 16 significant digits, 3.141592653589793, the nearest IEEE 754 binary64 value\", \"PREREQUISITES\": [], \"PARAMETERS\": [{\"NAME\": \"pi_c\", \"DIMENSION\": \"1\", \"SUPPLY\": \"DECLARED\", \"VALUE\": \"3.141592653589793\", \"UNIT\": \"1\", \"OVERRIDABLE\": \"NO\", \"LABEL\": \"pi, to 16 significant digits\"}], \"SUMS\": [], \"TERMS\": [], \"ASSUMPTIONS\": [], \"BOUNDARIES\": [], \"NOT_CHOSEN\": \"No mathematical constant: pi exists only if you declare it.\", \"NOT_INCLUDED\": [\"pi_c is pi rounded to 16 significant digits; no other mathematical constant is declared.\"], \"EXCLUDES\": [], \"INTERACTS_WITH\": [], \"TEST_BINDINGS\": [{\"NAME\": \"PROJECTILE_2D\", \"TPK\": {\"DOF\": [{\"NAME\": \"t\", \"DIMENSION\": \"T1\"}, {\"NAME\": \"x\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"z\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"v_x\", \"DIMENSION\": \"L1 T-1\"}, {\"NAME\": \"v_z\", \"DIMENSION\": \"L1 T-1\"}], \"CONSTANT\": [{\"NAME\": \"m\", \"DIMENSION\": \"M1\"}], \"LAW\": [{\"NAME\": \"KIN_X\", \"STATEMENT\": \"dx/dt = v_x\", \"REFS\": [\"t\", \"v_x\", \"x\"], \"ROLE\": \"EOM(x)\", \"EQUATION\": \"D(x,t)=v_x\"}, {\"NAME\": \"KIN_Z\", \"STATEMENT\": \"dz/dt = v_z\", \"REFS\": [\"t\", \"v_z\", \"z\"], \"ROLE\": \"EOM(z)\", \"EQUATION\": \"D(z,t)=v_z\"}, {\"NAME\": \"EOM_X\", \"STATEMENT\": \"m dv_x/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_x\"], \"ROLE\": \"EOM(v_x)\", \"EQUATION\": \"m*D(v_x,t)=0\"}, {\"NAME\": \"EOM_Z\", \"STATEMENT\": \"m dv_z/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_z\"], \"ROLE\": \"EOM(v_z)\", \"EQUATION\": \"m*D(v_z,t)=0\"}], \"ASSUMPTION\": [{\"NAME\": \"point_mass\", \"PROPOSITION\": \"the body is treated as a point mass\", \"REFS\": [\"m\"]}]}, \"BIND\": {}, \"VALUES\": {}, \"ANSWERS\": {}}]}"
]
},
"expected": "[\"REFUSED\",\"EXPAND: LAW EOM_Z: the composed EQUATION is refused: the form is longer than 4096 code points\"]",
"fn": "module_expand",
"hand_checked": true,
"name": "X51 a composed EQUATION over 4096 code points (D186.1)"
},
{
"args": {
"claims": [
{
"ANSWERS": {},
"BIND": {
"PULLED": [
"v_x"
],
"PUSHED": [
"v_x"
]
},
"DIGEST": "b6b691673ac7755590314caeba64e2cb06e1357cb67cfb3b55d4cb0581317657",
"ID": "TEST-PUSH",
"VALUES": {
"F_a": {},
"F_b": {}
},
"VERSION": "1.0.0"
}
],
"draft": {
"TPK": {
"ASSUMPTION": [
{
"NAME": "point_mass",
"PROPOSITION": "the body is treated as a point mass",
"REFS": [
"m"
]
}
],
"CONSTANT": [
{
"DIMENSION": "M1",
"NAME": "m"
}
],
"DOF": [
{
"DIMENSION": "T1",
"NAME": "t"
},
{
"DIMENSION": "L1",
"NAME": "x"
},
{
"DIMENSION": "L1",
"NAME": "z"
},
{
"DIMENSION": "L1 T-1",
"NAME": "v_x"
},
{
"DIMENSION": "L1 T-1",
"NAME": "v_z"
}
],
"LAW": [
{
"EQUATION": "D(x,t)=v_x",
"NAME": "KIN_X",
"REFS": [
"t",
"v_x",
"x"
],
"ROLE": "EOM(x)",
"STATEMENT": "dx/dt = v_x"
},
{
"EQUATION": "D(z,t)=v_z",
"NAME": "KIN_Z",
"REFS": [
"t",
"v_z",
"z"
],
"ROLE": "EOM(z)",
"STATEMENT": "dz/dt = v_z"
},
{
"EQUATION": "m*D(v_x,t)=0",
"NAME": "EOM_X",
"REFS": [
"m",
"t",
"v_x"
],
"ROLE": "EOM(v_x)",
"STATEMENT": "m dv_x/dt = 0"
},
{
"EQUATION": "m*D(v_z,t)=0",
"NAME": "EOM_Z",
"REFS": [
"m",
"t",
"v_z"
],
"ROLE": "EOM(v_z)",
"STATEMENT": "m dv_z/dt = 0"
}
]
}
},
"modules": [
"{\"ID\": \"TEST-PUSH\", \"VERSION\": \"1.0.0\", \"TITLE\": \"Test: a push and a pull\", \"SOURCE\": \"synthetic fixture\", \"PREREQUISITES\": [{\"SLOT\": \"PUSHED\", \"KIND\": \"DOF\", \"DIMENSION\": \"L1 T-1\", \"MIN\": 1, \"MAX\": 1, \"LABEL\": \"the velocity that receives the push\"}, {\"SLOT\": \"PULLED\", \"KIND\": \"DOF\", \"DIMENSION\": \"L1 T-1\", \"MIN\": 1, \"MAX\": 1, \"LABEL\": \"the velocity that receives the pull\"}], \"PARAMETERS\": [{\"NAME\": \"F_a\", \"DIMENSION\": \"L1 M1 T-2\", \"SUPPLY\": \"AUTHOR\", \"LABEL\": \"the first applied force\"}, {\"NAME\": \"F_b\", \"DIMENSION\": \"L1 M1 T-2\", \"SUPPLY\": \"AUTHOR\", \"LABEL\": \"the second applied force\"}], \"SUMS\": [], \"TERMS\": [{\"TARGET\": \"PUSHED\", \"SIGN\": \"+\", \"EXPR\": \"F_a+F_b\", \"LABEL\": \"the push\"}, {\"TARGET\": \"PULLED\", \"SIGN\": \"-\", \"EXPR\": \"F_a+F_b\", \"LABEL\": \"the pull\"}], \"ASSUMPTIONS\": [], \"BOUNDARIES\": [], \"NOT_CHOSEN\": \"No push or pull.\", \"NOT_INCLUDED\": [], \"EXCLUDES\": [], \"INTERACTS_WITH\": [], \"TEST_BINDINGS\": [{\"NAME\": \"PROJECTILE_2D\", \"TPK\": {\"DOF\": [{\"NAME\": \"t\", \"DIMENSION\": \"T1\"}, {\"NAME\": \"x\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"z\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"v_x\", \"DIMENSION\": \"L1 T-1\"}, {\"NAME\": \"v_z\", \"DIMENSION\": \"L1 T-1\"}], \"CONSTANT\": [{\"NAME\": \"m\", \"DIMENSION\": \"M1\"}], \"LAW\": [{\"NAME\": \"KIN_X\", \"STATEMENT\": \"dx/dt = v_x\", \"REFS\": [\"t\", \"v_x\", \"x\"], \"ROLE\": \"EOM(x)\", \"EQUATION\": \"D(x,t)=v_x\"}, {\"NAME\": \"KIN_Z\", \"STATEMENT\": \"dz/dt = v_z\", \"REFS\": [\"t\", \"v_z\", \"z\"], \"ROLE\": \"EOM(z)\", \"EQUATION\": \"D(z,t)=v_z\"}, {\"NAME\": \"EOM_X\", \"STATEMENT\": \"m dv_x/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_x\"], \"ROLE\": \"EOM(v_x)\", \"EQUATION\": \"m*D(v_x,t)=0\"}, {\"NAME\": \"EOM_Z\", \"STATEMENT\": \"m dv_z/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_z\"], \"ROLE\": \"EOM(v_z)\", \"EQUATION\": \"m*D(v_z,t)=0\"}], \"ASSUMPTION\": [{\"NAME\": \"point_mass\", \"PROPOSITION\": \"the body is treated as a point mass\", \"REFS\": [\"m\"]}]}, \"BIND\": {\"PULLED\": [\"v_z\"], \"PUSHED\": [\"v_x\"]}, \"VALUES\": {\"F_a\": {}, \"F_b\": {}}, \"ANSWERS\": {}}]}"
]
},
"expected": "[\"REFUSED\",\"CLAIM TEST-PUSH 1.0.0: BIND: v_x is bound to two slots, PUSHED and PULLED\"]",
"fn": "module_expand",
"hand_checked": true,
"name": "X52 one name bound to two slots, inside the expansion"
},
{
"args": {
"claims": [
{
"ANSWERS": {},
"BIND": {
"HEIGHT": [
"z"
],
"MASS": [
"m"
],
"UP_VELOCITY": [
"v_z"
]
},
"DIGEST": "24877ccb5c8ec300d29ed82ce6650592f35cf8899a3d878ccce9c08d4c72c025",
"ID": "GRAV-UNIFORM",
"VALUES": {
"h_max": {
"UNIT": "m",
"VALUE": "100"
}
},
"VERSION": "1.0.0"
}
],
"draft": {
"TMS": {
"PARAMETERS": {}
},
"TPK": {
"ASSUMPTION": [
{
"NAME": "point_mass",
"PROPOSITION": "the body is treated as a point mass",
"REFS": [
"m"
]
}
],
"CONSTANT": [
{
"DIMENSION": "M1",
"NAME": "m"
}
],
"DOF": [
{
"DIMENSION": "T1",
"NAME": "t"
},
{
"DIMENSION": "L1",
"NAME": "x"
},
{
"DIMENSION": "L1",
"NAME": "z"
},
{
"DIMENSION": "L1 T-1",
"NAME": "v_x"
},
{
"DIMENSION": "L1 T-1",
"NAME": "v_z"
}
],
"LAW": [
{
"EQUATION": "D(x,t)=v_x",
"NAME": "KIN_X",
"REFS": [
"t",
"v_x",
"x"
],
"ROLE": "EOM(x)",
"STATEMENT": "dx/dt = v_x"
},
{
"EQUATION": "D(z,t)=v_z",
"NAME": "KIN_Z",
"REFS": [
"t",
"v_z",
"z"
],
"ROLE": "EOM(z)",
"STATEMENT": "dz/dt = v_z"
},
{
"EQUATION": "m*D(v_x,t)=0",
"NAME": "EOM_X",
"REFS": [
"m",
"t",
"v_x"
],
"ROLE": "EOM(v_x)",
"STATEMENT": "m dv_x/dt = 0"
},
{
"EQUATION": "m*D(v_z,t)=0",
"NAME": "EOM_Z",
"REFS": [
"m",
"t",
"v_z"
],
"ROLE": "EOM(v_z)",
"STATEMENT": "m dv_z/dt = 0"
}
]
},
"TrM": {
"HEADER": {}
}
},
"modules": [
"{\"ID\": \"AIR-LINEAR\", \"VERSION\": \"1.0.0\", \"TITLE\": \"Air resistance at sea level, linear in the speed (Stokes drag on a sphere)\", \"SOURCE\": \"ISO 2533:1975, Standard Atmosphere, sea-level values: density 1.225 kg m-3, dynamic viscosity 1.7894e-5 Pa s\", \"PREREQUISITES\": [{\"SLOT\": \"VELOCITY\", \"KIND\": \"DOF\", \"DIMENSION\": \"L1 T-1\", \"MIN\": 1, \"MAX\": 3, \"LABEL\": \"the velocity components of the body, one per axis\"}], \"PARAMETERS\": [{\"NAME\": \"rho_air\", \"DIMENSION\": \"L-3 M1\", \"SUPPLY\": \"DECLARED\", \"VALUE\": \"1.225\", \"UNIT\": \"kg m-3\", \"OVERRIDABLE\": \"NO\", \"LABEL\": \"the density of air at sea level\"}, {\"NAME\": \"mu_air\", \"DIMENSION\": \"L-1 M1 T-1\", \"SUPPLY\": \"DECLARED\", \"VALUE\": \"1.7894e-5\", \"UNIT\": \"Pa s\", \"OVERRIDABLE\": \"NO\", \"LABEL\": \"the dynamic viscosity of air at sea level\"}, {\"NAME\": \"pi_c\", \"DIMENSION\": \"1\", \"SUPPLY\": \"DECLARED\", \"VALUE\": \"3.141592653589793\", \"UNIT\": \"1\", \"OVERRIDABLE\": \"NO\", \"LABEL\": \"pi, to 16 significant digits\"}, {\"NAME\": \"R_s\", \"DIMENSION\": \"L1\", \"SUPPLY\": \"AUTHOR\", \"LABEL\": \"the radius of the sphere\"}], \"SUMS\": [{\"NAME\": \"SPEED2\", \"OVER\": \"VELOCITY\", \"EACH\": \"VELOCITY^2\"}], \"TERMS\": [{\"TARGET\": \"VELOCITY\", \"SIGN\": \"-\", \"EXPR\": \"6*pi_c*mu_air*R_s*VELOCITY\", \"LABEL\": \"the linear (Stokes) drag\"}], \"ASSUMPTIONS\": [{\"NAME\": \"air_still\", \"PROPOSITION\": \"the air is at rest in the frame of the body's velocity\", \"REFS\": [\"VELOCITY\"]}, {\"NAME\": \"air_uniform\", \"PROPOSITION\": \"the air density is uniform over the region of motion\", \"REFS\": [\"rho_air\"]}, {\"NAME\": \"drag_sphere\", \"PROPOSITION\": \"the body is a rigid sphere of radius R_s\", \"REFS\": [\"R_s\"]}], \"BOUNDARIES\": [{\"NAME\": \"drag_linear_regime\", \"PREDICATE\": \"2 rho_air |v| R_s / mu_air < 1: the regime of the linear law\", \"CONDITION\": \"mu_air != 0 and SPEED2 >= 0 and 2*rho_air*sqrt(SPEED2)*R_s/mu_air < 1\"}], \"NOT_CHOSEN\": \"No linear (Stokes) air resistance.\", \"NOT_INCLUDED\": [\"No wind: the air is at rest.\", \"No change of air density or viscosity with altitude or temperature.\", \"No drag outside the regime of the linear law.\"], \"EXCLUDES\": [], \"INTERACTS_WITH\": [], \"TEST_BINDINGS\": [{\"NAME\": \"PROJECTILE_2D\", \"TPK\": {\"DOF\": [{\"NAME\": \"t\", \"DIMENSION\": \"T1\"}, {\"NAME\": \"x\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"z\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"v_x\", \"DIMENSION\": \"L1 T-1\"}, {\"NAME\": \"v_z\", \"DIMENSION\": \"L1 T-1\"}], \"CONSTANT\": [{\"NAME\": \"m\", \"DIMENSION\": \"M1\"}], \"LAW\": [{\"NAME\": \"KIN_X\", \"STATEMENT\": \"dx/dt = v_x\", \"REFS\": [\"t\", \"v_x\", \"x\"], \"ROLE\": \"EOM(x)\", \"EQUATION\": \"D(x,t)=v_x\"}, {\"NAME\": \"KIN_Z\", \"STATEMENT\": \"dz/dt = v_z\", \"REFS\": [\"t\", \"v_z\", \"z\"], \"ROLE\": \"EOM(z)\", \"EQUATION\": \"D(z,t)=v_z\"}, {\"NAME\": \"EOM_X\", \"STATEMENT\": \"m dv_x/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_x\"], \"ROLE\": \"EOM(v_x)\", \"EQUATION\": \"m*D(v_x,t)=0\"}, {\"NAME\": \"EOM_Z\", \"STATEMENT\": \"m dv_z/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_z\"], \"ROLE\": \"EOM(v_z)\", \"EQUATION\": \"m*D(v_z,t)=0\"}], \"ASSUMPTION\": [{\"NAME\": \"point_mass\", \"PROPOSITION\": \"the body is treated as a point mass\", \"REFS\": [\"m\"]}]}, \"BIND\": {\"VELOCITY\": [\"v_x\", \"v_z\"]}, \"VALUES\": {\"R_s\": {}}, \"ANSWERS\": {}}]}",
"{\"ID\": \"AIR-QUADRATIC\", \"VERSION\": \"1.0.0\", \"TITLE\": \"Air resistance at sea level, quadratic in the speed\", \"SOURCE\": \"ISO 2533:1975, Standard Atmosphere, sea-level values: density 1.225 kg m-3, dynamic viscosity 1.7894e-5 Pa s\", \"PREREQUISITES\": [{\"SLOT\": \"VELOCITY\", \"KIND\": \"DOF\", \"DIMENSION\": \"L1 T-1\", \"MIN\": 1, \"MAX\": 3, \"LABEL\": \"the velocity components of the body, one per axis\"}], \"PARAMETERS\": [{\"NAME\": \"rho_air\", \"DIMENSION\": \"L-3 M1\", \"SUPPLY\": \"DECLARED\", \"VALUE\": \"1.225\", \"UNIT\": \"kg m-3\", \"OVERRIDABLE\": \"NO\", \"LABEL\": \"the density of air at sea level\"}, {\"NAME\": \"mu_air\", \"DIMENSION\": \"L-1 M1 T-1\", \"SUPPLY\": \"DECLARED\", \"VALUE\": \"1.7894e-5\", \"UNIT\": \"Pa s\", \"OVERRIDABLE\": \"NO\", \"LABEL\": \"the dynamic viscosity of air at sea level\"}, {\"NAME\": \"C_d\", \"DIMENSION\": \"1\", \"SUPPLY\": \"AUTHOR\", \"LABEL\": \"the drag coefficient of the body\"}, {\"NAME\": \"A_ref\", \"DIMENSION\": \"L2\", \"SUPPLY\": \"AUTHOR\", \"LABEL\": \"the reference area of the drag coefficient\"}, {\"NAME\": \"L_ref\", \"DIMENSION\": \"L1\", \"SUPPLY\": \"AUTHOR\", \"LABEL\": \"the reference length of the Reynolds number\"}], \"SUMS\": [{\"NAME\": \"SPEED2\", \"OVER\": \"VELOCITY\", \"EACH\": \"VELOCITY^2\"}], \"TERMS\": [{\"TARGET\": \"VELOCITY\", \"SIGN\": \"-\", \"EXPR\": \"0.5*rho_air*C_d*A_ref*sqrt(SPEED2)*VELOCITY\", \"LABEL\": \"the quadratic drag\"}], \"ASSUMPTIONS\": [{\"NAME\": \"air_still\", \"PROPOSITION\": \"the air is at rest in the frame of the body's velocity\", \"REFS\": [\"VELOCITY\"]}, {\"NAME\": \"air_uniform\", \"PROPOSITION\": \"the air density is uniform over the region of motion\", \"REFS\": [\"rho_air\"]}, {\"NAME\": \"drag_cd_constant\", \"PROPOSITION\": \"the drag coefficient C_d is constant over the motion\", \"REFS\": [\"C_d\"]}, {\"NAME\": \"drag_no_lift\", \"PROPOSITION\": \"the body experiences no lift force\", \"REFS\": [\"VELOCITY\"]}, {\"NAME\": \"drag_no_magnus\", \"PROPOSITION\": \"the body experiences no Magnus force\", \"REFS\": [\"VELOCITY\"]}], \"BOUNDARIES\": [{\"NAME\": \"drag_quadratic_regime\", \"PREDICATE\": \"1e3 < rho_air |v| L_ref / mu_air < 2e5: the Reynolds window of the quadratic law\", \"CONDITION\": \"mu_air != 0 and SPEED2 >= 0 and rho_air*sqrt(SPEED2)*L_ref/mu_air > 1000 and rho_air*sqrt(SPEED2)*L_ref/mu_air < 200000\"}], \"NOT_CHOSEN\": \"No quadratic air resistance.\", \"NOT_INCLUDED\": [\"No wind: the air is at rest.\", \"No change of air density or viscosity with altitude or temperature.\", \"No lift, Magnus or added-mass force.\", \"No drag outside the Reynolds window of the quadratic law.\"], \"EXCLUDES\": [\"AIR-LINEAR\"], \"INTERACTS_WITH\": [], \"TEST_BINDINGS\": [{\"NAME\": \"PROJECTILE_2D\", \"TPK\": {\"DOF\": [{\"NAME\": \"t\", \"DIMENSION\": \"T1\"}, {\"NAME\": \"x\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"z\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"v_x\", \"DIMENSION\": \"L1 T-1\"}, {\"NAME\": \"v_z\", \"DIMENSION\": \"L1 T-1\"}], \"CONSTANT\": [{\"NAME\": \"m\", \"DIMENSION\": \"M1\"}], \"LAW\": [{\"NAME\": \"KIN_X\", \"STATEMENT\": \"dx/dt = v_x\", \"REFS\": [\"t\", \"v_x\", \"x\"], \"ROLE\": \"EOM(x)\", \"EQUATION\": \"D(x,t)=v_x\"}, {\"NAME\": \"KIN_Z\", \"STATEMENT\": \"dz/dt = v_z\", \"REFS\": [\"t\", \"v_z\", \"z\"], \"ROLE\": \"EOM(z)\", \"EQUATION\": \"D(z,t)=v_z\"}, {\"NAME\": \"EOM_X\", \"STATEMENT\": \"m dv_x/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_x\"], \"ROLE\": \"EOM(v_x)\", \"EQUATION\": \"m*D(v_x,t)=0\"}, {\"NAME\": \"EOM_Z\", \"STATEMENT\": \"m dv_z/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_z\"], \"ROLE\": \"EOM(v_z)\", \"EQUATION\": \"m*D(v_z,t)=0\"}], \"ASSUMPTION\": [{\"NAME\": \"point_mass\", \"PROPOSITION\": \"the body is treated as a point mass\", \"REFS\": [\"m\"]}]}, \"BIND\": {\"VELOCITY\": [\"v_x\", \"v_z\"]}, \"VALUES\": {\"A_ref\": {}, \"C_d\": {}, \"L_ref\": {}}, \"ANSWERS\": {}}]}",
"{\"ID\": \"GRAV-UNIFORM\", \"VERSION\": \"1.0.0\", \"TITLE\": \"Uniform gravity at the standard value g_n\", \"SOURCE\": \"g_n = 9.80665 m s-2, exact by definition: 3rd CGPM (1901), declaration on the unit of mass and on the definition of weight\", \"PREREQUISITES\": [{\"SLOT\": \"MASS\", \"KIND\": \"CONSTANT\", \"DIMENSION\": \"M1\", \"MIN\": 1, \"MAX\": 1, \"LABEL\": \"the mass of the body\"}, {\"SLOT\": \"UP_VELOCITY\", \"KIND\": \"DOF\", \"DIMENSION\": \"L1 T-1\", \"MIN\": 1, \"MAX\": 1, \"LABEL\": \"the velocity component pointing up; its equation of motion receives the weight\"}, {\"SLOT\": \"HEIGHT\", \"KIND\": \"DOF\", \"DIMENSION\": \"L1\", \"MIN\": 1, \"MAX\": 1, \"LABEL\": \"the position along the same upward axis\"}], \"PARAMETERS\": [{\"NAME\": \"g_n\", \"DIMENSION\": \"L1 T-2\", \"SUPPLY\": \"DECLARED\", \"VALUE\": \"9.80665\", \"UNIT\": \"m s-2\", \"OVERRIDABLE\": \"NO\", \"LABEL\": \"the standard acceleration of gravity\"}, {\"NAME\": \"h_max\", \"DIMENSION\": \"L1\", \"SUPPLY\": \"AUTHOR\", \"LABEL\": \"the largest height, above or below the origin, over which the field is taken as uniform\"}], \"SUMS\": [], \"TERMS\": [{\"TARGET\": \"UP_VELOCITY\", \"SIGN\": \"-\", \"EXPR\": \"MASS*g_n\", \"LABEL\": \"the weight\"}], \"ASSUMPTIONS\": [{\"NAME\": \"gravity_uniform\", \"PROPOSITION\": \"the gravitational field is uniform over the region abs({HEIGHT}) < h_max\", \"REFS\": [\"HEIGHT\", \"h_max\"]}, {\"NAME\": \"gravity_standard\", \"PROPOSITION\": \"the local gravitational acceleration equals the conventional standard value g_n\", \"REFS\": [\"g_n\"]}, {\"NAME\": \"frame_inertial\", \"PROPOSITION\": \"the frame in which {HEIGHT} is measured is treated as inertial\", \"REFS\": [\"HEIGHT\"]}], \"BOUNDARIES\": [{\"NAME\": \"gravity_region\", \"PREDICATE\": \"abs({HEIGHT}) < h_max\", \"CONDITION\": \"abs(HEIGHT) < h_max\"}], \"NOT_CHOSEN\": \"No gravity: no weight acts on any DOF.\", \"NOT_INCLUDED\": [\"No variation of gravity with height or latitude beyond what g_n contains.\", \"No Earth rotation (Coriolis or centrifugal force) beyond what g_n contains.\", \"No gravity of bodies other than the Earth.\"], \"EXCLUDES\": [], \"INTERACTS_WITH\": [{\"WITH\": \"AIR-*\", \"QUESTION_ID\": \"BUOYANCY\", \"QUESTION\": \"Does the air's buoyancy (upthrust) act on the body in the system you mean?\", \"YES_LINE\": \"Buoyancy acts (your answer): no module adds it; it acts in this kernel only where one of your own laws states it.\", \"NO_LINE\": \"No buoyancy: the air's upthrust on the body is not included.\"}], \"TEST_BINDINGS\": [{\"NAME\": \"PROJECTILE_2D\", \"TPK\": {\"DOF\": [{\"NAME\": \"t\", \"DIMENSION\": \"T1\"}, {\"NAME\": \"x\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"z\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"v_x\", \"DIMENSION\": \"L1 T-1\"}, {\"NAME\": \"v_z\", \"DIMENSION\": \"L1 T-1\"}], \"CONSTANT\": [{\"NAME\": \"m\", \"DIMENSION\": \"M1\"}], \"LAW\": [{\"NAME\": \"KIN_X\", \"STATEMENT\": \"dx/dt = v_x\", \"REFS\": [\"t\", \"v_x\", \"x\"], \"ROLE\": \"EOM(x)\", \"EQUATION\": \"D(x,t)=v_x\"}, {\"NAME\": \"KIN_Z\", \"STATEMENT\": \"dz/dt = v_z\", \"REFS\": [\"t\", \"v_z\", \"z\"], \"ROLE\": \"EOM(z)\", \"EQUATION\": \"D(z,t)=v_z\"}, {\"NAME\": \"EOM_X\", \"STATEMENT\": \"m dv_x/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_x\"], \"ROLE\": \"EOM(v_x)\", \"EQUATION\": \"m*D(v_x,t)=0\"}, {\"NAME\": \"EOM_Z\", \"STATEMENT\": \"m dv_z/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_z\"], \"ROLE\": \"EOM(v_z)\", \"EQUATION\": \"m*D(v_z,t)=0\"}], \"ASSUMPTION\": [{\"NAME\": \"point_mass\", \"PROPOSITION\": \"the body is treated as a point mass\", \"REFS\": [\"m\"]}]}, \"BIND\": {\"HEIGHT\": [\"z\"], \"MASS\": [\"m\"], \"UP_VELOCITY\": [\"v_z\"]}, \"VALUES\": {\"h_max\": {\"VALUE\": \"100\", \"UNIT\": \"m\"}}, \"ANSWERS\": {}}, {\"NAME\": \"TABLE\", \"TPK\": {\"DOF\": [{\"NAME\": \"t\", \"DIMENSION\": \"T1\"}, {\"NAME\": \"x\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"z\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"v_x\", \"DIMENSION\": \"L1 T-1\"}, {\"NAME\": \"v_z\", \"DIMENSION\": \"L1 T-1\"}], \"CONSTANT\": [{\"NAME\": \"m\", \"DIMENSION\": \"M1\"}], \"LAW\": [{\"NAME\": \"KIN_X\", \"STATEMENT\": \"dx/dt = v_x\", \"REFS\": [\"t\", \"v_x\", \"x\"], \"ROLE\": \"EOM(x)\", \"EQUATION\": \"D(x,t)=v_x\"}, {\"NAME\": \"KIN_Z\", \"STATEMENT\": \"dz/dt = v_z\", \"REFS\": [\"t\", \"v_z\", \"z\"], \"ROLE\": \"CONSTRAINT\", \"EQUATION\": \"D(z,t)=v_z\"}, {\"NAME\": \"EOM_X\", \"STATEMENT\": \"m dv_x/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_x\"], \"ROLE\": \"EOM(v_x)\", \"EQUATION\": \"m*D(v_x,t)=0\"}], \"CONSTRAINT\": [{\"NAME\": \"C_Z\", \"TARGET\": \"z\", \"ACTION\": \"FIX\", \"VALUE\": \"0\", \"UNIT\": \"m\", \"STATEMENT\": \"the puck stays on the table top, z = 0\"}, {\"NAME\": \"C_VZ\", \"TARGET\": \"v_z\", \"ACTION\": \"FIX\", \"VALUE\": \"0\", \"UNIT\": \"m s-1\", \"STATEMENT\": \"the puck has no vertical velocity\"}]}, \"BIND\": {\"HEIGHT\": [\"z\"], \"MASS\": [\"m\"], \"UP_VELOCITY\": [\"v_z\"]}, \"VALUES\": {\"h_max\": {\"VALUE\": \"1\", \"UNIT\": \"m\"}}, \"ANSWERS\": {\"FIXED:v_z\": \"YES\"}}]}",
"{\"ID\": \"MATH\", \"VERSION\": \"1.0.0\", \"TITLE\": \"The mathematical constant pi, as the CONSTANT pi_c\", \"SOURCE\": \"pi to 16 significant digits, 3.141592653589793, the nearest IEEE 754 binary64 value\", \"PREREQUISITES\": [], \"PARAMETERS\": [{\"NAME\": \"pi_c\", \"DIMENSION\": \"1\", \"SUPPLY\": \"DECLARED\", \"VALUE\": \"3.141592653589793\", \"UNIT\": \"1\", \"OVERRIDABLE\": \"NO\", \"LABEL\": \"pi, to 16 significant digits\"}], \"SUMS\": [], \"TERMS\": [], \"ASSUMPTIONS\": [], \"BOUNDARIES\": [], \"NOT_CHOSEN\": \"No mathematical constant: pi exists only if you declare it.\", \"NOT_INCLUDED\": [\"pi_c is pi rounded to 16 significant digits; no other mathematical constant is declared.\"], \"EXCLUDES\": [], \"INTERACTS_WITH\": [], \"TEST_BINDINGS\": [{\"NAME\": \"PROJECTILE_2D\", \"TPK\": {\"DOF\": [{\"NAME\": \"t\", \"DIMENSION\": \"T1\"}, {\"NAME\": \"x\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"z\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"v_x\", \"DIMENSION\": \"L1 T-1\"}, {\"NAME\": \"v_z\", \"DIMENSION\": \"L1 T-1\"}], \"CONSTANT\": [{\"NAME\": \"m\", \"DIMENSION\": \"M1\"}], \"LAW\": [{\"NAME\": \"KIN_X\", \"STATEMENT\": \"dx/dt = v_x\", \"REFS\": [\"t\", \"v_x\", \"x\"], \"ROLE\": \"EOM(x)\", \"EQUATION\": \"D(x,t)=v_x\"}, {\"NAME\": \"KIN_Z\", \"STATEMENT\": \"dz/dt = v_z\", \"REFS\": [\"t\", \"v_z\", \"z\"], \"ROLE\": \"EOM(z)\", \"EQUATION\": \"D(z,t)=v_z\"}, {\"NAME\": \"EOM_X\", \"STATEMENT\": \"m dv_x/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_x\"], \"ROLE\": \"EOM(v_x)\", \"EQUATION\": \"m*D(v_x,t)=0\"}, {\"NAME\": \"EOM_Z\", \"STATEMENT\": \"m dv_z/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_z\"], \"ROLE\": \"EOM(v_z)\", \"EQUATION\": \"m*D(v_z,t)=0\"}], \"ASSUMPTION\": [{\"NAME\": \"point_mass\", \"PROPOSITION\": \"the body is treated as a point mass\", \"REFS\": [\"m\"]}]}, \"BIND\": {}, \"VALUES\": {}, \"ANSWERS\": {}}]}"
]
},
"computed": "digests by existing TPC-PY functions over literal data",
"expected": "[\"OK\",[\"D(TPK)\",\"229430000c54914b08e179f1e62169eb90b4f41ae3c779845f6ce8184bd46f57\"],[\"COMPOSED\",[[\"EOM_Z\",\"m*D(v_z,t)=-m*g_n\"]]],[\"EMITTED\",[[\"CONSTANT\",\"g_n\",[\"GRAV-UNIFORM 1.0.0\"]],[\"CONSTANT\",\"h_max\",[\"GRAV-UNIFORM 1.0.0\"]],[\"ASSUMPTION\",\"gravity_uniform\",[\"GRAV-UNIFORM 1.0.0\"]],[\"ASSUMPTION\",\"gravity_standard\",[\"GRAV-UNIFORM 1.0.0\"]],[\"ASSUMPTION\",\"frame_inertial\",[\"GRAV-UNIFORM 1.0.0\"]],[\"BOUNDARY\",\"gravity_region\",[\"GRAV-UNIFORM 1.0.0\"]]]],[\"DROPPED\",[]]]",
"fn": "module_expand",
"hand_checked": false,
"name": "X53 TrM and TMS in the draft: the expansion as X01 (the RENDER shows D(TPK) only)"
},
{
"args": {
"claims": [
{
"ANSWERS": {
"FIXED:v_z": "YES"
},
"BIND": {
"PULLED": [
"v_z"
],
"PUSHED": [
"v_x"
]
},
"DIGEST": "b6b691673ac7755590314caeba64e2cb06e1357cb67cfb3b55d4cb0581317657",
"ID": "TEST-PUSH",
"VALUES": {
"F_a": {},
"F_b": {}
},
"VERSION": "1.0.0"
},
{
"ANSWERS": {
"FIXED:v_z": "YES"
},
"BIND": {
"HEIGHT": [
"z"
],
"MASS": [
"m"
],
"UP_VELOCITY": [
"v_z"
]
},
"DIGEST": "24877ccb5c8ec300d29ed82ce6650592f35cf8899a3d878ccce9c08d4c72c025",
"ID": "GRAV-UNIFORM",
"VALUES": {
"h_max": {
"UNIT": "m",
"VALUE": "1"
}
},
"VERSION": "1.0.0"
}
],
"draft": {
"TPK": {
"CONSTANT": [
{
"DIMENSION": "M1",
"NAME": "m"
}
],
"CONSTRAINT": [
{
"ACTION": "FIX",
"NAME": "C_Z",
"STATEMENT": "the puck stays on the table top, z = 0",
"TARGET": "z",
"UNIT": "m",
"VALUE": "0"
},
{
"ACTION": "FIX",
"NAME": "C_VZ",
"STATEMENT": "the puck has no vertical velocity",
"TARGET": "v_z",
"UNIT": "m s-1",
"VALUE": "0"
}
],
"DOF": [
{
"DIMENSION": "T1",
"NAME": "t"
},
{
"DIMENSION": "L1",
"NAME": "x"
},
{
"DIMENSION": "L1",
"NAME": "z"
},
{
"DIMENSION": "L1 T-1",
"NAME": "v_x"
},
{
"DIMENSION": "L1 T-1",
"NAME": "v_z"
}
],
"LAW": [
{
"EQUATION": "D(x,t)=v_x",
"NAME": "KIN_X",
"REFS": [
"t",
"v_x",
"x"
],
"ROLE": "EOM(x)",
"STATEMENT": "dx/dt = v_x"
},
{
"EQUATION": "D(z,t)=v_z",
"NAME": "KIN_Z",
"REFS": [
"t",
"v_z",
"z"
],
"ROLE": "CONSTRAINT",
"STATEMENT": "dz/dt = v_z"
},
{
"EQUATION": "m*D(v_x,t)=0",
"NAME": "EOM_X",
"REFS": [
"m",
"t",
"v_x"
],
"ROLE": "EOM(v_x)",
"STATEMENT": "m dv_x/dt = 0"
}
]
}
},
"modules": [
"{\"ID\": \"AIR-LINEAR\", \"VERSION\": \"1.0.0\", \"TITLE\": \"Air resistance at sea level, linear in the speed (Stokes drag on a sphere)\", \"SOURCE\": \"ISO 2533:1975, Standard Atmosphere, sea-level values: density 1.225 kg m-3, dynamic viscosity 1.7894e-5 Pa s\", \"PREREQUISITES\": [{\"SLOT\": \"VELOCITY\", \"KIND\": \"DOF\", \"DIMENSION\": \"L1 T-1\", \"MIN\": 1, \"MAX\": 3, \"LABEL\": \"the velocity components of the body, one per axis\"}], \"PARAMETERS\": [{\"NAME\": \"rho_air\", \"DIMENSION\": \"L-3 M1\", \"SUPPLY\": \"DECLARED\", \"VALUE\": \"1.225\", \"UNIT\": \"kg m-3\", \"OVERRIDABLE\": \"NO\", \"LABEL\": \"the density of air at sea level\"}, {\"NAME\": \"mu_air\", \"DIMENSION\": \"L-1 M1 T-1\", \"SUPPLY\": \"DECLARED\", \"VALUE\": \"1.7894e-5\", \"UNIT\": \"Pa s\", \"OVERRIDABLE\": \"NO\", \"LABEL\": \"the dynamic viscosity of air at sea level\"}, {\"NAME\": \"pi_c\", \"DIMENSION\": \"1\", \"SUPPLY\": \"DECLARED\", \"VALUE\": \"3.141592653589793\", \"UNIT\": \"1\", \"OVERRIDABLE\": \"NO\", \"LABEL\": \"pi, to 16 significant digits\"}, {\"NAME\": \"R_s\", \"DIMENSION\": \"L1\", \"SUPPLY\": \"AUTHOR\", \"LABEL\": \"the radius of the sphere\"}], \"SUMS\": [{\"NAME\": \"SPEED2\", \"OVER\": \"VELOCITY\", \"EACH\": \"VELOCITY^2\"}], \"TERMS\": [{\"TARGET\": \"VELOCITY\", \"SIGN\": \"-\", \"EXPR\": \"6*pi_c*mu_air*R_s*VELOCITY\", \"LABEL\": \"the linear (Stokes) drag\"}], \"ASSUMPTIONS\": [{\"NAME\": \"air_still\", \"PROPOSITION\": \"the air is at rest in the frame of the body's velocity\", \"REFS\": [\"VELOCITY\"]}, {\"NAME\": \"air_uniform\", \"PROPOSITION\": \"the air density is uniform over the region of motion\", \"REFS\": [\"rho_air\"]}, {\"NAME\": \"drag_sphere\", \"PROPOSITION\": \"the body is a rigid sphere of radius R_s\", \"REFS\": [\"R_s\"]}], \"BOUNDARIES\": [{\"NAME\": \"drag_linear_regime\", \"PREDICATE\": \"2 rho_air |v| R_s / mu_air < 1: the regime of the linear law\", \"CONDITION\": \"mu_air != 0 and SPEED2 >= 0 and 2*rho_air*sqrt(SPEED2)*R_s/mu_air < 1\"}], \"NOT_CHOSEN\": \"No linear (Stokes) air resistance.\", \"NOT_INCLUDED\": [\"No wind: the air is at rest.\", \"No change of air density or viscosity with altitude or temperature.\", \"No drag outside the regime of the linear law.\"], \"EXCLUDES\": [], \"INTERACTS_WITH\": [], \"TEST_BINDINGS\": [{\"NAME\": \"PROJECTILE_2D\", \"TPK\": {\"DOF\": [{\"NAME\": \"t\", \"DIMENSION\": \"T1\"}, {\"NAME\": \"x\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"z\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"v_x\", \"DIMENSION\": \"L1 T-1\"}, {\"NAME\": \"v_z\", \"DIMENSION\": \"L1 T-1\"}], \"CONSTANT\": [{\"NAME\": \"m\", \"DIMENSION\": \"M1\"}], \"LAW\": [{\"NAME\": \"KIN_X\", \"STATEMENT\": \"dx/dt = v_x\", \"REFS\": [\"t\", \"v_x\", \"x\"], \"ROLE\": \"EOM(x)\", \"EQUATION\": \"D(x,t)=v_x\"}, {\"NAME\": \"KIN_Z\", \"STATEMENT\": \"dz/dt = v_z\", \"REFS\": [\"t\", \"v_z\", \"z\"], \"ROLE\": \"EOM(z)\", \"EQUATION\": \"D(z,t)=v_z\"}, {\"NAME\": \"EOM_X\", \"STATEMENT\": \"m dv_x/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_x\"], \"ROLE\": \"EOM(v_x)\", \"EQUATION\": \"m*D(v_x,t)=0\"}, {\"NAME\": \"EOM_Z\", \"STATEMENT\": \"m dv_z/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_z\"], \"ROLE\": \"EOM(v_z)\", \"EQUATION\": \"m*D(v_z,t)=0\"}], \"ASSUMPTION\": [{\"NAME\": \"point_mass\", \"PROPOSITION\": \"the body is treated as a point mass\", \"REFS\": [\"m\"]}]}, \"BIND\": {\"VELOCITY\": [\"v_x\", \"v_z\"]}, \"VALUES\": {\"R_s\": {}}, \"ANSWERS\": {}}]}",
"{\"ID\": \"AIR-QUADRATIC\", \"VERSION\": \"1.0.0\", \"TITLE\": \"Air resistance at sea level, quadratic in the speed\", \"SOURCE\": \"ISO 2533:1975, Standard Atmosphere, sea-level values: density 1.225 kg m-3, dynamic viscosity 1.7894e-5 Pa s\", \"PREREQUISITES\": [{\"SLOT\": \"VELOCITY\", \"KIND\": \"DOF\", \"DIMENSION\": \"L1 T-1\", \"MIN\": 1, \"MAX\": 3, \"LABEL\": \"the velocity components of the body, one per axis\"}], \"PARAMETERS\": [{\"NAME\": \"rho_air\", \"DIMENSION\": \"L-3 M1\", \"SUPPLY\": \"DECLARED\", \"VALUE\": \"1.225\", \"UNIT\": \"kg m-3\", \"OVERRIDABLE\": \"NO\", \"LABEL\": \"the density of air at sea level\"}, {\"NAME\": \"mu_air\", \"DIMENSION\": \"L-1 M1 T-1\", \"SUPPLY\": \"DECLARED\", \"VALUE\": \"1.7894e-5\", \"UNIT\": \"Pa s\", \"OVERRIDABLE\": \"NO\", \"LABEL\": \"the dynamic viscosity of air at sea level\"}, {\"NAME\": \"C_d\", \"DIMENSION\": \"1\", \"SUPPLY\": \"AUTHOR\", \"LABEL\": \"the drag coefficient of the body\"}, {\"NAME\": \"A_ref\", \"DIMENSION\": \"L2\", \"SUPPLY\": \"AUTHOR\", \"LABEL\": \"the reference area of the drag coefficient\"}, {\"NAME\": \"L_ref\", \"DIMENSION\": \"L1\", \"SUPPLY\": \"AUTHOR\", \"LABEL\": \"the reference length of the Reynolds number\"}], \"SUMS\": [{\"NAME\": \"SPEED2\", \"OVER\": \"VELOCITY\", \"EACH\": \"VELOCITY^2\"}], \"TERMS\": [{\"TARGET\": \"VELOCITY\", \"SIGN\": \"-\", \"EXPR\": \"0.5*rho_air*C_d*A_ref*sqrt(SPEED2)*VELOCITY\", \"LABEL\": \"the quadratic drag\"}], \"ASSUMPTIONS\": [{\"NAME\": \"air_still\", \"PROPOSITION\": \"the air is at rest in the frame of the body's velocity\", \"REFS\": [\"VELOCITY\"]}, {\"NAME\": \"air_uniform\", \"PROPOSITION\": \"the air density is uniform over the region of motion\", \"REFS\": [\"rho_air\"]}, {\"NAME\": \"drag_cd_constant\", \"PROPOSITION\": \"the drag coefficient C_d is constant over the motion\", \"REFS\": [\"C_d\"]}, {\"NAME\": \"drag_no_lift\", \"PROPOSITION\": \"the body experiences no lift force\", \"REFS\": [\"VELOCITY\"]}, {\"NAME\": \"drag_no_magnus\", \"PROPOSITION\": \"the body experiences no Magnus force\", \"REFS\": [\"VELOCITY\"]}], \"BOUNDARIES\": [{\"NAME\": \"drag_quadratic_regime\", \"PREDICATE\": \"1e3 < rho_air |v| L_ref / mu_air < 2e5: the Reynolds window of the quadratic law\", \"CONDITION\": \"mu_air != 0 and SPEED2 >= 0 and rho_air*sqrt(SPEED2)*L_ref/mu_air > 1000 and rho_air*sqrt(SPEED2)*L_ref/mu_air < 200000\"}], \"NOT_CHOSEN\": \"No quadratic air resistance.\", \"NOT_INCLUDED\": [\"No wind: the air is at rest.\", \"No change of air density or viscosity with altitude or temperature.\", \"No lift, Magnus or added-mass force.\", \"No drag outside the Reynolds window of the quadratic law.\"], \"EXCLUDES\": [\"AIR-LINEAR\"], \"INTERACTS_WITH\": [], \"TEST_BINDINGS\": [{\"NAME\": \"PROJECTILE_2D\", \"TPK\": {\"DOF\": [{\"NAME\": \"t\", \"DIMENSION\": \"T1\"}, {\"NAME\": \"x\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"z\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"v_x\", \"DIMENSION\": \"L1 T-1\"}, {\"NAME\": \"v_z\", \"DIMENSION\": \"L1 T-1\"}], \"CONSTANT\": [{\"NAME\": \"m\", \"DIMENSION\": \"M1\"}], \"LAW\": [{\"NAME\": \"KIN_X\", \"STATEMENT\": \"dx/dt = v_x\", \"REFS\": [\"t\", \"v_x\", \"x\"], \"ROLE\": \"EOM(x)\", \"EQUATION\": \"D(x,t)=v_x\"}, {\"NAME\": \"KIN_Z\", \"STATEMENT\": \"dz/dt = v_z\", \"REFS\": [\"t\", \"v_z\", \"z\"], \"ROLE\": \"EOM(z)\", \"EQUATION\": \"D(z,t)=v_z\"}, {\"NAME\": \"EOM_X\", \"STATEMENT\": \"m dv_x/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_x\"], \"ROLE\": \"EOM(v_x)\", \"EQUATION\": \"m*D(v_x,t)=0\"}, {\"NAME\": \"EOM_Z\", \"STATEMENT\": \"m dv_z/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_z\"], \"ROLE\": \"EOM(v_z)\", \"EQUATION\": \"m*D(v_z,t)=0\"}], \"ASSUMPTION\": [{\"NAME\": \"point_mass\", \"PROPOSITION\": \"the body is treated as a point mass\", \"REFS\": [\"m\"]}]}, \"BIND\": {\"VELOCITY\": [\"v_x\", \"v_z\"]}, \"VALUES\": {\"A_ref\": {}, \"C_d\": {}, \"L_ref\": {}}, \"ANSWERS\": {}}]}",
"{\"ID\": \"GRAV-UNIFORM\", \"VERSION\": \"1.0.0\", \"TITLE\": \"Uniform gravity at the standard value g_n\", \"SOURCE\": \"g_n = 9.80665 m s-2, exact by definition: 3rd CGPM (1901), declaration on the unit of mass and on the definition of weight\", \"PREREQUISITES\": [{\"SLOT\": \"MASS\", \"KIND\": \"CONSTANT\", \"DIMENSION\": \"M1\", \"MIN\": 1, \"MAX\": 1, \"LABEL\": \"the mass of the body\"}, {\"SLOT\": \"UP_VELOCITY\", \"KIND\": \"DOF\", \"DIMENSION\": \"L1 T-1\", \"MIN\": 1, \"MAX\": 1, \"LABEL\": \"the velocity component pointing up; its equation of motion receives the weight\"}, {\"SLOT\": \"HEIGHT\", \"KIND\": \"DOF\", \"DIMENSION\": \"L1\", \"MIN\": 1, \"MAX\": 1, \"LABEL\": \"the position along the same upward axis\"}], \"PARAMETERS\": [{\"NAME\": \"g_n\", \"DIMENSION\": \"L1 T-2\", \"SUPPLY\": \"DECLARED\", \"VALUE\": \"9.80665\", \"UNIT\": \"m s-2\", \"OVERRIDABLE\": \"NO\", \"LABEL\": \"the standard acceleration of gravity\"}, {\"NAME\": \"h_max\", \"DIMENSION\": \"L1\", \"SUPPLY\": \"AUTHOR\", \"LABEL\": \"the largest height, above or below the origin, over which the field is taken as uniform\"}], \"SUMS\": [], \"TERMS\": [{\"TARGET\": \"UP_VELOCITY\", \"SIGN\": \"-\", \"EXPR\": \"MASS*g_n\", \"LABEL\": \"the weight\"}], \"ASSUMPTIONS\": [{\"NAME\": \"gravity_uniform\", \"PROPOSITION\": \"the gravitational field is uniform over the region abs({HEIGHT}) < h_max\", \"REFS\": [\"HEIGHT\", \"h_max\"]}, {\"NAME\": \"gravity_standard\", \"PROPOSITION\": \"the local gravitational acceleration equals the conventional standard value g_n\", \"REFS\": [\"g_n\"]}, {\"NAME\": \"frame_inertial\", \"PROPOSITION\": \"the frame in which {HEIGHT} is measured is treated as inertial\", \"REFS\": [\"HEIGHT\"]}], \"BOUNDARIES\": [{\"NAME\": \"gravity_region\", \"PREDICATE\": \"abs({HEIGHT}) < h_max\", \"CONDITION\": \"abs(HEIGHT) < h_max\"}], \"NOT_CHOSEN\": \"No gravity: no weight acts on any DOF.\", \"NOT_INCLUDED\": [\"No variation of gravity with height or latitude beyond what g_n contains.\", \"No Earth rotation (Coriolis or centrifugal force) beyond what g_n contains.\", \"No gravity of bodies other than the Earth.\"], \"EXCLUDES\": [], \"INTERACTS_WITH\": [{\"WITH\": \"AIR-*\", \"QUESTION_ID\": \"BUOYANCY\", \"QUESTION\": \"Does the air's buoyancy (upthrust) act on the body in the system you mean?\", \"YES_LINE\": \"Buoyancy acts (your answer): no module adds it; it acts in this kernel only where one of your own laws states it.\", \"NO_LINE\": \"No buoyancy: the air's upthrust on the body is not included.\"}], \"TEST_BINDINGS\": [{\"NAME\": \"PROJECTILE_2D\", \"TPK\": {\"DOF\": [{\"NAME\": \"t\", \"DIMENSION\": \"T1\"}, {\"NAME\": \"x\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"z\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"v_x\", \"DIMENSION\": \"L1 T-1\"}, {\"NAME\": \"v_z\", \"DIMENSION\": \"L1 T-1\"}], \"CONSTANT\": [{\"NAME\": \"m\", \"DIMENSION\": \"M1\"}], \"LAW\": [{\"NAME\": \"KIN_X\", \"STATEMENT\": \"dx/dt = v_x\", \"REFS\": [\"t\", \"v_x\", \"x\"], \"ROLE\": \"EOM(x)\", \"EQUATION\": \"D(x,t)=v_x\"}, {\"NAME\": \"KIN_Z\", \"STATEMENT\": \"dz/dt = v_z\", \"REFS\": [\"t\", \"v_z\", \"z\"], \"ROLE\": \"EOM(z)\", \"EQUATION\": \"D(z,t)=v_z\"}, {\"NAME\": \"EOM_X\", \"STATEMENT\": \"m dv_x/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_x\"], \"ROLE\": \"EOM(v_x)\", \"EQUATION\": \"m*D(v_x,t)=0\"}, {\"NAME\": \"EOM_Z\", \"STATEMENT\": \"m dv_z/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_z\"], \"ROLE\": \"EOM(v_z)\", \"EQUATION\": \"m*D(v_z,t)=0\"}], \"ASSUMPTION\": [{\"NAME\": \"point_mass\", \"PROPOSITION\": \"the body is treated as a point mass\", \"REFS\": [\"m\"]}]}, \"BIND\": {\"HEIGHT\": [\"z\"], \"MASS\": [\"m\"], \"UP_VELOCITY\": [\"v_z\"]}, \"VALUES\": {\"h_max\": {\"VALUE\": \"100\", \"UNIT\": \"m\"}}, \"ANSWERS\": {}}, {\"NAME\": \"TABLE\", \"TPK\": {\"DOF\": [{\"NAME\": \"t\", \"DIMENSION\": \"T1\"}, {\"NAME\": \"x\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"z\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"v_x\", \"DIMENSION\": \"L1 T-1\"}, {\"NAME\": \"v_z\", \"DIMENSION\": \"L1 T-1\"}], \"CONSTANT\": [{\"NAME\": \"m\", \"DIMENSION\": \"M1\"}], \"LAW\": [{\"NAME\": \"KIN_X\", \"STATEMENT\": \"dx/dt = v_x\", \"REFS\": [\"t\", \"v_x\", \"x\"], \"ROLE\": \"EOM(x)\", \"EQUATION\": \"D(x,t)=v_x\"}, {\"NAME\": \"KIN_Z\", \"STATEMENT\": \"dz/dt = v_z\", \"REFS\": [\"t\", \"v_z\", \"z\"], \"ROLE\": \"CONSTRAINT\", \"EQUATION\": \"D(z,t)=v_z\"}, {\"NAME\": \"EOM_X\", \"STATEMENT\": \"m dv_x/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_x\"], \"ROLE\": \"EOM(v_x)\", \"EQUATION\": \"m*D(v_x,t)=0\"}], \"CONSTRAINT\": [{\"NAME\": \"C_Z\", \"TARGET\": \"z\", \"ACTION\": \"FIX\", \"VALUE\": \"0\", \"UNIT\": \"m\", \"STATEMENT\": \"the puck stays on the table top, z = 0\"}, {\"NAME\": \"C_VZ\", \"TARGET\": \"v_z\", \"ACTION\": \"FIX\", \"VALUE\": \"0\", \"UNIT\": \"m s-1\", \"STATEMENT\": \"the puck has no vertical velocity\"}]}, \"BIND\": {\"HEIGHT\": [\"z\"], \"MASS\": [\"m\"], \"UP_VELOCITY\": [\"v_z\"]}, \"VALUES\": {\"h_max\": {\"VALUE\": \"1\", \"UNIT\": \"m\"}}, \"ANSWERS\": {\"FIXED:v_z\": \"YES\"}}]}",
"{\"ID\": \"MATH\", \"VERSION\": \"1.0.0\", \"TITLE\": \"The mathematical constant pi, as the CONSTANT pi_c\", \"SOURCE\": \"pi to 16 significant digits, 3.141592653589793, the nearest IEEE 754 binary64 value\", \"PREREQUISITES\": [], \"PARAMETERS\": [{\"NAME\": \"pi_c\", \"DIMENSION\": \"1\", \"SUPPLY\": \"DECLARED\", \"VALUE\": \"3.141592653589793\", \"UNIT\": \"1\", \"OVERRIDABLE\": \"NO\", \"LABEL\": \"pi, to 16 significant digits\"}], \"SUMS\": [], \"TERMS\": [], \"ASSUMPTIONS\": [], \"BOUNDARIES\": [], \"NOT_CHOSEN\": \"No mathematical constant: pi exists only if you declare it.\", \"NOT_INCLUDED\": [\"pi_c is pi rounded to 16 significant digits; no other mathematical constant is declared.\"], \"EXCLUDES\": [], \"INTERACTS_WITH\": [], \"TEST_BINDINGS\": [{\"NAME\": \"PROJECTILE_2D\", \"TPK\": {\"DOF\": [{\"NAME\": \"t\", \"DIMENSION\": \"T1\"}, {\"NAME\": \"x\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"z\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"v_x\", \"DIMENSION\": \"L1 T-1\"}, {\"NAME\": \"v_z\", \"DIMENSION\": \"L1 T-1\"}], \"CONSTANT\": [{\"NAME\": \"m\", \"DIMENSION\": \"M1\"}], \"LAW\": [{\"NAME\": \"KIN_X\", \"STATEMENT\": \"dx/dt = v_x\", \"REFS\": [\"t\", \"v_x\", \"x\"], \"ROLE\": \"EOM(x)\", \"EQUATION\": \"D(x,t)=v_x\"}, {\"NAME\": \"KIN_Z\", \"STATEMENT\": \"dz/dt = v_z\", \"REFS\": [\"t\", \"v_z\", \"z\"], \"ROLE\": \"EOM(z)\", \"EQUATION\": \"D(z,t)=v_z\"}, {\"NAME\": \"EOM_X\", \"STATEMENT\": \"m dv_x/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_x\"], \"ROLE\": \"EOM(v_x)\", \"EQUATION\": \"m*D(v_x,t)=0\"}, {\"NAME\": \"EOM_Z\", \"STATEMENT\": \"m dv_z/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_z\"], \"ROLE\": \"EOM(v_z)\", \"EQUATION\": \"m*D(v_z,t)=0\"}], \"ASSUMPTION\": [{\"NAME\": \"point_mass\", \"PROPOSITION\": \"the body is treated as a point mass\", \"REFS\": [\"m\"]}]}, \"BIND\": {}, \"VALUES\": {}, \"ANSWERS\": {}}]}",
"{\"ID\": \"TEST-PUSH\", \"VERSION\": \"1.0.0\", \"TITLE\": \"Test: a push and a pull\", \"SOURCE\": \"synthetic fixture\", \"PREREQUISITES\": [{\"SLOT\": \"PUSHED\", \"KIND\": \"DOF\", \"DIMENSION\": \"L1 T-1\", \"MIN\": 1, \"MAX\": 1, \"LABEL\": \"the velocity that receives the push\"}, {\"SLOT\": \"PULLED\", \"KIND\": \"DOF\", \"DIMENSION\": \"L1 T-1\", \"MIN\": 1, \"MAX\": 1, \"LABEL\": \"the velocity that receives the pull\"}], \"PARAMETERS\": [{\"NAME\": \"F_a\", \"DIMENSION\": \"L1 M1 T-2\", \"SUPPLY\": \"AUTHOR\", \"LABEL\": \"the first applied force\"}, {\"NAME\": \"F_b\", \"DIMENSION\": \"L1 M1 T-2\", \"SUPPLY\": \"AUTHOR\", \"LABEL\": \"the second applied force\"}], \"SUMS\": [], \"TERMS\": [{\"TARGET\": \"PUSHED\", \"SIGN\": \"+\", \"EXPR\": \"F_a+F_b\", \"LABEL\": \"the push\"}, {\"TARGET\": \"PULLED\", \"SIGN\": \"-\", \"EXPR\": \"F_a+F_b\", \"LABEL\": \"the pull\"}], \"ASSUMPTIONS\": [], \"BOUNDARIES\": [], \"NOT_CHOSEN\": \"No push or pull.\", \"NOT_INCLUDED\": [], \"EXCLUDES\": [], \"INTERACTS_WITH\": [], \"TEST_BINDINGS\": [{\"NAME\": \"PROJECTILE_2D\", \"TPK\": {\"DOF\": [{\"NAME\": \"t\", \"DIMENSION\": \"T1\"}, {\"NAME\": \"x\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"z\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"v_x\", \"DIMENSION\": \"L1 T-1\"}, {\"NAME\": \"v_z\", \"DIMENSION\": \"L1 T-1\"}], \"CONSTANT\": [{\"NAME\": \"m\", \"DIMENSION\": \"M1\"}], \"LAW\": [{\"NAME\": \"KIN_X\", \"STATEMENT\": \"dx/dt = v_x\", \"REFS\": [\"t\", \"v_x\", \"x\"], \"ROLE\": \"EOM(x)\", \"EQUATION\": \"D(x,t)=v_x\"}, {\"NAME\": \"KIN_Z\", \"STATEMENT\": \"dz/dt = v_z\", \"REFS\": [\"t\", \"v_z\", \"z\"], \"ROLE\": \"EOM(z)\", \"EQUATION\": \"D(z,t)=v_z\"}, {\"NAME\": \"EOM_X\", \"STATEMENT\": \"m dv_x/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_x\"], \"ROLE\": \"EOM(v_x)\", \"EQUATION\": \"m*D(v_x,t)=0\"}, {\"NAME\": \"EOM_Z\", \"STATEMENT\": \"m dv_z/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_z\"], \"ROLE\": \"EOM(v_z)\", \"EQUATION\": \"m*D(v_z,t)=0\"}], \"ASSUMPTION\": [{\"NAME\": \"point_mass\", \"PROPOSITION\": \"the body is treated as a point mass\", \"REFS\": [\"m\"]}]}, \"BIND\": {\"PULLED\": [\"v_z\"], \"PUSHED\": [\"v_x\"]}, \"VALUES\": {\"F_a\": {}, \"F_b\": {}}, \"ANSWERS\": {}}]}"
]
},
"computed": "digests by existing TPC-PY functions over literal data",
"expected": "[\"OK\",[\"D(TPK)\",\"4b845b45a26745ae30d77643b7a7fb4270259c8febcc096d32cdec4ddefdd382\"],[\"COMPOSED\",[[\"EOM_X\",\"m*D(v_x,t)=F_a+F_b\"]]],[\"EMITTED\",[[\"CONSTANT\",\"g_n\",[\"GRAV-UNIFORM 1.0.0\"]],[\"CONSTANT\",\"h_max\",[\"GRAV-UNIFORM 1.0.0\"]],[\"ASSUMPTION\",\"gravity_uniform\",[\"GRAV-UNIFORM 1.0.0\"]],[\"ASSUMPTION\",\"gravity_standard\",[\"GRAV-UNIFORM 1.0.0\"]],[\"ASSUMPTION\",\"frame_inertial\",[\"GRAV-UNIFORM 1.0.0\"]],[\"BOUNDARY\",\"gravity_region\",[\"GRAV-UNIFORM 1.0.0\"]],[\"ASSUMPTION\",\"fixed_v_z_balanced\",[\"GRAV-UNIFORM 1.0.0\",\"TEST-PUSH 1.0.0\"]],[\"CONSTANT\",\"F_a\",[\"TEST-PUSH 1.0.0\"]],[\"CONSTANT\",\"F_b\",[\"TEST-PUSH 1.0.0\"]]]],[\"DROPPED\",[[\"GRAV-UNIFORM 1.0.0\",\"v_z\"],[\"TEST-PUSH 1.0.0\",\"v_z\"]]]]",
"fn": "module_expand",
"hand_checked": false,
"name": "X54 two modules drop terms on one FIXED DOF: the balance assumption merges"
},
{
"args": {
"claims": [
{
"ANSWERS": {},
"BIND": {
"HEIGHT": [
"z"
],
"MASS": [
"m"
],
"UP_VELOCITY": [
"v_z"
]
},
"DIGEST": "24877ccb5c8ec300d29ed82ce6650592f35cf8899a3d878ccce9c08d4c72c025",
"ID": "GRAV-UNIFORM",
"VALUES": {
"h_max": {
"UNIT": "m",
"VALUE": "100"
}
},
"VERSION": "1.0.0"
}
],
"draft": {
"TPK": {
"ASSUMPTION": [
{
"NAME": "point_mass",
"PROPOSITION": "the body is treated as a point mass",
"REFS": [
"m"
]
}
],
"CONSTANT": [
{
"DIMENSION": "M1",
"NAME": "m"
}
],
"DOF": [
{
"DIMENSION": "T1",
"NAME": "t"
},
{
"DIMENSION": "L1",
"NAME": "x"
},
{
"DIMENSION": "L1",
"NAME": "z"
},
{
"DIMENSION": "L1 T-1",
"NAME": "v_x"
},
{
"DIMENSION": "L1 T-1",
"NAME": "v_z"
},
{
"DIMENSION": "L1 M1 T-2",
"NAME": "w"
}
],
"LAW": [
{
"EQUATION": "D(x,t)=v_x",
"NAME": "KIN_X",
"REFS": [
"t",
"v_x",
"x"
],
"ROLE": "EOM(x)",
"STATEMENT": "dx/dt = v_x"
},
{
"EQUATION": "D(z,t)=v_z",
"NAME": "KIN_Z",
"REFS": [
"t",
"v_z",
"z"
],
"ROLE": "EOM(z)",
"STATEMENT": "dz/dt = v_z"
},
{
"EQUATION": "m*D(v_x,t)=0",
"NAME": "EOM_X",
"REFS": [
"m",
"t",
"v_x"
],
"ROLE": "EOM(v_x)",
"STATEMENT": "m dv_x/dt = 0"
},
{
"EQUATION": "m*D(v_z,t)=w",
"NAME": "EOM_Z",
"REFS": [
"m",
"t",
"v_z",
"w"
],
"ROLE": "EOM(v_z)",
"STATEMENT": "m dv_z/dt = w"
}
]
}
},
"modules": [
"{\"ID\": \"AIR-LINEAR\", \"VERSION\": \"1.0.0\", \"TITLE\": \"Air resistance at sea level, linear in the speed (Stokes drag on a sphere)\", \"SOURCE\": \"ISO 2533:1975, Standard Atmosphere, sea-level values: density 1.225 kg m-3, dynamic viscosity 1.7894e-5 Pa s\", \"PREREQUISITES\": [{\"SLOT\": \"VELOCITY\", \"KIND\": \"DOF\", \"DIMENSION\": \"L1 T-1\", \"MIN\": 1, \"MAX\": 3, \"LABEL\": \"the velocity components of the body, one per axis\"}], \"PARAMETERS\": [{\"NAME\": \"rho_air\", \"DIMENSION\": \"L-3 M1\", \"SUPPLY\": \"DECLARED\", \"VALUE\": \"1.225\", \"UNIT\": \"kg m-3\", \"OVERRIDABLE\": \"NO\", \"LABEL\": \"the density of air at sea level\"}, {\"NAME\": \"mu_air\", \"DIMENSION\": \"L-1 M1 T-1\", \"SUPPLY\": \"DECLARED\", \"VALUE\": \"1.7894e-5\", \"UNIT\": \"Pa s\", \"OVERRIDABLE\": \"NO\", \"LABEL\": \"the dynamic viscosity of air at sea level\"}, {\"NAME\": \"pi_c\", \"DIMENSION\": \"1\", \"SUPPLY\": \"DECLARED\", \"VALUE\": \"3.141592653589793\", \"UNIT\": \"1\", \"OVERRIDABLE\": \"NO\", \"LABEL\": \"pi, to 16 significant digits\"}, {\"NAME\": \"R_s\", \"DIMENSION\": \"L1\", \"SUPPLY\": \"AUTHOR\", \"LABEL\": \"the radius of the sphere\"}], \"SUMS\": [{\"NAME\": \"SPEED2\", \"OVER\": \"VELOCITY\", \"EACH\": \"VELOCITY^2\"}], \"TERMS\": [{\"TARGET\": \"VELOCITY\", \"SIGN\": \"-\", \"EXPR\": \"6*pi_c*mu_air*R_s*VELOCITY\", \"LABEL\": \"the linear (Stokes) drag\"}], \"ASSUMPTIONS\": [{\"NAME\": \"air_still\", \"PROPOSITION\": \"the air is at rest in the frame of the body's velocity\", \"REFS\": [\"VELOCITY\"]}, {\"NAME\": \"air_uniform\", \"PROPOSITION\": \"the air density is uniform over the region of motion\", \"REFS\": [\"rho_air\"]}, {\"NAME\": \"drag_sphere\", \"PROPOSITION\": \"the body is a rigid sphere of radius R_s\", \"REFS\": [\"R_s\"]}], \"BOUNDARIES\": [{\"NAME\": \"drag_linear_regime\", \"PREDICATE\": \"2 rho_air |v| R_s / mu_air < 1: the regime of the linear law\", \"CONDITION\": \"mu_air != 0 and SPEED2 >= 0 and 2*rho_air*sqrt(SPEED2)*R_s/mu_air < 1\"}], \"NOT_CHOSEN\": \"No linear (Stokes) air resistance.\", \"NOT_INCLUDED\": [\"No wind: the air is at rest.\", \"No change of air density or viscosity with altitude or temperature.\", \"No drag outside the regime of the linear law.\"], \"EXCLUDES\": [], \"INTERACTS_WITH\": [], \"TEST_BINDINGS\": [{\"NAME\": \"PROJECTILE_2D\", \"TPK\": {\"DOF\": [{\"NAME\": \"t\", \"DIMENSION\": \"T1\"}, {\"NAME\": \"x\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"z\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"v_x\", \"DIMENSION\": \"L1 T-1\"}, {\"NAME\": \"v_z\", \"DIMENSION\": \"L1 T-1\"}], \"CONSTANT\": [{\"NAME\": \"m\", \"DIMENSION\": \"M1\"}], \"LAW\": [{\"NAME\": \"KIN_X\", \"STATEMENT\": \"dx/dt = v_x\", \"REFS\": [\"t\", \"v_x\", \"x\"], \"ROLE\": \"EOM(x)\", \"EQUATION\": \"D(x,t)=v_x\"}, {\"NAME\": \"KIN_Z\", \"STATEMENT\": \"dz/dt = v_z\", \"REFS\": [\"t\", \"v_z\", \"z\"], \"ROLE\": \"EOM(z)\", \"EQUATION\": \"D(z,t)=v_z\"}, {\"NAME\": \"EOM_X\", \"STATEMENT\": \"m dv_x/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_x\"], \"ROLE\": \"EOM(v_x)\", \"EQUATION\": \"m*D(v_x,t)=0\"}, {\"NAME\": \"EOM_Z\", \"STATEMENT\": \"m dv_z/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_z\"], \"ROLE\": \"EOM(v_z)\", \"EQUATION\": \"m*D(v_z,t)=0\"}], \"ASSUMPTION\": [{\"NAME\": \"point_mass\", \"PROPOSITION\": \"the body is treated as a point mass\", \"REFS\": [\"m\"]}]}, \"BIND\": {\"VELOCITY\": [\"v_x\", \"v_z\"]}, \"VALUES\": {\"R_s\": {}}, \"ANSWERS\": {}}]}",
"{\"ID\": \"AIR-QUADRATIC\", \"VERSION\": \"1.0.0\", \"TITLE\": \"Air resistance at sea level, quadratic in the speed\", \"SOURCE\": \"ISO 2533:1975, Standard Atmosphere, sea-level values: density 1.225 kg m-3, dynamic viscosity 1.7894e-5 Pa s\", \"PREREQUISITES\": [{\"SLOT\": \"VELOCITY\", \"KIND\": \"DOF\", \"DIMENSION\": \"L1 T-1\", \"MIN\": 1, \"MAX\": 3, \"LABEL\": \"the velocity components of the body, one per axis\"}], \"PARAMETERS\": [{\"NAME\": \"rho_air\", \"DIMENSION\": \"L-3 M1\", \"SUPPLY\": \"DECLARED\", \"VALUE\": \"1.225\", \"UNIT\": \"kg m-3\", \"OVERRIDABLE\": \"NO\", \"LABEL\": \"the density of air at sea level\"}, {\"NAME\": \"mu_air\", \"DIMENSION\": \"L-1 M1 T-1\", \"SUPPLY\": \"DECLARED\", \"VALUE\": \"1.7894e-5\", \"UNIT\": \"Pa s\", \"OVERRIDABLE\": \"NO\", \"LABEL\": \"the dynamic viscosity of air at sea level\"}, {\"NAME\": \"C_d\", \"DIMENSION\": \"1\", \"SUPPLY\": \"AUTHOR\", \"LABEL\": \"the drag coefficient of the body\"}, {\"NAME\": \"A_ref\", \"DIMENSION\": \"L2\", \"SUPPLY\": \"AUTHOR\", \"LABEL\": \"the reference area of the drag coefficient\"}, {\"NAME\": \"L_ref\", \"DIMENSION\": \"L1\", \"SUPPLY\": \"AUTHOR\", \"LABEL\": \"the reference length of the Reynolds number\"}], \"SUMS\": [{\"NAME\": \"SPEED2\", \"OVER\": \"VELOCITY\", \"EACH\": \"VELOCITY^2\"}], \"TERMS\": [{\"TARGET\": \"VELOCITY\", \"SIGN\": \"-\", \"EXPR\": \"0.5*rho_air*C_d*A_ref*sqrt(SPEED2)*VELOCITY\", \"LABEL\": \"the quadratic drag\"}], \"ASSUMPTIONS\": [{\"NAME\": \"air_still\", \"PROPOSITION\": \"the air is at rest in the frame of the body's velocity\", \"REFS\": [\"VELOCITY\"]}, {\"NAME\": \"air_uniform\", \"PROPOSITION\": \"the air density is uniform over the region of motion\", \"REFS\": [\"rho_air\"]}, {\"NAME\": \"drag_cd_constant\", \"PROPOSITION\": \"the drag coefficient C_d is constant over the motion\", \"REFS\": [\"C_d\"]}, {\"NAME\": \"drag_no_lift\", \"PROPOSITION\": \"the body experiences no lift force\", \"REFS\": [\"VELOCITY\"]}, {\"NAME\": \"drag_no_magnus\", \"PROPOSITION\": \"the body experiences no Magnus force\", \"REFS\": [\"VELOCITY\"]}], \"BOUNDARIES\": [{\"NAME\": \"drag_quadratic_regime\", \"PREDICATE\": \"1e3 < rho_air |v| L_ref / mu_air < 2e5: the Reynolds window of the quadratic law\", \"CONDITION\": \"mu_air != 0 and SPEED2 >= 0 and rho_air*sqrt(SPEED2)*L_ref/mu_air > 1000 and rho_air*sqrt(SPEED2)*L_ref/mu_air < 200000\"}], \"NOT_CHOSEN\": \"No quadratic air resistance.\", \"NOT_INCLUDED\": [\"No wind: the air is at rest.\", \"No change of air density or viscosity with altitude or temperature.\", \"No lift, Magnus or added-mass force.\", \"No drag outside the Reynolds window of the quadratic law.\"], \"EXCLUDES\": [\"AIR-LINEAR\"], \"INTERACTS_WITH\": [], \"TEST_BINDINGS\": [{\"NAME\": \"PROJECTILE_2D\", \"TPK\": {\"DOF\": [{\"NAME\": \"t\", \"DIMENSION\": \"T1\"}, {\"NAME\": \"x\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"z\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"v_x\", \"DIMENSION\": \"L1 T-1\"}, {\"NAME\": \"v_z\", \"DIMENSION\": \"L1 T-1\"}], \"CONSTANT\": [{\"NAME\": \"m\", \"DIMENSION\": \"M1\"}], \"LAW\": [{\"NAME\": \"KIN_X\", \"STATEMENT\": \"dx/dt = v_x\", \"REFS\": [\"t\", \"v_x\", \"x\"], \"ROLE\": \"EOM(x)\", \"EQUATION\": \"D(x,t)=v_x\"}, {\"NAME\": \"KIN_Z\", \"STATEMENT\": \"dz/dt = v_z\", \"REFS\": [\"t\", \"v_z\", \"z\"], \"ROLE\": \"EOM(z)\", \"EQUATION\": \"D(z,t)=v_z\"}, {\"NAME\": \"EOM_X\", \"STATEMENT\": \"m dv_x/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_x\"], \"ROLE\": \"EOM(v_x)\", \"EQUATION\": \"m*D(v_x,t)=0\"}, {\"NAME\": \"EOM_Z\", \"STATEMENT\": \"m dv_z/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_z\"], \"ROLE\": \"EOM(v_z)\", \"EQUATION\": \"m*D(v_z,t)=0\"}], \"ASSUMPTION\": [{\"NAME\": \"point_mass\", \"PROPOSITION\": \"the body is treated as a point mass\", \"REFS\": [\"m\"]}]}, \"BIND\": {\"VELOCITY\": [\"v_x\", \"v_z\"]}, \"VALUES\": {\"A_ref\": {}, \"C_d\": {}, \"L_ref\": {}}, \"ANSWERS\": {}}]}",
"{\"ID\": \"GRAV-UNIFORM\", \"VERSION\": \"1.0.0\", \"TITLE\": \"Uniform gravity at the standard value g_n\", \"SOURCE\": \"g_n = 9.80665 m s-2, exact by definition: 3rd CGPM (1901), declaration on the unit of mass and on the definition of weight\", \"PREREQUISITES\": [{\"SLOT\": \"MASS\", \"KIND\": \"CONSTANT\", \"DIMENSION\": \"M1\", \"MIN\": 1, \"MAX\": 1, \"LABEL\": \"the mass of the body\"}, {\"SLOT\": \"UP_VELOCITY\", \"KIND\": \"DOF\", \"DIMENSION\": \"L1 T-1\", \"MIN\": 1, \"MAX\": 1, \"LABEL\": \"the velocity component pointing up; its equation of motion receives the weight\"}, {\"SLOT\": \"HEIGHT\", \"KIND\": \"DOF\", \"DIMENSION\": \"L1\", \"MIN\": 1, \"MAX\": 1, \"LABEL\": \"the position along the same upward axis\"}], \"PARAMETERS\": [{\"NAME\": \"g_n\", \"DIMENSION\": \"L1 T-2\", \"SUPPLY\": \"DECLARED\", \"VALUE\": \"9.80665\", \"UNIT\": \"m s-2\", \"OVERRIDABLE\": \"NO\", \"LABEL\": \"the standard acceleration of gravity\"}, {\"NAME\": \"h_max\", \"DIMENSION\": \"L1\", \"SUPPLY\": \"AUTHOR\", \"LABEL\": \"the largest height, above or below the origin, over which the field is taken as uniform\"}], \"SUMS\": [], \"TERMS\": [{\"TARGET\": \"UP_VELOCITY\", \"SIGN\": \"-\", \"EXPR\": \"MASS*g_n\", \"LABEL\": \"the weight\"}], \"ASSUMPTIONS\": [{\"NAME\": \"gravity_uniform\", \"PROPOSITION\": \"the gravitational field is uniform over the region abs({HEIGHT}) < h_max\", \"REFS\": [\"HEIGHT\", \"h_max\"]}, {\"NAME\": \"gravity_standard\", \"PROPOSITION\": \"the local gravitational acceleration equals the conventional standard value g_n\", \"REFS\": [\"g_n\"]}, {\"NAME\": \"frame_inertial\", \"PROPOSITION\": \"the frame in which {HEIGHT} is measured is treated as inertial\", \"REFS\": [\"HEIGHT\"]}], \"BOUNDARIES\": [{\"NAME\": \"gravity_region\", \"PREDICATE\": \"abs({HEIGHT}) < h_max\", \"CONDITION\": \"abs(HEIGHT) < h_max\"}], \"NOT_CHOSEN\": \"No gravity: no weight acts on any DOF.\", \"NOT_INCLUDED\": [\"No variation of gravity with height or latitude beyond what g_n contains.\", \"No Earth rotation (Coriolis or centrifugal force) beyond what g_n contains.\", \"No gravity of bodies other than the Earth.\"], \"EXCLUDES\": [], \"INTERACTS_WITH\": [{\"WITH\": \"AIR-*\", \"QUESTION_ID\": \"BUOYANCY\", \"QUESTION\": \"Does the air's buoyancy (upthrust) act on the body in the system you mean?\", \"YES_LINE\": \"Buoyancy acts (your answer): no module adds it; it acts in this kernel only where one of your own laws states it.\", \"NO_LINE\": \"No buoyancy: the air's upthrust on the body is not included.\"}], \"TEST_BINDINGS\": [{\"NAME\": \"PROJECTILE_2D\", \"TPK\": {\"DOF\": [{\"NAME\": \"t\", \"DIMENSION\": \"T1\"}, {\"NAME\": \"x\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"z\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"v_x\", \"DIMENSION\": \"L1 T-1\"}, {\"NAME\": \"v_z\", \"DIMENSION\": \"L1 T-1\"}], \"CONSTANT\": [{\"NAME\": \"m\", \"DIMENSION\": \"M1\"}], \"LAW\": [{\"NAME\": \"KIN_X\", \"STATEMENT\": \"dx/dt = v_x\", \"REFS\": [\"t\", \"v_x\", \"x\"], \"ROLE\": \"EOM(x)\", \"EQUATION\": \"D(x,t)=v_x\"}, {\"NAME\": \"KIN_Z\", \"STATEMENT\": \"dz/dt = v_z\", \"REFS\": [\"t\", \"v_z\", \"z\"], \"ROLE\": \"EOM(z)\", \"EQUATION\": \"D(z,t)=v_z\"}, {\"NAME\": \"EOM_X\", \"STATEMENT\": \"m dv_x/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_x\"], \"ROLE\": \"EOM(v_x)\", \"EQUATION\": \"m*D(v_x,t)=0\"}, {\"NAME\": \"EOM_Z\", \"STATEMENT\": \"m dv_z/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_z\"], \"ROLE\": \"EOM(v_z)\", \"EQUATION\": \"m*D(v_z,t)=0\"}], \"ASSUMPTION\": [{\"NAME\": \"point_mass\", \"PROPOSITION\": \"the body is treated as a point mass\", \"REFS\": [\"m\"]}]}, \"BIND\": {\"HEIGHT\": [\"z\"], \"MASS\": [\"m\"], \"UP_VELOCITY\": [\"v_z\"]}, \"VALUES\": {\"h_max\": {\"VALUE\": \"100\", \"UNIT\": \"m\"}}, \"ANSWERS\": {}}, {\"NAME\": \"TABLE\", \"TPK\": {\"DOF\": [{\"NAME\": \"t\", \"DIMENSION\": \"T1\"}, {\"NAME\": \"x\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"z\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"v_x\", \"DIMENSION\": \"L1 T-1\"}, {\"NAME\": \"v_z\", \"DIMENSION\": \"L1 T-1\"}], \"CONSTANT\": [{\"NAME\": \"m\", \"DIMENSION\": \"M1\"}], \"LAW\": [{\"NAME\": \"KIN_X\", \"STATEMENT\": \"dx/dt = v_x\", \"REFS\": [\"t\", \"v_x\", \"x\"], \"ROLE\": \"EOM(x)\", \"EQUATION\": \"D(x,t)=v_x\"}, {\"NAME\": \"KIN_Z\", \"STATEMENT\": \"dz/dt = v_z\", \"REFS\": [\"t\", \"v_z\", \"z\"], \"ROLE\": \"CONSTRAINT\", \"EQUATION\": \"D(z,t)=v_z\"}, {\"NAME\": \"EOM_X\", \"STATEMENT\": \"m dv_x/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_x\"], \"ROLE\": \"EOM(v_x)\", \"EQUATION\": \"m*D(v_x,t)=0\"}], \"CONSTRAINT\": [{\"NAME\": \"C_Z\", \"TARGET\": \"z\", \"ACTION\": \"FIX\", \"VALUE\": \"0\", \"UNIT\": \"m\", \"STATEMENT\": \"the puck stays on the table top, z = 0\"}, {\"NAME\": \"C_VZ\", \"TARGET\": \"v_z\", \"ACTION\": \"FIX\", \"VALUE\": \"0\", \"UNIT\": \"m s-1\", \"STATEMENT\": \"the puck has no vertical velocity\"}]}, \"BIND\": {\"HEIGHT\": [\"z\"], \"MASS\": [\"m\"], \"UP_VELOCITY\": [\"v_z\"]}, \"VALUES\": {\"h_max\": {\"VALUE\": \"1\", \"UNIT\": \"m\"}}, \"ANSWERS\": {\"FIXED:v_z\": \"YES\"}}]}",
"{\"ID\": \"MATH\", \"VERSION\": \"1.0.0\", \"TITLE\": \"The mathematical constant pi, as the CONSTANT pi_c\", \"SOURCE\": \"pi to 16 significant digits, 3.141592653589793, the nearest IEEE 754 binary64 value\", \"PREREQUISITES\": [], \"PARAMETERS\": [{\"NAME\": \"pi_c\", \"DIMENSION\": \"1\", \"SUPPLY\": \"DECLARED\", \"VALUE\": \"3.141592653589793\", \"UNIT\": \"1\", \"OVERRIDABLE\": \"NO\", \"LABEL\": \"pi, to 16 significant digits\"}], \"SUMS\": [], \"TERMS\": [], \"ASSUMPTIONS\": [], \"BOUNDARIES\": [], \"NOT_CHOSEN\": \"No mathematical constant: pi exists only if you declare it.\", \"NOT_INCLUDED\": [\"pi_c is pi rounded to 16 significant digits; no other mathematical constant is declared.\"], \"EXCLUDES\": [], \"INTERACTS_WITH\": [], \"TEST_BINDINGS\": [{\"NAME\": \"PROJECTILE_2D\", \"TPK\": {\"DOF\": [{\"NAME\": \"t\", \"DIMENSION\": \"T1\"}, {\"NAME\": \"x\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"z\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"v_x\", \"DIMENSION\": \"L1 T-1\"}, {\"NAME\": \"v_z\", \"DIMENSION\": \"L1 T-1\"}], \"CONSTANT\": [{\"NAME\": \"m\", \"DIMENSION\": \"M1\"}], \"LAW\": [{\"NAME\": \"KIN_X\", \"STATEMENT\": \"dx/dt = v_x\", \"REFS\": [\"t\", \"v_x\", \"x\"], \"ROLE\": \"EOM(x)\", \"EQUATION\": \"D(x,t)=v_x\"}, {\"NAME\": \"KIN_Z\", \"STATEMENT\": \"dz/dt = v_z\", \"REFS\": [\"t\", \"v_z\", \"z\"], \"ROLE\": \"EOM(z)\", \"EQUATION\": \"D(z,t)=v_z\"}, {\"NAME\": \"EOM_X\", \"STATEMENT\": \"m dv_x/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_x\"], \"ROLE\": \"EOM(v_x)\", \"EQUATION\": \"m*D(v_x,t)=0\"}, {\"NAME\": \"EOM_Z\", \"STATEMENT\": \"m dv_z/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_z\"], \"ROLE\": \"EOM(v_z)\", \"EQUATION\": \"m*D(v_z,t)=0\"}], \"ASSUMPTION\": [{\"NAME\": \"point_mass\", \"PROPOSITION\": \"the body is treated as a point mass\", \"REFS\": [\"m\"]}]}, \"BIND\": {}, \"VALUES\": {}, \"ANSWERS\": {}}]}"
]
},
"expected": "[\"REFUSED\",\"CLAIM GRAV-UNIFORM 1.0.0: TERM 1: v_z's equation of motion is not determined (UNDER); resolve it, then bind the module\"]",
"fn": "module_expand",
"hand_checked": true,
"name": "X55 the target in the UNDER part"
},
{
"args": {
"claims": [
{
"ANSWERS": {},
"BIND": {
"HEIGHT": [
"z"
],
"MASS": [
"m"
],
"UP_VELOCITY": [
"v_z"
]
},
"DIGEST": "24877ccb5c8ec300d29ed82ce6650592f35cf8899a3d878ccce9c08d4c72c025",
"ID": "GRAV-UNIFORM",
"VALUES": {
"h_max": {
"UNIT": "m",
"VALUE": "100"
}
},
"VERSION": "1.0.0"
}
],
"draft": {
"TPK": {
"ASSUMPTION": [
{
"NAME": "point_mass",
"PROPOSITION": "the body is treated as a point mass",
"REFS": [
"m"
]
}
],
"CONSTANT": [
{
"DIMENSION": "M1",
"NAME": "m"
}
],
"DOF": [
{
"DIMENSION": "T1",
"NAME": "t"
},
{
"DIMENSION": "L1",
"NAME": "x"
},
{
"DIMENSION": "L1",
"NAME": "z"
},
{
"DIMENSION": "L1 T-1",
"NAME": "v_x"
},
{
"DIMENSION": "L1 T-1",
"NAME": "v_z"
}
],
"LAW": [
{
"EQUATION": "D(x,t)=v_x",
"NAME": "KIN_X",
"REFS": [
"t",
"v_x",
"x"
],
"ROLE": "EOM(x)",
"STATEMENT": "dx/dt = v_x"
},
{
"EQUATION": "D(z,t)=v_z",
"NAME": "KIN_Z",
"REFS": [
"t",
"v_z",
"z"
],
"ROLE": "EOM(z)",
"STATEMENT": "dz/dt = v_z"
},
{
"EQUATION": "m*D(v_x,t)=0",
"NAME": "EOM_X",
"REFS": [
"m",
"t",
"v_x"
],
"ROLE": "EOM(v_x)",
"STATEMENT": "m dv_x/dt = 0"
},
{
"EQUATION": "m*D(v_z,t)=0",
"NAME": "EOM_Z",
"REFS": [
"m",
"t",
"v_z"
],
"ROLE": "EOM(v_z)",
"STATEMENT": "m dv_z/dt = 0"
},
{
"EQUATION": "m*D(v_z,t)=0",
"NAME": "EOM_Z2",
"REFS": [
"m",
"t",
"v_z"
],
"ROLE": "EOM(v_z)",
"STATEMENT": "m dv_z/dt = 0, again"
}
]
}
},
"modules": [
"{\"ID\": \"AIR-LINEAR\", \"VERSION\": \"1.0.0\", \"TITLE\": \"Air resistance at sea level, linear in the speed (Stokes drag on a sphere)\", \"SOURCE\": \"ISO 2533:1975, Standard Atmosphere, sea-level values: density 1.225 kg m-3, dynamic viscosity 1.7894e-5 Pa s\", \"PREREQUISITES\": [{\"SLOT\": \"VELOCITY\", \"KIND\": \"DOF\", \"DIMENSION\": \"L1 T-1\", \"MIN\": 1, \"MAX\": 3, \"LABEL\": \"the velocity components of the body, one per axis\"}], \"PARAMETERS\": [{\"NAME\": \"rho_air\", \"DIMENSION\": \"L-3 M1\", \"SUPPLY\": \"DECLARED\", \"VALUE\": \"1.225\", \"UNIT\": \"kg m-3\", \"OVERRIDABLE\": \"NO\", \"LABEL\": \"the density of air at sea level\"}, {\"NAME\": \"mu_air\", \"DIMENSION\": \"L-1 M1 T-1\", \"SUPPLY\": \"DECLARED\", \"VALUE\": \"1.7894e-5\", \"UNIT\": \"Pa s\", \"OVERRIDABLE\": \"NO\", \"LABEL\": \"the dynamic viscosity of air at sea level\"}, {\"NAME\": \"pi_c\", \"DIMENSION\": \"1\", \"SUPPLY\": \"DECLARED\", \"VALUE\": \"3.141592653589793\", \"UNIT\": \"1\", \"OVERRIDABLE\": \"NO\", \"LABEL\": \"pi, to 16 significant digits\"}, {\"NAME\": \"R_s\", \"DIMENSION\": \"L1\", \"SUPPLY\": \"AUTHOR\", \"LABEL\": \"the radius of the sphere\"}], \"SUMS\": [{\"NAME\": \"SPEED2\", \"OVER\": \"VELOCITY\", \"EACH\": \"VELOCITY^2\"}], \"TERMS\": [{\"TARGET\": \"VELOCITY\", \"SIGN\": \"-\", \"EXPR\": \"6*pi_c*mu_air*R_s*VELOCITY\", \"LABEL\": \"the linear (Stokes) drag\"}], \"ASSUMPTIONS\": [{\"NAME\": \"air_still\", \"PROPOSITION\": \"the air is at rest in the frame of the body's velocity\", \"REFS\": [\"VELOCITY\"]}, {\"NAME\": \"air_uniform\", \"PROPOSITION\": \"the air density is uniform over the region of motion\", \"REFS\": [\"rho_air\"]}, {\"NAME\": \"drag_sphere\", \"PROPOSITION\": \"the body is a rigid sphere of radius R_s\", \"REFS\": [\"R_s\"]}], \"BOUNDARIES\": [{\"NAME\": \"drag_linear_regime\", \"PREDICATE\": \"2 rho_air |v| R_s / mu_air < 1: the regime of the linear law\", \"CONDITION\": \"mu_air != 0 and SPEED2 >= 0 and 2*rho_air*sqrt(SPEED2)*R_s/mu_air < 1\"}], \"NOT_CHOSEN\": \"No linear (Stokes) air resistance.\", \"NOT_INCLUDED\": [\"No wind: the air is at rest.\", \"No change of air density or viscosity with altitude or temperature.\", \"No drag outside the regime of the linear law.\"], \"EXCLUDES\": [], \"INTERACTS_WITH\": [], \"TEST_BINDINGS\": [{\"NAME\": \"PROJECTILE_2D\", \"TPK\": {\"DOF\": [{\"NAME\": \"t\", \"DIMENSION\": \"T1\"}, {\"NAME\": \"x\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"z\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"v_x\", \"DIMENSION\": \"L1 T-1\"}, {\"NAME\": \"v_z\", \"DIMENSION\": \"L1 T-1\"}], \"CONSTANT\": [{\"NAME\": \"m\", \"DIMENSION\": \"M1\"}], \"LAW\": [{\"NAME\": \"KIN_X\", \"STATEMENT\": \"dx/dt = v_x\", \"REFS\": [\"t\", \"v_x\", \"x\"], \"ROLE\": \"EOM(x)\", \"EQUATION\": \"D(x,t)=v_x\"}, {\"NAME\": \"KIN_Z\", \"STATEMENT\": \"dz/dt = v_z\", \"REFS\": [\"t\", \"v_z\", \"z\"], \"ROLE\": \"EOM(z)\", \"EQUATION\": \"D(z,t)=v_z\"}, {\"NAME\": \"EOM_X\", \"STATEMENT\": \"m dv_x/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_x\"], \"ROLE\": \"EOM(v_x)\", \"EQUATION\": \"m*D(v_x,t)=0\"}, {\"NAME\": \"EOM_Z\", \"STATEMENT\": \"m dv_z/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_z\"], \"ROLE\": \"EOM(v_z)\", \"EQUATION\": \"m*D(v_z,t)=0\"}], \"ASSUMPTION\": [{\"NAME\": \"point_mass\", \"PROPOSITION\": \"the body is treated as a point mass\", \"REFS\": [\"m\"]}]}, \"BIND\": {\"VELOCITY\": [\"v_x\", \"v_z\"]}, \"VALUES\": {\"R_s\": {}}, \"ANSWERS\": {}}]}",
"{\"ID\": \"AIR-QUADRATIC\", \"VERSION\": \"1.0.0\", \"TITLE\": \"Air resistance at sea level, quadratic in the speed\", \"SOURCE\": \"ISO 2533:1975, Standard Atmosphere, sea-level values: density 1.225 kg m-3, dynamic viscosity 1.7894e-5 Pa s\", \"PREREQUISITES\": [{\"SLOT\": \"VELOCITY\", \"KIND\": \"DOF\", \"DIMENSION\": \"L1 T-1\", \"MIN\": 1, \"MAX\": 3, \"LABEL\": \"the velocity components of the body, one per axis\"}], \"PARAMETERS\": [{\"NAME\": \"rho_air\", \"DIMENSION\": \"L-3 M1\", \"SUPPLY\": \"DECLARED\", \"VALUE\": \"1.225\", \"UNIT\": \"kg m-3\", \"OVERRIDABLE\": \"NO\", \"LABEL\": \"the density of air at sea level\"}, {\"NAME\": \"mu_air\", \"DIMENSION\": \"L-1 M1 T-1\", \"SUPPLY\": \"DECLARED\", \"VALUE\": \"1.7894e-5\", \"UNIT\": \"Pa s\", \"OVERRIDABLE\": \"NO\", \"LABEL\": \"the dynamic viscosity of air at sea level\"}, {\"NAME\": \"C_d\", \"DIMENSION\": \"1\", \"SUPPLY\": \"AUTHOR\", \"LABEL\": \"the drag coefficient of the body\"}, {\"NAME\": \"A_ref\", \"DIMENSION\": \"L2\", \"SUPPLY\": \"AUTHOR\", \"LABEL\": \"the reference area of the drag coefficient\"}, {\"NAME\": \"L_ref\", \"DIMENSION\": \"L1\", \"SUPPLY\": \"AUTHOR\", \"LABEL\": \"the reference length of the Reynolds number\"}], \"SUMS\": [{\"NAME\": \"SPEED2\", \"OVER\": \"VELOCITY\", \"EACH\": \"VELOCITY^2\"}], \"TERMS\": [{\"TARGET\": \"VELOCITY\", \"SIGN\": \"-\", \"EXPR\": \"0.5*rho_air*C_d*A_ref*sqrt(SPEED2)*VELOCITY\", \"LABEL\": \"the quadratic drag\"}], \"ASSUMPTIONS\": [{\"NAME\": \"air_still\", \"PROPOSITION\": \"the air is at rest in the frame of the body's velocity\", \"REFS\": [\"VELOCITY\"]}, {\"NAME\": \"air_uniform\", \"PROPOSITION\": \"the air density is uniform over the region of motion\", \"REFS\": [\"rho_air\"]}, {\"NAME\": \"drag_cd_constant\", \"PROPOSITION\": \"the drag coefficient C_d is constant over the motion\", \"REFS\": [\"C_d\"]}, {\"NAME\": \"drag_no_lift\", \"PROPOSITION\": \"the body experiences no lift force\", \"REFS\": [\"VELOCITY\"]}, {\"NAME\": \"drag_no_magnus\", \"PROPOSITION\": \"the body experiences no Magnus force\", \"REFS\": [\"VELOCITY\"]}], \"BOUNDARIES\": [{\"NAME\": \"drag_quadratic_regime\", \"PREDICATE\": \"1e3 < rho_air |v| L_ref / mu_air < 2e5: the Reynolds window of the quadratic law\", \"CONDITION\": \"mu_air != 0 and SPEED2 >= 0 and rho_air*sqrt(SPEED2)*L_ref/mu_air > 1000 and rho_air*sqrt(SPEED2)*L_ref/mu_air < 200000\"}], \"NOT_CHOSEN\": \"No quadratic air resistance.\", \"NOT_INCLUDED\": [\"No wind: the air is at rest.\", \"No change of air density or viscosity with altitude or temperature.\", \"No lift, Magnus or added-mass force.\", \"No drag outside the Reynolds window of the quadratic law.\"], \"EXCLUDES\": [\"AIR-LINEAR\"], \"INTERACTS_WITH\": [], \"TEST_BINDINGS\": [{\"NAME\": \"PROJECTILE_2D\", \"TPK\": {\"DOF\": [{\"NAME\": \"t\", \"DIMENSION\": \"T1\"}, {\"NAME\": \"x\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"z\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"v_x\", \"DIMENSION\": \"L1 T-1\"}, {\"NAME\": \"v_z\", \"DIMENSION\": \"L1 T-1\"}], \"CONSTANT\": [{\"NAME\": \"m\", \"DIMENSION\": \"M1\"}], \"LAW\": [{\"NAME\": \"KIN_X\", \"STATEMENT\": \"dx/dt = v_x\", \"REFS\": [\"t\", \"v_x\", \"x\"], \"ROLE\": \"EOM(x)\", \"EQUATION\": \"D(x,t)=v_x\"}, {\"NAME\": \"KIN_Z\", \"STATEMENT\": \"dz/dt = v_z\", \"REFS\": [\"t\", \"v_z\", \"z\"], \"ROLE\": \"EOM(z)\", \"EQUATION\": \"D(z,t)=v_z\"}, {\"NAME\": \"EOM_X\", \"STATEMENT\": \"m dv_x/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_x\"], \"ROLE\": \"EOM(v_x)\", \"EQUATION\": \"m*D(v_x,t)=0\"}, {\"NAME\": \"EOM_Z\", \"STATEMENT\": \"m dv_z/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_z\"], \"ROLE\": \"EOM(v_z)\", \"EQUATION\": \"m*D(v_z,t)=0\"}], \"ASSUMPTION\": [{\"NAME\": \"point_mass\", \"PROPOSITION\": \"the body is treated as a point mass\", \"REFS\": [\"m\"]}]}, \"BIND\": {\"VELOCITY\": [\"v_x\", \"v_z\"]}, \"VALUES\": {\"A_ref\": {}, \"C_d\": {}, \"L_ref\": {}}, \"ANSWERS\": {}}]}",
"{\"ID\": \"GRAV-UNIFORM\", \"VERSION\": \"1.0.0\", \"TITLE\": \"Uniform gravity at the standard value g_n\", \"SOURCE\": \"g_n = 9.80665 m s-2, exact by definition: 3rd CGPM (1901), declaration on the unit of mass and on the definition of weight\", \"PREREQUISITES\": [{\"SLOT\": \"MASS\", \"KIND\": \"CONSTANT\", \"DIMENSION\": \"M1\", \"MIN\": 1, \"MAX\": 1, \"LABEL\": \"the mass of the body\"}, {\"SLOT\": \"UP_VELOCITY\", \"KIND\": \"DOF\", \"DIMENSION\": \"L1 T-1\", \"MIN\": 1, \"MAX\": 1, \"LABEL\": \"the velocity component pointing up; its equation of motion receives the weight\"}, {\"SLOT\": \"HEIGHT\", \"KIND\": \"DOF\", \"DIMENSION\": \"L1\", \"MIN\": 1, \"MAX\": 1, \"LABEL\": \"the position along the same upward axis\"}], \"PARAMETERS\": [{\"NAME\": \"g_n\", \"DIMENSION\": \"L1 T-2\", \"SUPPLY\": \"DECLARED\", \"VALUE\": \"9.80665\", \"UNIT\": \"m s-2\", \"OVERRIDABLE\": \"NO\", \"LABEL\": \"the standard acceleration of gravity\"}, {\"NAME\": \"h_max\", \"DIMENSION\": \"L1\", \"SUPPLY\": \"AUTHOR\", \"LABEL\": \"the largest height, above or below the origin, over which the field is taken as uniform\"}], \"SUMS\": [], \"TERMS\": [{\"TARGET\": \"UP_VELOCITY\", \"SIGN\": \"-\", \"EXPR\": \"MASS*g_n\", \"LABEL\": \"the weight\"}], \"ASSUMPTIONS\": [{\"NAME\": \"gravity_uniform\", \"PROPOSITION\": \"the gravitational field is uniform over the region abs({HEIGHT}) < h_max\", \"REFS\": [\"HEIGHT\", \"h_max\"]}, {\"NAME\": \"gravity_standard\", \"PROPOSITION\": \"the local gravitational acceleration equals the conventional standard value g_n\", \"REFS\": [\"g_n\"]}, {\"NAME\": \"frame_inertial\", \"PROPOSITION\": \"the frame in which {HEIGHT} is measured is treated as inertial\", \"REFS\": [\"HEIGHT\"]}], \"BOUNDARIES\": [{\"NAME\": \"gravity_region\", \"PREDICATE\": \"abs({HEIGHT}) < h_max\", \"CONDITION\": \"abs(HEIGHT) < h_max\"}], \"NOT_CHOSEN\": \"No gravity: no weight acts on any DOF.\", \"NOT_INCLUDED\": [\"No variation of gravity with height or latitude beyond what g_n contains.\", \"No Earth rotation (Coriolis or centrifugal force) beyond what g_n contains.\", \"No gravity of bodies other than the Earth.\"], \"EXCLUDES\": [], \"INTERACTS_WITH\": [{\"WITH\": \"AIR-*\", \"QUESTION_ID\": \"BUOYANCY\", \"QUESTION\": \"Does the air's buoyancy (upthrust) act on the body in the system you mean?\", \"YES_LINE\": \"Buoyancy acts (your answer): no module adds it; it acts in this kernel only where one of your own laws states it.\", \"NO_LINE\": \"No buoyancy: the air's upthrust on the body is not included.\"}], \"TEST_BINDINGS\": [{\"NAME\": \"PROJECTILE_2D\", \"TPK\": {\"DOF\": [{\"NAME\": \"t\", \"DIMENSION\": \"T1\"}, {\"NAME\": \"x\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"z\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"v_x\", \"DIMENSION\": \"L1 T-1\"}, {\"NAME\": \"v_z\", \"DIMENSION\": \"L1 T-1\"}], \"CONSTANT\": [{\"NAME\": \"m\", \"DIMENSION\": \"M1\"}], \"LAW\": [{\"NAME\": \"KIN_X\", \"STATEMENT\": \"dx/dt = v_x\", \"REFS\": [\"t\", \"v_x\", \"x\"], \"ROLE\": \"EOM(x)\", \"EQUATION\": \"D(x,t)=v_x\"}, {\"NAME\": \"KIN_Z\", \"STATEMENT\": \"dz/dt = v_z\", \"REFS\": [\"t\", \"v_z\", \"z\"], \"ROLE\": \"EOM(z)\", \"EQUATION\": \"D(z,t)=v_z\"}, {\"NAME\": \"EOM_X\", \"STATEMENT\": \"m dv_x/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_x\"], \"ROLE\": \"EOM(v_x)\", \"EQUATION\": \"m*D(v_x,t)=0\"}, {\"NAME\": \"EOM_Z\", \"STATEMENT\": \"m dv_z/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_z\"], \"ROLE\": \"EOM(v_z)\", \"EQUATION\": \"m*D(v_z,t)=0\"}], \"ASSUMPTION\": [{\"NAME\": \"point_mass\", \"PROPOSITION\": \"the body is treated as a point mass\", \"REFS\": [\"m\"]}]}, \"BIND\": {\"HEIGHT\": [\"z\"], \"MASS\": [\"m\"], \"UP_VELOCITY\": [\"v_z\"]}, \"VALUES\": {\"h_max\": {\"VALUE\": \"100\", \"UNIT\": \"m\"}}, \"ANSWERS\": {}}, {\"NAME\": \"TABLE\", \"TPK\": {\"DOF\": [{\"NAME\": \"t\", \"DIMENSION\": \"T1\"}, {\"NAME\": \"x\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"z\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"v_x\", \"DIMENSION\": \"L1 T-1\"}, {\"NAME\": \"v_z\", \"DIMENSION\": \"L1 T-1\"}], \"CONSTANT\": [{\"NAME\": \"m\", \"DIMENSION\": \"M1\"}], \"LAW\": [{\"NAME\": \"KIN_X\", \"STATEMENT\": \"dx/dt = v_x\", \"REFS\": [\"t\", \"v_x\", \"x\"], \"ROLE\": \"EOM(x)\", \"EQUATION\": \"D(x,t)=v_x\"}, {\"NAME\": \"KIN_Z\", \"STATEMENT\": \"dz/dt = v_z\", \"REFS\": [\"t\", \"v_z\", \"z\"], \"ROLE\": \"CONSTRAINT\", \"EQUATION\": \"D(z,t)=v_z\"}, {\"NAME\": \"EOM_X\", \"STATEMENT\": \"m dv_x/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_x\"], \"ROLE\": \"EOM(v_x)\", \"EQUATION\": \"m*D(v_x,t)=0\"}], \"CONSTRAINT\": [{\"NAME\": \"C_Z\", \"TARGET\": \"z\", \"ACTION\": \"FIX\", \"VALUE\": \"0\", \"UNIT\": \"m\", \"STATEMENT\": \"the puck stays on the table top, z = 0\"}, {\"NAME\": \"C_VZ\", \"TARGET\": \"v_z\", \"ACTION\": \"FIX\", \"VALUE\": \"0\", \"UNIT\": \"m s-1\", \"STATEMENT\": \"the puck has no vertical velocity\"}]}, \"BIND\": {\"HEIGHT\": [\"z\"], \"MASS\": [\"m\"], \"UP_VELOCITY\": [\"v_z\"]}, \"VALUES\": {\"h_max\": {\"VALUE\": \"1\", \"UNIT\": \"m\"}}, \"ANSWERS\": {\"FIXED:v_z\": \"YES\"}}]}",
"{\"ID\": \"MATH\", \"VERSION\": \"1.0.0\", \"TITLE\": \"The mathematical constant pi, as the CONSTANT pi_c\", \"SOURCE\": \"pi to 16 significant digits, 3.141592653589793, the nearest IEEE 754 binary64 value\", \"PREREQUISITES\": [], \"PARAMETERS\": [{\"NAME\": \"pi_c\", \"DIMENSION\": \"1\", \"SUPPLY\": \"DECLARED\", \"VALUE\": \"3.141592653589793\", \"UNIT\": \"1\", \"OVERRIDABLE\": \"NO\", \"LABEL\": \"pi, to 16 significant digits\"}], \"SUMS\": [], \"TERMS\": [], \"ASSUMPTIONS\": [], \"BOUNDARIES\": [], \"NOT_CHOSEN\": \"No mathematical constant: pi exists only if you declare it.\", \"NOT_INCLUDED\": [\"pi_c is pi rounded to 16 significant digits; no other mathematical constant is declared.\"], \"EXCLUDES\": [], \"INTERACTS_WITH\": [], \"TEST_BINDINGS\": [{\"NAME\": \"PROJECTILE_2D\", \"TPK\": {\"DOF\": [{\"NAME\": \"t\", \"DIMENSION\": \"T1\"}, {\"NAME\": \"x\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"z\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"v_x\", \"DIMENSION\": \"L1 T-1\"}, {\"NAME\": \"v_z\", \"DIMENSION\": \"L1 T-1\"}], \"CONSTANT\": [{\"NAME\": \"m\", \"DIMENSION\": \"M1\"}], \"LAW\": [{\"NAME\": \"KIN_X\", \"STATEMENT\": \"dx/dt = v_x\", \"REFS\": [\"t\", \"v_x\", \"x\"], \"ROLE\": \"EOM(x)\", \"EQUATION\": \"D(x,t)=v_x\"}, {\"NAME\": \"KIN_Z\", \"STATEMENT\": \"dz/dt = v_z\", \"REFS\": [\"t\", \"v_z\", \"z\"], \"ROLE\": \"EOM(z)\", \"EQUATION\": \"D(z,t)=v_z\"}, {\"NAME\": \"EOM_X\", \"STATEMENT\": \"m dv_x/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_x\"], \"ROLE\": \"EOM(v_x)\", \"EQUATION\": \"m*D(v_x,t)=0\"}, {\"NAME\": \"EOM_Z\", \"STATEMENT\": \"m dv_z/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_z\"], \"ROLE\": \"EOM(v_z)\", \"EQUATION\": \"m*D(v_z,t)=0\"}], \"ASSUMPTION\": [{\"NAME\": \"point_mass\", \"PROPOSITION\": \"the body is treated as a point mass\", \"REFS\": [\"m\"]}]}, \"BIND\": {}, \"VALUES\": {}, \"ANSWERS\": {}}]}"
]
},
"expected": "[\"REFUSED\",\"CLAIM GRAV-UNIFORM 1.0.0: TERM 1: v_z's equation of motion is not determined (OVER); resolve it, then bind the module\"]",
"fn": "module_expand",
"hand_checked": true,
"name": "X56 two equations of motion for the target (OVER)"
},
{
"args": {
"claims": [
{
"ANSWERS": {},
"BIND": {
"VELOCITY": [
"v_x",
"v_z"
]
},
"DIGEST": "d2c0eaf665eb165b5c7e311008011349e146564f0679f8ca32f5c98a5924bd8b",
"ID": "TEST-SUMP",
"VALUES": {
"k_q": {}
},
"VERSION": "1.0.0"
}
],
"draft": {
"TPK": {
"ASSUMPTION": [
{
"NAME": "point_mass",
"PROPOSITION": "the body is treated as a point mass",
"REFS": [
"m"
]
}
],
"CONSTANT": [
{
"DIMENSION": "M1",
"NAME": "m"
}
],
"DOF": [
{
"DIMENSION": "T1",
"NAME": "t"
},
{
"DIMENSION": "L1",
"NAME": "x"
},
{
"DIMENSION": "L1",
"NAME": "z"
},
{
"DIMENSION": "L1 T-1",
"NAME": "v_x"
},
{
"DIMENSION": "L1 T-1",
"NAME": "v_z"
}
],
"LAW": [
{
"EQUATION": "D(x,t)=v_x",
"NAME": "KIN_X",
"REFS": [
"t",
"v_x",
"x"
],
"ROLE": "EOM(x)",
"STATEMENT": "dx/dt = v_x"
},
{
"EQUATION": "D(z,t)=v_z",
"NAME": "KIN_Z",
"REFS": [
"t",
"v_z",
"z"
],
"ROLE": "EOM(z)",
"STATEMENT": "dz/dt = v_z"
},
{
"EQUATION": "m*D(v_x,t)=0",
"NAME": "EOM_X",
"REFS": [
"m",
"t",
"v_x"
],
"ROLE": "EOM(v_x)",
"STATEMENT": "m dv_x/dt = 0"
},
{
"EQUATION": "m*D(v_z,t)=0",
"NAME": "EOM_Z",
"REFS": [
"m",
"t",
"v_z"
],
"ROLE": "EOM(v_z)",
"STATEMENT": "m dv_z/dt = 0"
}
]
}
},
"modules": [
"{\"ID\": \"TEST-SUMP\", \"VERSION\": \"1.0.0\", \"TITLE\": \"Test: a sum inside a product\", \"SOURCE\": \"synthetic fixture\", \"PREREQUISITES\": [{\"SLOT\": \"VELOCITY\", \"KIND\": \"DOF\", \"DIMENSION\": \"L1 T-1\", \"MIN\": 1, \"MAX\": 3, \"LABEL\": \"the velocity components of the body, one per axis\"}], \"PARAMETERS\": [{\"NAME\": \"k_q\", \"DIMENSION\": \"L-1 M1\", \"SUPPLY\": \"AUTHOR\", \"LABEL\": \"a quadratic coefficient\"}], \"SUMS\": [{\"NAME\": \"SPEED2\", \"OVER\": \"VELOCITY\", \"EACH\": \"VELOCITY^2\"}], \"TERMS\": [{\"TARGET\": \"VELOCITY\", \"SIGN\": \"-\", \"EXPR\": \"k_q*SPEED2\", \"LABEL\": \"the test force\"}], \"ASSUMPTIONS\": [], \"BOUNDARIES\": [], \"NOT_CHOSEN\": \"No sum test.\", \"NOT_INCLUDED\": [], \"EXCLUDES\": [], \"INTERACTS_WITH\": [], \"TEST_BINDINGS\": [{\"NAME\": \"PROJECTILE_2D\", \"TPK\": {\"DOF\": [{\"NAME\": \"t\", \"DIMENSION\": \"T1\"}, {\"NAME\": \"x\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"z\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"v_x\", \"DIMENSION\": \"L1 T-1\"}, {\"NAME\": \"v_z\", \"DIMENSION\": \"L1 T-1\"}], \"CONSTANT\": [{\"NAME\": \"m\", \"DIMENSION\": \"M1\"}], \"LAW\": [{\"NAME\": \"KIN_X\", \"STATEMENT\": \"dx/dt = v_x\", \"REFS\": [\"t\", \"v_x\", \"x\"], \"ROLE\": \"EOM(x)\", \"EQUATION\": \"D(x,t)=v_x\"}, {\"NAME\": \"KIN_Z\", \"STATEMENT\": \"dz/dt = v_z\", \"REFS\": [\"t\", \"v_z\", \"z\"], \"ROLE\": \"EOM(z)\", \"EQUATION\": \"D(z,t)=v_z\"}, {\"NAME\": \"EOM_X\", \"STATEMENT\": \"m dv_x/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_x\"], \"ROLE\": \"EOM(v_x)\", \"EQUATION\": \"m*D(v_x,t)=0\"}, {\"NAME\": \"EOM_Z\", \"STATEMENT\": \"m dv_z/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_z\"], \"ROLE\": \"EOM(v_z)\", \"EQUATION\": \"m*D(v_z,t)=0\"}], \"ASSUMPTION\": [{\"NAME\": \"point_mass\", \"PROPOSITION\": \"the body is treated as a point mass\", \"REFS\": [\"m\"]}]}, \"BIND\": {\"VELOCITY\": [\"v_x\", \"v_z\"]}, \"VALUES\": {\"k_q\": {}}, \"ANSWERS\": {}}]}"
]
},
"computed": "digests by existing TPC-PY functions over literal data",
"expected": "[\"OK\",[\"D(TPK)\",\"e1cff39ece3129f139b8b74d9e94d7e33718d2a94920165f2f5b6cd471acf187\"],[\"COMPOSED\",[[\"EOM_X\",\"m*D(v_x,t)=-k_q*(v_x^2+v_z^2)\"],[\"EOM_Z\",\"m*D(v_z,t)=-k_q*(v_x^2+v_z^2)\"]]],[\"EMITTED\",[[\"CONSTANT\",\"k_q\",[\"TEST-SUMP 1.0.0\"]]]],[\"DROPPED\",[]]]",
"fn": "module_expand",
"hand_checked": false,
"name": "X57 a sum inside a product keeps its parentheses (3.4)"
},
{
"args": {
"claims": [
"GRAV-UNIFORM"
],
"draft": {
"TPK": {
"ASSUMPTION": [
{
"NAME": "point_mass",
"PROPOSITION": "the body is treated as a point mass",
"REFS": [
"m"
]
}
],
"CONSTANT": [
{
"DIMENSION": "M1",
"NAME": "m"
}
],
"DOF": [
{
"DIMENSION": "T1",
"NAME": "t"
},
{
"DIMENSION": "L1",
"NAME": "x"
},
{
"DIMENSION": "L1",
"NAME": "z"
},
{
"DIMENSION": "L1 T-1",
"NAME": "v_x"
},
{
"DIMENSION": "L1 T-1",
"NAME": "v_z"
}
],
"LAW": [
{
"EQUATION": "D(x,t)=v_x",
"NAME": "KIN_X",
"REFS": [
"t",
"v_x",
"x"
],
"ROLE": "EOM(x)",
"STATEMENT": "dx/dt = v_x"
},
{
"EQUATION": "D(z,t)=v_z",
"NAME": "KIN_Z",
"REFS": [
"t",
"v_z",
"z"
],
"ROLE": "EOM(z)",
"STATEMENT": "dz/dt = v_z"
},
{
"EQUATION": "m*D(v_x,t)=0",
"NAME": "EOM_X",
"REFS": [
"m",
"t",
"v_x"
],
"ROLE": "EOM(v_x)",
"STATEMENT": "m dv_x/dt = 0"
},
{
"EQUATION": "m*D(v_z,t)=0",
"NAME": "EOM_Z",
"REFS": [
"m",
"t",
"v_z"
],
"ROLE": "EOM(v_z)",
"STATEMENT": "m dv_z/dt = 0"
}
]
}
},
"modules": [
"{\"ID\": \"AIR-LINEAR\", \"VERSION\": \"1.0.0\", \"TITLE\": \"Air resistance at sea level, linear in the speed (Stokes drag on a sphere)\", \"SOURCE\": \"ISO 2533:1975, Standard Atmosphere, sea-level values: density 1.225 kg m-3, dynamic viscosity 1.7894e-5 Pa s\", \"PREREQUISITES\": [{\"SLOT\": \"VELOCITY\", \"KIND\": \"DOF\", \"DIMENSION\": \"L1 T-1\", \"MIN\": 1, \"MAX\": 3, \"LABEL\": \"the velocity components of the body, one per axis\"}], \"PARAMETERS\": [{\"NAME\": \"rho_air\", \"DIMENSION\": \"L-3 M1\", \"SUPPLY\": \"DECLARED\", \"VALUE\": \"1.225\", \"UNIT\": \"kg m-3\", \"OVERRIDABLE\": \"NO\", \"LABEL\": \"the density of air at sea level\"}, {\"NAME\": \"mu_air\", \"DIMENSION\": \"L-1 M1 T-1\", \"SUPPLY\": \"DECLARED\", \"VALUE\": \"1.7894e-5\", \"UNIT\": \"Pa s\", \"OVERRIDABLE\": \"NO\", \"LABEL\": \"the dynamic viscosity of air at sea level\"}, {\"NAME\": \"pi_c\", \"DIMENSION\": \"1\", \"SUPPLY\": \"DECLARED\", \"VALUE\": \"3.141592653589793\", \"UNIT\": \"1\", \"OVERRIDABLE\": \"NO\", \"LABEL\": \"pi, to 16 significant digits\"}, {\"NAME\": \"R_s\", \"DIMENSION\": \"L1\", \"SUPPLY\": \"AUTHOR\", \"LABEL\": \"the radius of the sphere\"}], \"SUMS\": [{\"NAME\": \"SPEED2\", \"OVER\": \"VELOCITY\", \"EACH\": \"VELOCITY^2\"}], \"TERMS\": [{\"TARGET\": \"VELOCITY\", \"SIGN\": \"-\", \"EXPR\": \"6*pi_c*mu_air*R_s*VELOCITY\", \"LABEL\": \"the linear (Stokes) drag\"}], \"ASSUMPTIONS\": [{\"NAME\": \"air_still\", \"PROPOSITION\": \"the air is at rest in the frame of the body's velocity\", \"REFS\": [\"VELOCITY\"]}, {\"NAME\": \"air_uniform\", \"PROPOSITION\": \"the air density is uniform over the region of motion\", \"REFS\": [\"rho_air\"]}, {\"NAME\": \"drag_sphere\", \"PROPOSITION\": \"the body is a rigid sphere of radius R_s\", \"REFS\": [\"R_s\"]}], \"BOUNDARIES\": [{\"NAME\": \"drag_linear_regime\", \"PREDICATE\": \"2 rho_air |v| R_s / mu_air < 1: the regime of the linear law\", \"CONDITION\": \"mu_air != 0 and SPEED2 >= 0 and 2*rho_air*sqrt(SPEED2)*R_s/mu_air < 1\"}], \"NOT_CHOSEN\": \"No linear (Stokes) air resistance.\", \"NOT_INCLUDED\": [\"No wind: the air is at rest.\", \"No change of air density or viscosity with altitude or temperature.\", \"No drag outside the regime of the linear law.\"], \"EXCLUDES\": [], \"INTERACTS_WITH\": [], \"TEST_BINDINGS\": [{\"NAME\": \"PROJECTILE_2D\", \"TPK\": {\"DOF\": [{\"NAME\": \"t\", \"DIMENSION\": \"T1\"}, {\"NAME\": \"x\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"z\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"v_x\", \"DIMENSION\": \"L1 T-1\"}, {\"NAME\": \"v_z\", \"DIMENSION\": \"L1 T-1\"}], \"CONSTANT\": [{\"NAME\": \"m\", \"DIMENSION\": \"M1\"}], \"LAW\": [{\"NAME\": \"KIN_X\", \"STATEMENT\": \"dx/dt = v_x\", \"REFS\": [\"t\", \"v_x\", \"x\"], \"ROLE\": \"EOM(x)\", \"EQUATION\": \"D(x,t)=v_x\"}, {\"NAME\": \"KIN_Z\", \"STATEMENT\": \"dz/dt = v_z\", \"REFS\": [\"t\", \"v_z\", \"z\"], \"ROLE\": \"EOM(z)\", \"EQUATION\": \"D(z,t)=v_z\"}, {\"NAME\": \"EOM_X\", \"STATEMENT\": \"m dv_x/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_x\"], \"ROLE\": \"EOM(v_x)\", \"EQUATION\": \"m*D(v_x,t)=0\"}, {\"NAME\": \"EOM_Z\", \"STATEMENT\": \"m dv_z/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_z\"], \"ROLE\": \"EOM(v_z)\", \"EQUATION\": \"m*D(v_z,t)=0\"}], \"ASSUMPTION\": [{\"NAME\": \"point_mass\", \"PROPOSITION\": \"the body is treated as a point mass\", \"REFS\": [\"m\"]}]}, \"BIND\": {\"VELOCITY\": [\"v_x\", \"v_z\"]}, \"VALUES\": {\"R_s\": {}}, \"ANSWERS\": {}}]}",
"{\"ID\": \"AIR-QUADRATIC\", \"VERSION\": \"1.0.0\", \"TITLE\": \"Air resistance at sea level, quadratic in the speed\", \"SOURCE\": \"ISO 2533:1975, Standard Atmosphere, sea-level values: density 1.225 kg m-3, dynamic viscosity 1.7894e-5 Pa s\", \"PREREQUISITES\": [{\"SLOT\": \"VELOCITY\", \"KIND\": \"DOF\", \"DIMENSION\": \"L1 T-1\", \"MIN\": 1, \"MAX\": 3, \"LABEL\": \"the velocity components of the body, one per axis\"}], \"PARAMETERS\": [{\"NAME\": \"rho_air\", \"DIMENSION\": \"L-3 M1\", \"SUPPLY\": \"DECLARED\", \"VALUE\": \"1.225\", \"UNIT\": \"kg m-3\", \"OVERRIDABLE\": \"NO\", \"LABEL\": \"the density of air at sea level\"}, {\"NAME\": \"mu_air\", \"DIMENSION\": \"L-1 M1 T-1\", \"SUPPLY\": \"DECLARED\", \"VALUE\": \"1.7894e-5\", \"UNIT\": \"Pa s\", \"OVERRIDABLE\": \"NO\", \"LABEL\": \"the dynamic viscosity of air at sea level\"}, {\"NAME\": \"C_d\", \"DIMENSION\": \"1\", \"SUPPLY\": \"AUTHOR\", \"LABEL\": \"the drag coefficient of the body\"}, {\"NAME\": \"A_ref\", \"DIMENSION\": \"L2\", \"SUPPLY\": \"AUTHOR\", \"LABEL\": \"the reference area of the drag coefficient\"}, {\"NAME\": \"L_ref\", \"DIMENSION\": \"L1\", \"SUPPLY\": \"AUTHOR\", \"LABEL\": \"the reference length of the Reynolds number\"}], \"SUMS\": [{\"NAME\": \"SPEED2\", \"OVER\": \"VELOCITY\", \"EACH\": \"VELOCITY^2\"}], \"TERMS\": [{\"TARGET\": \"VELOCITY\", \"SIGN\": \"-\", \"EXPR\": \"0.5*rho_air*C_d*A_ref*sqrt(SPEED2)*VELOCITY\", \"LABEL\": \"the quadratic drag\"}], \"ASSUMPTIONS\": [{\"NAME\": \"air_still\", \"PROPOSITION\": \"the air is at rest in the frame of the body's velocity\", \"REFS\": [\"VELOCITY\"]}, {\"NAME\": \"air_uniform\", \"PROPOSITION\": \"the air density is uniform over the region of motion\", \"REFS\": [\"rho_air\"]}, {\"NAME\": \"drag_cd_constant\", \"PROPOSITION\": \"the drag coefficient C_d is constant over the motion\", \"REFS\": [\"C_d\"]}, {\"NAME\": \"drag_no_lift\", \"PROPOSITION\": \"the body experiences no lift force\", \"REFS\": [\"VELOCITY\"]}, {\"NAME\": \"drag_no_magnus\", \"PROPOSITION\": \"the body experiences no Magnus force\", \"REFS\": [\"VELOCITY\"]}], \"BOUNDARIES\": [{\"NAME\": \"drag_quadratic_regime\", \"PREDICATE\": \"1e3 < rho_air |v| L_ref / mu_air < 2e5: the Reynolds window of the quadratic law\", \"CONDITION\": \"mu_air != 0 and SPEED2 >= 0 and rho_air*sqrt(SPEED2)*L_ref/mu_air > 1000 and rho_air*sqrt(SPEED2)*L_ref/mu_air < 200000\"}], \"NOT_CHOSEN\": \"No quadratic air resistance.\", \"NOT_INCLUDED\": [\"No wind: the air is at rest.\", \"No change of air density or viscosity with altitude or temperature.\", \"No lift, Magnus or added-mass force.\", \"No drag outside the Reynolds window of the quadratic law.\"], \"EXCLUDES\": [\"AIR-LINEAR\"], \"INTERACTS_WITH\": [], \"TEST_BINDINGS\": [{\"NAME\": \"PROJECTILE_2D\", \"TPK\": {\"DOF\": [{\"NAME\": \"t\", \"DIMENSION\": \"T1\"}, {\"NAME\": \"x\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"z\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"v_x\", \"DIMENSION\": \"L1 T-1\"}, {\"NAME\": \"v_z\", \"DIMENSION\": \"L1 T-1\"}], \"CONSTANT\": [{\"NAME\": \"m\", \"DIMENSION\": \"M1\"}], \"LAW\": [{\"NAME\": \"KIN_X\", \"STATEMENT\": \"dx/dt = v_x\", \"REFS\": [\"t\", \"v_x\", \"x\"], \"ROLE\": \"EOM(x)\", \"EQUATION\": \"D(x,t)=v_x\"}, {\"NAME\": \"KIN_Z\", \"STATEMENT\": \"dz/dt = v_z\", \"REFS\": [\"t\", \"v_z\", \"z\"], \"ROLE\": \"EOM(z)\", \"EQUATION\": \"D(z,t)=v_z\"}, {\"NAME\": \"EOM_X\", \"STATEMENT\": \"m dv_x/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_x\"], \"ROLE\": \"EOM(v_x)\", \"EQUATION\": \"m*D(v_x,t)=0\"}, {\"NAME\": \"EOM_Z\", \"STATEMENT\": \"m dv_z/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_z\"], \"ROLE\": \"EOM(v_z)\", \"EQUATION\": \"m*D(v_z,t)=0\"}], \"ASSUMPTION\": [{\"NAME\": \"point_mass\", \"PROPOSITION\": \"the body is treated as a point mass\", \"REFS\": [\"m\"]}]}, \"BIND\": {\"VELOCITY\": [\"v_x\", \"v_z\"]}, \"VALUES\": {\"A_ref\": {}, \"C_d\": {}, \"L_ref\": {}}, \"ANSWERS\": {}}]}",
"{\"ID\": \"GRAV-UNIFORM\", \"VERSION\": \"1.0.0\", \"TITLE\": \"Uniform gravity at the standard value g_n\", \"SOURCE\": \"g_n = 9.80665 m s-2, exact by definition: 3rd CGPM (1901), declaration on the unit of mass and on the definition of weight\", \"PREREQUISITES\": [{\"SLOT\": \"MASS\", \"KIND\": \"CONSTANT\", \"DIMENSION\": \"M1\", \"MIN\": 1, \"MAX\": 1, \"LABEL\": \"the mass of the body\"}, {\"SLOT\": \"UP_VELOCITY\", \"KIND\": \"DOF\", \"DIMENSION\": \"L1 T-1\", \"MIN\": 1, \"MAX\": 1, \"LABEL\": \"the velocity component pointing up; its equation of motion receives the weight\"}, {\"SLOT\": \"HEIGHT\", \"KIND\": \"DOF\", \"DIMENSION\": \"L1\", \"MIN\": 1, \"MAX\": 1, \"LABEL\": \"the position along the same upward axis\"}], \"PARAMETERS\": [{\"NAME\": \"g_n\", \"DIMENSION\": \"L1 T-2\", \"SUPPLY\": \"DECLARED\", \"VALUE\": \"9.80665\", \"UNIT\": \"m s-2\", \"OVERRIDABLE\": \"NO\", \"LABEL\": \"the standard acceleration of gravity\"}, {\"NAME\": \"h_max\", \"DIMENSION\": \"L1\", \"SUPPLY\": \"AUTHOR\", \"LABEL\": \"the largest height, above or below the origin, over which the field is taken as uniform\"}], \"SUMS\": [], \"TERMS\": [{\"TARGET\": \"UP_VELOCITY\", \"SIGN\": \"-\", \"EXPR\": \"MASS*g_n\", \"LABEL\": \"the weight\"}], \"ASSUMPTIONS\": [{\"NAME\": \"gravity_uniform\", \"PROPOSITION\": \"the gravitational field is uniform over the region abs({HEIGHT}) < h_max\", \"REFS\": [\"HEIGHT\", \"h_max\"]}, {\"NAME\": \"gravity_standard\", \"PROPOSITION\": \"the local gravitational acceleration equals the conventional standard value g_n\", \"REFS\": [\"g_n\"]}, {\"NAME\": \"frame_inertial\", \"PROPOSITION\": \"the frame in which {HEIGHT} is measured is treated as inertial\", \"REFS\": [\"HEIGHT\"]}], \"BOUNDARIES\": [{\"NAME\": \"gravity_region\", \"PREDICATE\": \"abs({HEIGHT}) < h_max\", \"CONDITION\": \"abs(HEIGHT) < h_max\"}], \"NOT_CHOSEN\": \"No gravity: no weight acts on any DOF.\", \"NOT_INCLUDED\": [\"No variation of gravity with height or latitude beyond what g_n contains.\", \"No Earth rotation (Coriolis or centrifugal force) beyond what g_n contains.\", \"No gravity of bodies other than the Earth.\"], \"EXCLUDES\": [], \"INTERACTS_WITH\": [{\"WITH\": \"AIR-*\", \"QUESTION_ID\": \"BUOYANCY\", \"QUESTION\": \"Does the air's buoyancy (upthrust) act on the body in the system you mean?\", \"YES_LINE\": \"Buoyancy acts (your answer): no module adds it; it acts in this kernel only where one of your own laws states it.\", \"NO_LINE\": \"No buoyancy: the air's upthrust on the body is not included.\"}], \"TEST_BINDINGS\": [{\"NAME\": \"PROJECTILE_2D\", \"TPK\": {\"DOF\": [{\"NAME\": \"t\", \"DIMENSION\": \"T1\"}, {\"NAME\": \"x\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"z\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"v_x\", \"DIMENSION\": \"L1 T-1\"}, {\"NAME\": \"v_z\", \"DIMENSION\": \"L1 T-1\"}], \"CONSTANT\": [{\"NAME\": \"m\", \"DIMENSION\": \"M1\"}], \"LAW\": [{\"NAME\": \"KIN_X\", \"STATEMENT\": \"dx/dt = v_x\", \"REFS\": [\"t\", \"v_x\", \"x\"], \"ROLE\": \"EOM(x)\", \"EQUATION\": \"D(x,t)=v_x\"}, {\"NAME\": \"KIN_Z\", \"STATEMENT\": \"dz/dt = v_z\", \"REFS\": [\"t\", \"v_z\", \"z\"], \"ROLE\": \"EOM(z)\", \"EQUATION\": \"D(z,t)=v_z\"}, {\"NAME\": \"EOM_X\", \"STATEMENT\": \"m dv_x/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_x\"], \"ROLE\": \"EOM(v_x)\", \"EQUATION\": \"m*D(v_x,t)=0\"}, {\"NAME\": \"EOM_Z\", \"STATEMENT\": \"m dv_z/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_z\"], \"ROLE\": \"EOM(v_z)\", \"EQUATION\": \"m*D(v_z,t)=0\"}], \"ASSUMPTION\": [{\"NAME\": \"point_mass\", \"PROPOSITION\": \"the body is treated as a point mass\", \"REFS\": [\"m\"]}]}, \"BIND\": {\"HEIGHT\": [\"z\"], \"MASS\": [\"m\"], \"UP_VELOCITY\": [\"v_z\"]}, \"VALUES\": {\"h_max\": {\"VALUE\": \"100\", \"UNIT\": \"m\"}}, \"ANSWERS\": {}}, {\"NAME\": \"TABLE\", \"TPK\": {\"DOF\": [{\"NAME\": \"t\", \"DIMENSION\": \"T1\"}, {\"NAME\": \"x\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"z\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"v_x\", \"DIMENSION\": \"L1 T-1\"}, {\"NAME\": \"v_z\", \"DIMENSION\": \"L1 T-1\"}], \"CONSTANT\": [{\"NAME\": \"m\", \"DIMENSION\": \"M1\"}], \"LAW\": [{\"NAME\": \"KIN_X\", \"STATEMENT\": \"dx/dt = v_x\", \"REFS\": [\"t\", \"v_x\", \"x\"], \"ROLE\": \"EOM(x)\", \"EQUATION\": \"D(x,t)=v_x\"}, {\"NAME\": \"KIN_Z\", \"STATEMENT\": \"dz/dt = v_z\", \"REFS\": [\"t\", \"v_z\", \"z\"], \"ROLE\": \"CONSTRAINT\", \"EQUATION\": \"D(z,t)=v_z\"}, {\"NAME\": \"EOM_X\", \"STATEMENT\": \"m dv_x/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_x\"], \"ROLE\": \"EOM(v_x)\", \"EQUATION\": \"m*D(v_x,t)=0\"}], \"CONSTRAINT\": [{\"NAME\": \"C_Z\", \"TARGET\": \"z\", \"ACTION\": \"FIX\", \"VALUE\": \"0\", \"UNIT\": \"m\", \"STATEMENT\": \"the puck stays on the table top, z = 0\"}, {\"NAME\": \"C_VZ\", \"TARGET\": \"v_z\", \"ACTION\": \"FIX\", \"VALUE\": \"0\", \"UNIT\": \"m s-1\", \"STATEMENT\": \"the puck has no vertical velocity\"}]}, \"BIND\": {\"HEIGHT\": [\"z\"], \"MASS\": [\"m\"], \"UP_VELOCITY\": [\"v_z\"]}, \"VALUES\": {\"h_max\": {\"VALUE\": \"1\", \"UNIT\": \"m\"}}, \"ANSWERS\": {\"FIXED:v_z\": \"YES\"}}]}",
"{\"ID\": \"MATH\", \"VERSION\": \"1.0.0\", \"TITLE\": \"The mathematical constant pi, as the CONSTANT pi_c\", \"SOURCE\": \"pi to 16 significant digits, 3.141592653589793, the nearest IEEE 754 binary64 value\", \"PREREQUISITES\": [], \"PARAMETERS\": [{\"NAME\": \"pi_c\", \"DIMENSION\": \"1\", \"SUPPLY\": \"DECLARED\", \"VALUE\": \"3.141592653589793\", \"UNIT\": \"1\", \"OVERRIDABLE\": \"NO\", \"LABEL\": \"pi, to 16 significant digits\"}], \"SUMS\": [], \"TERMS\": [], \"ASSUMPTIONS\": [], \"BOUNDARIES\": [], \"NOT_CHOSEN\": \"No mathematical constant: pi exists only if you declare it.\", \"NOT_INCLUDED\": [\"pi_c is pi rounded to 16 significant digits; no other mathematical constant is declared.\"], \"EXCLUDES\": [], \"INTERACTS_WITH\": [], \"TEST_BINDINGS\": [{\"NAME\": \"PROJECTILE_2D\", \"TPK\": {\"DOF\": [{\"NAME\": \"t\", \"DIMENSION\": \"T1\"}, {\"NAME\": \"x\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"z\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"v_x\", \"DIMENSION\": \"L1 T-1\"}, {\"NAME\": \"v_z\", \"DIMENSION\": \"L1 T-1\"}], \"CONSTANT\": [{\"NAME\": \"m\", \"DIMENSION\": \"M1\"}], \"LAW\": [{\"NAME\": \"KIN_X\", \"STATEMENT\": \"dx/dt = v_x\", \"REFS\": [\"t\", \"v_x\", \"x\"], \"ROLE\": \"EOM(x)\", \"EQUATION\": \"D(x,t)=v_x\"}, {\"NAME\": \"KIN_Z\", \"STATEMENT\": \"dz/dt = v_z\", \"REFS\": [\"t\", \"v_z\", \"z\"], \"ROLE\": \"EOM(z)\", \"EQUATION\": \"D(z,t)=v_z\"}, {\"NAME\": \"EOM_X\", \"STATEMENT\": \"m dv_x/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_x\"], \"ROLE\": \"EOM(v_x)\", \"EQUATION\": \"m*D(v_x,t)=0\"}, {\"NAME\": \"EOM_Z\", \"STATEMENT\": \"m dv_z/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_z\"], \"ROLE\": \"EOM(v_z)\", \"EQUATION\": \"m*D(v_z,t)=0\"}], \"ASSUMPTION\": [{\"NAME\": \"point_mass\", \"PROPOSITION\": \"the body is treated as a point mass\", \"REFS\": [\"m\"]}]}, \"BIND\": {}, \"VALUES\": {}, \"ANSWERS\": {}}]}"
]
},
"expected": "[\"REFUSED\",\"CLAIM 1: not an object\"]",
"fn": "module_expand",
"hand_checked": true,
"name": "X58 a claim that is not an object"
},
{
"args": {
"claims": [
{
"ANSWERS": {},
"BIND": {
"HEIGHT": [
"z"
],
"MASS": [
"m"
],
"UP_VELOCITY": [
"v_z"
]
},
"DIGEST": "24877ccb5c8ec300d29ed82ce6650592f35cf8899a3d878ccce9c08d4c72c025",
"ID": "grav",
"VALUES": {
"h_max": {
"UNIT": "m",
"VALUE": "100"
}
},
"VERSION": "1.0.0"
}
],
"draft": {
"TPK": {
"ASSUMPTION": [
{
"NAME": "point_mass",
"PROPOSITION": "the body is treated as a point mass",
"REFS": [
"m"
]
}
],
"CONSTANT": [
{
"DIMENSION": "M1",
"NAME": "m"
}
],
"DOF": [
{
"DIMENSION": "T1",
"NAME": "t"
},
{
"DIMENSION": "L1",
"NAME": "x"
},
{
"DIMENSION": "L1",
"NAME": "z"
},
{
"DIMENSION": "L1 T-1",
"NAME": "v_x"
},
{
"DIMENSION": "L1 T-1",
"NAME": "v_z"
}
],
"LAW": [
{
"EQUATION": "D(x,t)=v_x",
"NAME": "KIN_X",
"REFS": [
"t",
"v_x",
"x"
],
"ROLE": "EOM(x)",
"STATEMENT": "dx/dt = v_x"
},
{
"EQUATION": "D(z,t)=v_z",
"NAME": "KIN_Z",
"REFS": [
"t",
"v_z",
"z"
],
"ROLE": "EOM(z)",
"STATEMENT": "dz/dt = v_z"
},
{
"EQUATION": "m*D(v_x,t)=0",
"NAME": "EOM_X",
"REFS": [
"m",
"t",
"v_x"
],
"ROLE": "EOM(v_x)",
"STATEMENT": "m dv_x/dt = 0"
},
{
"EQUATION": "m*D(v_z,t)=0",
"NAME": "EOM_Z",
"REFS": [
"m",
"t",
"v_z"
],
"ROLE": "EOM(v_z)",
"STATEMENT": "m dv_z/dt = 0"
}
]
}
},
"modules": [
"{\"ID\": \"AIR-LINEAR\", \"VERSION\": \"1.0.0\", \"TITLE\": \"Air resistance at sea level, linear in the speed (Stokes drag on a sphere)\", \"SOURCE\": \"ISO 2533:1975, Standard Atmosphere, sea-level values: density 1.225 kg m-3, dynamic viscosity 1.7894e-5 Pa s\", \"PREREQUISITES\": [{\"SLOT\": \"VELOCITY\", \"KIND\": \"DOF\", \"DIMENSION\": \"L1 T-1\", \"MIN\": 1, \"MAX\": 3, \"LABEL\": \"the velocity components of the body, one per axis\"}], \"PARAMETERS\": [{\"NAME\": \"rho_air\", \"DIMENSION\": \"L-3 M1\", \"SUPPLY\": \"DECLARED\", \"VALUE\": \"1.225\", \"UNIT\": \"kg m-3\", \"OVERRIDABLE\": \"NO\", \"LABEL\": \"the density of air at sea level\"}, {\"NAME\": \"mu_air\", \"DIMENSION\": \"L-1 M1 T-1\", \"SUPPLY\": \"DECLARED\", \"VALUE\": \"1.7894e-5\", \"UNIT\": \"Pa s\", \"OVERRIDABLE\": \"NO\", \"LABEL\": \"the dynamic viscosity of air at sea level\"}, {\"NAME\": \"pi_c\", \"DIMENSION\": \"1\", \"SUPPLY\": \"DECLARED\", \"VALUE\": \"3.141592653589793\", \"UNIT\": \"1\", \"OVERRIDABLE\": \"NO\", \"LABEL\": \"pi, to 16 significant digits\"}, {\"NAME\": \"R_s\", \"DIMENSION\": \"L1\", \"SUPPLY\": \"AUTHOR\", \"LABEL\": \"the radius of the sphere\"}], \"SUMS\": [{\"NAME\": \"SPEED2\", \"OVER\": \"VELOCITY\", \"EACH\": \"VELOCITY^2\"}], \"TERMS\": [{\"TARGET\": \"VELOCITY\", \"SIGN\": \"-\", \"EXPR\": \"6*pi_c*mu_air*R_s*VELOCITY\", \"LABEL\": \"the linear (Stokes) drag\"}], \"ASSUMPTIONS\": [{\"NAME\": \"air_still\", \"PROPOSITION\": \"the air is at rest in the frame of the body's velocity\", \"REFS\": [\"VELOCITY\"]}, {\"NAME\": \"air_uniform\", \"PROPOSITION\": \"the air density is uniform over the region of motion\", \"REFS\": [\"rho_air\"]}, {\"NAME\": \"drag_sphere\", \"PROPOSITION\": \"the body is a rigid sphere of radius R_s\", \"REFS\": [\"R_s\"]}], \"BOUNDARIES\": [{\"NAME\": \"drag_linear_regime\", \"PREDICATE\": \"2 rho_air |v| R_s / mu_air < 1: the regime of the linear law\", \"CONDITION\": \"mu_air != 0 and SPEED2 >= 0 and 2*rho_air*sqrt(SPEED2)*R_s/mu_air < 1\"}], \"NOT_CHOSEN\": \"No linear (Stokes) air resistance.\", \"NOT_INCLUDED\": [\"No wind: the air is at rest.\", \"No change of air density or viscosity with altitude or temperature.\", \"No drag outside the regime of the linear law.\"], \"EXCLUDES\": [], \"INTERACTS_WITH\": [], \"TEST_BINDINGS\": [{\"NAME\": \"PROJECTILE_2D\", \"TPK\": {\"DOF\": [{\"NAME\": \"t\", \"DIMENSION\": \"T1\"}, {\"NAME\": \"x\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"z\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"v_x\", \"DIMENSION\": \"L1 T-1\"}, {\"NAME\": \"v_z\", \"DIMENSION\": \"L1 T-1\"}], \"CONSTANT\": [{\"NAME\": \"m\", \"DIMENSION\": \"M1\"}], \"LAW\": [{\"NAME\": \"KIN_X\", \"STATEMENT\": \"dx/dt = v_x\", \"REFS\": [\"t\", \"v_x\", \"x\"], \"ROLE\": \"EOM(x)\", \"EQUATION\": \"D(x,t)=v_x\"}, {\"NAME\": \"KIN_Z\", \"STATEMENT\": \"dz/dt = v_z\", \"REFS\": [\"t\", \"v_z\", \"z\"], \"ROLE\": \"EOM(z)\", \"EQUATION\": \"D(z,t)=v_z\"}, {\"NAME\": \"EOM_X\", \"STATEMENT\": \"m dv_x/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_x\"], \"ROLE\": \"EOM(v_x)\", \"EQUATION\": \"m*D(v_x,t)=0\"}, {\"NAME\": \"EOM_Z\", \"STATEMENT\": \"m dv_z/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_z\"], \"ROLE\": \"EOM(v_z)\", \"EQUATION\": \"m*D(v_z,t)=0\"}], \"ASSUMPTION\": [{\"NAME\": \"point_mass\", \"PROPOSITION\": \"the body is treated as a point mass\", \"REFS\": [\"m\"]}]}, \"BIND\": {\"VELOCITY\": [\"v_x\", \"v_z\"]}, \"VALUES\": {\"R_s\": {}}, \"ANSWERS\": {}}]}",
"{\"ID\": \"AIR-QUADRATIC\", \"VERSION\": \"1.0.0\", \"TITLE\": \"Air resistance at sea level, quadratic in the speed\", \"SOURCE\": \"ISO 2533:1975, Standard Atmosphere, sea-level values: density 1.225 kg m-3, dynamic viscosity 1.7894e-5 Pa s\", \"PREREQUISITES\": [{\"SLOT\": \"VELOCITY\", \"KIND\": \"DOF\", \"DIMENSION\": \"L1 T-1\", \"MIN\": 1, \"MAX\": 3, \"LABEL\": \"the velocity components of the body, one per axis\"}], \"PARAMETERS\": [{\"NAME\": \"rho_air\", \"DIMENSION\": \"L-3 M1\", \"SUPPLY\": \"DECLARED\", \"VALUE\": \"1.225\", \"UNIT\": \"kg m-3\", \"OVERRIDABLE\": \"NO\", \"LABEL\": \"the density of air at sea level\"}, {\"NAME\": \"mu_air\", \"DIMENSION\": \"L-1 M1 T-1\", \"SUPPLY\": \"DECLARED\", \"VALUE\": \"1.7894e-5\", \"UNIT\": \"Pa s\", \"OVERRIDABLE\": \"NO\", \"LABEL\": \"the dynamic viscosity of air at sea level\"}, {\"NAME\": \"C_d\", \"DIMENSION\": \"1\", \"SUPPLY\": \"AUTHOR\", \"LABEL\": \"the drag coefficient of the body\"}, {\"NAME\": \"A_ref\", \"DIMENSION\": \"L2\", \"SUPPLY\": \"AUTHOR\", \"LABEL\": \"the reference area of the drag coefficient\"}, {\"NAME\": \"L_ref\", \"DIMENSION\": \"L1\", \"SUPPLY\": \"AUTHOR\", \"LABEL\": \"the reference length of the Reynolds number\"}], \"SUMS\": [{\"NAME\": \"SPEED2\", \"OVER\": \"VELOCITY\", \"EACH\": \"VELOCITY^2\"}], \"TERMS\": [{\"TARGET\": \"VELOCITY\", \"SIGN\": \"-\", \"EXPR\": \"0.5*rho_air*C_d*A_ref*sqrt(SPEED2)*VELOCITY\", \"LABEL\": \"the quadratic drag\"}], \"ASSUMPTIONS\": [{\"NAME\": \"air_still\", \"PROPOSITION\": \"the air is at rest in the frame of the body's velocity\", \"REFS\": [\"VELOCITY\"]}, {\"NAME\": \"air_uniform\", \"PROPOSITION\": \"the air density is uniform over the region of motion\", \"REFS\": [\"rho_air\"]}, {\"NAME\": \"drag_cd_constant\", \"PROPOSITION\": \"the drag coefficient C_d is constant over the motion\", \"REFS\": [\"C_d\"]}, {\"NAME\": \"drag_no_lift\", \"PROPOSITION\": \"the body experiences no lift force\", \"REFS\": [\"VELOCITY\"]}, {\"NAME\": \"drag_no_magnus\", \"PROPOSITION\": \"the body experiences no Magnus force\", \"REFS\": [\"VELOCITY\"]}], \"BOUNDARIES\": [{\"NAME\": \"drag_quadratic_regime\", \"PREDICATE\": \"1e3 < rho_air |v| L_ref / mu_air < 2e5: the Reynolds window of the quadratic law\", \"CONDITION\": \"mu_air != 0 and SPEED2 >= 0 and rho_air*sqrt(SPEED2)*L_ref/mu_air > 1000 and rho_air*sqrt(SPEED2)*L_ref/mu_air < 200000\"}], \"NOT_CHOSEN\": \"No quadratic air resistance.\", \"NOT_INCLUDED\": [\"No wind: the air is at rest.\", \"No change of air density or viscosity with altitude or temperature.\", \"No lift, Magnus or added-mass force.\", \"No drag outside the Reynolds window of the quadratic law.\"], \"EXCLUDES\": [\"AIR-LINEAR\"], \"INTERACTS_WITH\": [], \"TEST_BINDINGS\": [{\"NAME\": \"PROJECTILE_2D\", \"TPK\": {\"DOF\": [{\"NAME\": \"t\", \"DIMENSION\": \"T1\"}, {\"NAME\": \"x\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"z\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"v_x\", \"DIMENSION\": \"L1 T-1\"}, {\"NAME\": \"v_z\", \"DIMENSION\": \"L1 T-1\"}], \"CONSTANT\": [{\"NAME\": \"m\", \"DIMENSION\": \"M1\"}], \"LAW\": [{\"NAME\": \"KIN_X\", \"STATEMENT\": \"dx/dt = v_x\", \"REFS\": [\"t\", \"v_x\", \"x\"], \"ROLE\": \"EOM(x)\", \"EQUATION\": \"D(x,t)=v_x\"}, {\"NAME\": \"KIN_Z\", \"STATEMENT\": \"dz/dt = v_z\", \"REFS\": [\"t\", \"v_z\", \"z\"], \"ROLE\": \"EOM(z)\", \"EQUATION\": \"D(z,t)=v_z\"}, {\"NAME\": \"EOM_X\", \"STATEMENT\": \"m dv_x/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_x\"], \"ROLE\": \"EOM(v_x)\", \"EQUATION\": \"m*D(v_x,t)=0\"}, {\"NAME\": \"EOM_Z\", \"STATEMENT\": \"m dv_z/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_z\"], \"ROLE\": \"EOM(v_z)\", \"EQUATION\": \"m*D(v_z,t)=0\"}], \"ASSUMPTION\": [{\"NAME\": \"point_mass\", \"PROPOSITION\": \"the body is treated as a point mass\", \"REFS\": [\"m\"]}]}, \"BIND\": {\"VELOCITY\": [\"v_x\", \"v_z\"]}, \"VALUES\": {\"A_ref\": {}, \"C_d\": {}, \"L_ref\": {}}, \"ANSWERS\": {}}]}",
"{\"ID\": \"GRAV-UNIFORM\", \"VERSION\": \"1.0.0\", \"TITLE\": \"Uniform gravity at the standard value g_n\", \"SOURCE\": \"g_n = 9.80665 m s-2, exact by definition: 3rd CGPM (1901), declaration on the unit of mass and on the definition of weight\", \"PREREQUISITES\": [{\"SLOT\": \"MASS\", \"KIND\": \"CONSTANT\", \"DIMENSION\": \"M1\", \"MIN\": 1, \"MAX\": 1, \"LABEL\": \"the mass of the body\"}, {\"SLOT\": \"UP_VELOCITY\", \"KIND\": \"DOF\", \"DIMENSION\": \"L1 T-1\", \"MIN\": 1, \"MAX\": 1, \"LABEL\": \"the velocity component pointing up; its equation of motion receives the weight\"}, {\"SLOT\": \"HEIGHT\", \"KIND\": \"DOF\", \"DIMENSION\": \"L1\", \"MIN\": 1, \"MAX\": 1, \"LABEL\": \"the position along the same upward axis\"}], \"PARAMETERS\": [{\"NAME\": \"g_n\", \"DIMENSION\": \"L1 T-2\", \"SUPPLY\": \"DECLARED\", \"VALUE\": \"9.80665\", \"UNIT\": \"m s-2\", \"OVERRIDABLE\": \"NO\", \"LABEL\": \"the standard acceleration of gravity\"}, {\"NAME\": \"h_max\", \"DIMENSION\": \"L1\", \"SUPPLY\": \"AUTHOR\", \"LABEL\": \"the largest height, above or below the origin, over which the field is taken as uniform\"}], \"SUMS\": [], \"TERMS\": [{\"TARGET\": \"UP_VELOCITY\", \"SIGN\": \"-\", \"EXPR\": \"MASS*g_n\", \"LABEL\": \"the weight\"}], \"ASSUMPTIONS\": [{\"NAME\": \"gravity_uniform\", \"PROPOSITION\": \"the gravitational field is uniform over the region abs({HEIGHT}) < h_max\", \"REFS\": [\"HEIGHT\", \"h_max\"]}, {\"NAME\": \"gravity_standard\", \"PROPOSITION\": \"the local gravitational acceleration equals the conventional standard value g_n\", \"REFS\": [\"g_n\"]}, {\"NAME\": \"frame_inertial\", \"PROPOSITION\": \"the frame in which {HEIGHT} is measured is treated as inertial\", \"REFS\": [\"HEIGHT\"]}], \"BOUNDARIES\": [{\"NAME\": \"gravity_region\", \"PREDICATE\": \"abs({HEIGHT}) < h_max\", \"CONDITION\": \"abs(HEIGHT) < h_max\"}], \"NOT_CHOSEN\": \"No gravity: no weight acts on any DOF.\", \"NOT_INCLUDED\": [\"No variation of gravity with height or latitude beyond what g_n contains.\", \"No Earth rotation (Coriolis or centrifugal force) beyond what g_n contains.\", \"No gravity of bodies other than the Earth.\"], \"EXCLUDES\": [], \"INTERACTS_WITH\": [{\"WITH\": \"AIR-*\", \"QUESTION_ID\": \"BUOYANCY\", \"QUESTION\": \"Does the air's buoyancy (upthrust) act on the body in the system you mean?\", \"YES_LINE\": \"Buoyancy acts (your answer): no module adds it; it acts in this kernel only where one of your own laws states it.\", \"NO_LINE\": \"No buoyancy: the air's upthrust on the body is not included.\"}], \"TEST_BINDINGS\": [{\"NAME\": \"PROJECTILE_2D\", \"TPK\": {\"DOF\": [{\"NAME\": \"t\", \"DIMENSION\": \"T1\"}, {\"NAME\": \"x\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"z\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"v_x\", \"DIMENSION\": \"L1 T-1\"}, {\"NAME\": \"v_z\", \"DIMENSION\": \"L1 T-1\"}], \"CONSTANT\": [{\"NAME\": \"m\", \"DIMENSION\": \"M1\"}], \"LAW\": [{\"NAME\": \"KIN_X\", \"STATEMENT\": \"dx/dt = v_x\", \"REFS\": [\"t\", \"v_x\", \"x\"], \"ROLE\": \"EOM(x)\", \"EQUATION\": \"D(x,t)=v_x\"}, {\"NAME\": \"KIN_Z\", \"STATEMENT\": \"dz/dt = v_z\", \"REFS\": [\"t\", \"v_z\", \"z\"], \"ROLE\": \"EOM(z)\", \"EQUATION\": \"D(z,t)=v_z\"}, {\"NAME\": \"EOM_X\", \"STATEMENT\": \"m dv_x/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_x\"], \"ROLE\": \"EOM(v_x)\", \"EQUATION\": \"m*D(v_x,t)=0\"}, {\"NAME\": \"EOM_Z\", \"STATEMENT\": \"m dv_z/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_z\"], \"ROLE\": \"EOM(v_z)\", \"EQUATION\": \"m*D(v_z,t)=0\"}], \"ASSUMPTION\": [{\"NAME\": \"point_mass\", \"PROPOSITION\": \"the body is treated as a point mass\", \"REFS\": [\"m\"]}]}, \"BIND\": {\"HEIGHT\": [\"z\"], \"MASS\": [\"m\"], \"UP_VELOCITY\": [\"v_z\"]}, \"VALUES\": {\"h_max\": {\"VALUE\": \"100\", \"UNIT\": \"m\"}}, \"ANSWERS\": {}}, {\"NAME\": \"TABLE\", \"TPK\": {\"DOF\": [{\"NAME\": \"t\", \"DIMENSION\": \"T1\"}, {\"NAME\": \"x\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"z\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"v_x\", \"DIMENSION\": \"L1 T-1\"}, {\"NAME\": \"v_z\", \"DIMENSION\": \"L1 T-1\"}], \"CONSTANT\": [{\"NAME\": \"m\", \"DIMENSION\": \"M1\"}], \"LAW\": [{\"NAME\": \"KIN_X\", \"STATEMENT\": \"dx/dt = v_x\", \"REFS\": [\"t\", \"v_x\", \"x\"], \"ROLE\": \"EOM(x)\", \"EQUATION\": \"D(x,t)=v_x\"}, {\"NAME\": \"KIN_Z\", \"STATEMENT\": \"dz/dt = v_z\", \"REFS\": [\"t\", \"v_z\", \"z\"], \"ROLE\": \"CONSTRAINT\", \"EQUATION\": \"D(z,t)=v_z\"}, {\"NAME\": \"EOM_X\", \"STATEMENT\": \"m dv_x/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_x\"], \"ROLE\": \"EOM(v_x)\", \"EQUATION\": \"m*D(v_x,t)=0\"}], \"CONSTRAINT\": [{\"NAME\": \"C_Z\", \"TARGET\": \"z\", \"ACTION\": \"FIX\", \"VALUE\": \"0\", \"UNIT\": \"m\", \"STATEMENT\": \"the puck stays on the table top, z = 0\"}, {\"NAME\": \"C_VZ\", \"TARGET\": \"v_z\", \"ACTION\": \"FIX\", \"VALUE\": \"0\", \"UNIT\": \"m s-1\", \"STATEMENT\": \"the puck has no vertical velocity\"}]}, \"BIND\": {\"HEIGHT\": [\"z\"], \"MASS\": [\"m\"], \"UP_VELOCITY\": [\"v_z\"]}, \"VALUES\": {\"h_max\": {\"VALUE\": \"1\", \"UNIT\": \"m\"}}, \"ANSWERS\": {\"FIXED:v_z\": \"YES\"}}]}",
"{\"ID\": \"MATH\", \"VERSION\": \"1.0.0\", \"TITLE\": \"The mathematical constant pi, as the CONSTANT pi_c\", \"SOURCE\": \"pi to 16 significant digits, 3.141592653589793, the nearest IEEE 754 binary64 value\", \"PREREQUISITES\": [], \"PARAMETERS\": [{\"NAME\": \"pi_c\", \"DIMENSION\": \"1\", \"SUPPLY\": \"DECLARED\", \"VALUE\": \"3.141592653589793\", \"UNIT\": \"1\", \"OVERRIDABLE\": \"NO\", \"LABEL\": \"pi, to 16 significant digits\"}], \"SUMS\": [], \"TERMS\": [], \"ASSUMPTIONS\": [], \"BOUNDARIES\": [], \"NOT_CHOSEN\": \"No mathematical constant: pi exists only if you declare it.\", \"NOT_INCLUDED\": [\"pi_c is pi rounded to 16 significant digits; no other mathematical constant is declared.\"], \"EXCLUDES\": [], \"INTERACTS_WITH\": [], \"TEST_BINDINGS\": [{\"NAME\": \"PROJECTILE_2D\", \"TPK\": {\"DOF\": [{\"NAME\": \"t\", \"DIMENSION\": \"T1\"}, {\"NAME\": \"x\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"z\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"v_x\", \"DIMENSION\": \"L1 T-1\"}, {\"NAME\": \"v_z\", \"DIMENSION\": \"L1 T-1\"}], \"CONSTANT\": [{\"NAME\": \"m\", \"DIMENSION\": \"M1\"}], \"LAW\": [{\"NAME\": \"KIN_X\", \"STATEMENT\": \"dx/dt = v_x\", \"REFS\": [\"t\", \"v_x\", \"x\"], \"ROLE\": \"EOM(x)\", \"EQUATION\": \"D(x,t)=v_x\"}, {\"NAME\": \"KIN_Z\", \"STATEMENT\": \"dz/dt = v_z\", \"REFS\": [\"t\", \"v_z\", \"z\"], \"ROLE\": \"EOM(z)\", \"EQUATION\": \"D(z,t)=v_z\"}, {\"NAME\": \"EOM_X\", \"STATEMENT\": \"m dv_x/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_x\"], \"ROLE\": \"EOM(v_x)\", \"EQUATION\": \"m*D(v_x,t)=0\"}, {\"NAME\": \"EOM_Z\", \"STATEMENT\": \"m dv_z/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_z\"], \"ROLE\": \"EOM(v_z)\", \"EQUATION\": \"m*D(v_z,t)=0\"}], \"ASSUMPTION\": [{\"NAME\": \"point_mass\", \"PROPOSITION\": \"the body is treated as a point mass\", \"REFS\": [\"m\"]}]}, \"BIND\": {}, \"VALUES\": {}, \"ANSWERS\": {}}]}"
]
},
"expected": "[\"REFUSED\",\"CLAIM 1: ID is not a module ID\"]",
"fn": "module_expand",
"hand_checked": true,
"name": "X59 a claim ID that is not a module ID"
},
{
"args": {
"claims": [
{
"ANSWERS": {},
"BIND": {
"HEIGHT": [
"z"
],
"MASS": [
"m"
],
"UP_VELOCITY": [
"v_z"
]
},
"DIGEST": "24877ccb5c8ec300d29ed82ce6650592f35cf8899a3d878ccce9c08d4c72c025",
"ID": "GRAV-UNIFORM",
"VALUES": {
"h_max": {
"UNIT": "m",
"VALUE": "100"
}
},
"VERSION": "1"
}
],
"draft": {
"TPK": {
"ASSUMPTION": [
{
"NAME": "point_mass",
"PROPOSITION": "the body is treated as a point mass",
"REFS": [
"m"
]
}
],
"CONSTANT": [
{
"DIMENSION": "M1",
"NAME": "m"
}
],
"DOF": [
{
"DIMENSION": "T1",
"NAME": "t"
},
{
"DIMENSION": "L1",
"NAME": "x"
},
{
"DIMENSION": "L1",
"NAME": "z"
},
{
"DIMENSION": "L1 T-1",
"NAME": "v_x"
},
{
"DIMENSION": "L1 T-1",
"NAME": "v_z"
}
],
"LAW": [
{
"EQUATION": "D(x,t)=v_x",
"NAME": "KIN_X",
"REFS": [
"t",
"v_x",
"x"
],
"ROLE": "EOM(x)",
"STATEMENT": "dx/dt = v_x"
},
{
"EQUATION": "D(z,t)=v_z",
"NAME": "KIN_Z",
"REFS": [
"t",
"v_z",
"z"
],
"ROLE": "EOM(z)",
"STATEMENT": "dz/dt = v_z"
},
{
"EQUATION": "m*D(v_x,t)=0",
"NAME": "EOM_X",
"REFS": [
"m",
"t",
"v_x"
],
"ROLE": "EOM(v_x)",
"STATEMENT": "m dv_x/dt = 0"
},
{
"EQUATION": "m*D(v_z,t)=0",
"NAME": "EOM_Z",
"REFS": [
"m",
"t",
"v_z"
],
"ROLE": "EOM(v_z)",
"STATEMENT": "m dv_z/dt = 0"
}
]
}
},
"modules": [
"{\"ID\": \"AIR-LINEAR\", \"VERSION\": \"1.0.0\", \"TITLE\": \"Air resistance at sea level, linear in the speed (Stokes drag on a sphere)\", \"SOURCE\": \"ISO 2533:1975, Standard Atmosphere, sea-level values: density 1.225 kg m-3, dynamic viscosity 1.7894e-5 Pa s\", \"PREREQUISITES\": [{\"SLOT\": \"VELOCITY\", \"KIND\": \"DOF\", \"DIMENSION\": \"L1 T-1\", \"MIN\": 1, \"MAX\": 3, \"LABEL\": \"the velocity components of the body, one per axis\"}], \"PARAMETERS\": [{\"NAME\": \"rho_air\", \"DIMENSION\": \"L-3 M1\", \"SUPPLY\": \"DECLARED\", \"VALUE\": \"1.225\", \"UNIT\": \"kg m-3\", \"OVERRIDABLE\": \"NO\", \"LABEL\": \"the density of air at sea level\"}, {\"NAME\": \"mu_air\", \"DIMENSION\": \"L-1 M1 T-1\", \"SUPPLY\": \"DECLARED\", \"VALUE\": \"1.7894e-5\", \"UNIT\": \"Pa s\", \"OVERRIDABLE\": \"NO\", \"LABEL\": \"the dynamic viscosity of air at sea level\"}, {\"NAME\": \"pi_c\", \"DIMENSION\": \"1\", \"SUPPLY\": \"DECLARED\", \"VALUE\": \"3.141592653589793\", \"UNIT\": \"1\", \"OVERRIDABLE\": \"NO\", \"LABEL\": \"pi, to 16 significant digits\"}, {\"NAME\": \"R_s\", \"DIMENSION\": \"L1\", \"SUPPLY\": \"AUTHOR\", \"LABEL\": \"the radius of the sphere\"}], \"SUMS\": [{\"NAME\": \"SPEED2\", \"OVER\": \"VELOCITY\", \"EACH\": \"VELOCITY^2\"}], \"TERMS\": [{\"TARGET\": \"VELOCITY\", \"SIGN\": \"-\", \"EXPR\": \"6*pi_c*mu_air*R_s*VELOCITY\", \"LABEL\": \"the linear (Stokes) drag\"}], \"ASSUMPTIONS\": [{\"NAME\": \"air_still\", \"PROPOSITION\": \"the air is at rest in the frame of the body's velocity\", \"REFS\": [\"VELOCITY\"]}, {\"NAME\": \"air_uniform\", \"PROPOSITION\": \"the air density is uniform over the region of motion\", \"REFS\": [\"rho_air\"]}, {\"NAME\": \"drag_sphere\", \"PROPOSITION\": \"the body is a rigid sphere of radius R_s\", \"REFS\": [\"R_s\"]}], \"BOUNDARIES\": [{\"NAME\": \"drag_linear_regime\", \"PREDICATE\": \"2 rho_air |v| R_s / mu_air < 1: the regime of the linear law\", \"CONDITION\": \"mu_air != 0 and SPEED2 >= 0 and 2*rho_air*sqrt(SPEED2)*R_s/mu_air < 1\"}], \"NOT_CHOSEN\": \"No linear (Stokes) air resistance.\", \"NOT_INCLUDED\": [\"No wind: the air is at rest.\", \"No change of air density or viscosity with altitude or temperature.\", \"No drag outside the regime of the linear law.\"], \"EXCLUDES\": [], \"INTERACTS_WITH\": [], \"TEST_BINDINGS\": [{\"NAME\": \"PROJECTILE_2D\", \"TPK\": {\"DOF\": [{\"NAME\": \"t\", \"DIMENSION\": \"T1\"}, {\"NAME\": \"x\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"z\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"v_x\", \"DIMENSION\": \"L1 T-1\"}, {\"NAME\": \"v_z\", \"DIMENSION\": \"L1 T-1\"}], \"CONSTANT\": [{\"NAME\": \"m\", \"DIMENSION\": \"M1\"}], \"LAW\": [{\"NAME\": \"KIN_X\", \"STATEMENT\": \"dx/dt = v_x\", \"REFS\": [\"t\", \"v_x\", \"x\"], \"ROLE\": \"EOM(x)\", \"EQUATION\": \"D(x,t)=v_x\"}, {\"NAME\": \"KIN_Z\", \"STATEMENT\": \"dz/dt = v_z\", \"REFS\": [\"t\", \"v_z\", \"z\"], \"ROLE\": \"EOM(z)\", \"EQUATION\": \"D(z,t)=v_z\"}, {\"NAME\": \"EOM_X\", \"STATEMENT\": \"m dv_x/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_x\"], \"ROLE\": \"EOM(v_x)\", \"EQUATION\": \"m*D(v_x,t)=0\"}, {\"NAME\": \"EOM_Z\", \"STATEMENT\": \"m dv_z/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_z\"], \"ROLE\": \"EOM(v_z)\", \"EQUATION\": \"m*D(v_z,t)=0\"}], \"ASSUMPTION\": [{\"NAME\": \"point_mass\", \"PROPOSITION\": \"the body is treated as a point mass\", \"REFS\": [\"m\"]}]}, \"BIND\": {\"VELOCITY\": [\"v_x\", \"v_z\"]}, \"VALUES\": {\"R_s\": {}}, \"ANSWERS\": {}}]}",
"{\"ID\": \"AIR-QUADRATIC\", \"VERSION\": \"1.0.0\", \"TITLE\": \"Air resistance at sea level, quadratic in the speed\", \"SOURCE\": \"ISO 2533:1975, Standard Atmosphere, sea-level values: density 1.225 kg m-3, dynamic viscosity 1.7894e-5 Pa s\", \"PREREQUISITES\": [{\"SLOT\": \"VELOCITY\", \"KIND\": \"DOF\", \"DIMENSION\": \"L1 T-1\", \"MIN\": 1, \"MAX\": 3, \"LABEL\": \"the velocity components of the body, one per axis\"}], \"PARAMETERS\": [{\"NAME\": \"rho_air\", \"DIMENSION\": \"L-3 M1\", \"SUPPLY\": \"DECLARED\", \"VALUE\": \"1.225\", \"UNIT\": \"kg m-3\", \"OVERRIDABLE\": \"NO\", \"LABEL\": \"the density of air at sea level\"}, {\"NAME\": \"mu_air\", \"DIMENSION\": \"L-1 M1 T-1\", \"SUPPLY\": \"DECLARED\", \"VALUE\": \"1.7894e-5\", \"UNIT\": \"Pa s\", \"OVERRIDABLE\": \"NO\", \"LABEL\": \"the dynamic viscosity of air at sea level\"}, {\"NAME\": \"C_d\", \"DIMENSION\": \"1\", \"SUPPLY\": \"AUTHOR\", \"LABEL\": \"the drag coefficient of the body\"}, {\"NAME\": \"A_ref\", \"DIMENSION\": \"L2\", \"SUPPLY\": \"AUTHOR\", \"LABEL\": \"the reference area of the drag coefficient\"}, {\"NAME\": \"L_ref\", \"DIMENSION\": \"L1\", \"SUPPLY\": \"AUTHOR\", \"LABEL\": \"the reference length of the Reynolds number\"}], \"SUMS\": [{\"NAME\": \"SPEED2\", \"OVER\": \"VELOCITY\", \"EACH\": \"VELOCITY^2\"}], \"TERMS\": [{\"TARGET\": \"VELOCITY\", \"SIGN\": \"-\", \"EXPR\": \"0.5*rho_air*C_d*A_ref*sqrt(SPEED2)*VELOCITY\", \"LABEL\": \"the quadratic drag\"}], \"ASSUMPTIONS\": [{\"NAME\": \"air_still\", \"PROPOSITION\": \"the air is at rest in the frame of the body's velocity\", \"REFS\": [\"VELOCITY\"]}, {\"NAME\": \"air_uniform\", \"PROPOSITION\": \"the air density is uniform over the region of motion\", \"REFS\": [\"rho_air\"]}, {\"NAME\": \"drag_cd_constant\", \"PROPOSITION\": \"the drag coefficient C_d is constant over the motion\", \"REFS\": [\"C_d\"]}, {\"NAME\": \"drag_no_lift\", \"PROPOSITION\": \"the body experiences no lift force\", \"REFS\": [\"VELOCITY\"]}, {\"NAME\": \"drag_no_magnus\", \"PROPOSITION\": \"the body experiences no Magnus force\", \"REFS\": [\"VELOCITY\"]}], \"BOUNDARIES\": [{\"NAME\": \"drag_quadratic_regime\", \"PREDICATE\": \"1e3 < rho_air |v| L_ref / mu_air < 2e5: the Reynolds window of the quadratic law\", \"CONDITION\": \"mu_air != 0 and SPEED2 >= 0 and rho_air*sqrt(SPEED2)*L_ref/mu_air > 1000 and rho_air*sqrt(SPEED2)*L_ref/mu_air < 200000\"}], \"NOT_CHOSEN\": \"No quadratic air resistance.\", \"NOT_INCLUDED\": [\"No wind: the air is at rest.\", \"No change of air density or viscosity with altitude or temperature.\", \"No lift, Magnus or added-mass force.\", \"No drag outside the Reynolds window of the quadratic law.\"], \"EXCLUDES\": [\"AIR-LINEAR\"], \"INTERACTS_WITH\": [], \"TEST_BINDINGS\": [{\"NAME\": \"PROJECTILE_2D\", \"TPK\": {\"DOF\": [{\"NAME\": \"t\", \"DIMENSION\": \"T1\"}, {\"NAME\": \"x\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"z\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"v_x\", \"DIMENSION\": \"L1 T-1\"}, {\"NAME\": \"v_z\", \"DIMENSION\": \"L1 T-1\"}], \"CONSTANT\": [{\"NAME\": \"m\", \"DIMENSION\": \"M1\"}], \"LAW\": [{\"NAME\": \"KIN_X\", \"STATEMENT\": \"dx/dt = v_x\", \"REFS\": [\"t\", \"v_x\", \"x\"], \"ROLE\": \"EOM(x)\", \"EQUATION\": \"D(x,t)=v_x\"}, {\"NAME\": \"KIN_Z\", \"STATEMENT\": \"dz/dt = v_z\", \"REFS\": [\"t\", \"v_z\", \"z\"], \"ROLE\": \"EOM(z)\", \"EQUATION\": \"D(z,t)=v_z\"}, {\"NAME\": \"EOM_X\", \"STATEMENT\": \"m dv_x/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_x\"], \"ROLE\": \"EOM(v_x)\", \"EQUATION\": \"m*D(v_x,t)=0\"}, {\"NAME\": \"EOM_Z\", \"STATEMENT\": \"m dv_z/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_z\"], \"ROLE\": \"EOM(v_z)\", \"EQUATION\": \"m*D(v_z,t)=0\"}], \"ASSUMPTION\": [{\"NAME\": \"point_mass\", \"PROPOSITION\": \"the body is treated as a point mass\", \"REFS\": [\"m\"]}]}, \"BIND\": {\"VELOCITY\": [\"v_x\", \"v_z\"]}, \"VALUES\": {\"A_ref\": {}, \"C_d\": {}, \"L_ref\": {}}, \"ANSWERS\": {}}]}",
"{\"ID\": \"GRAV-UNIFORM\", \"VERSION\": \"1.0.0\", \"TITLE\": \"Uniform gravity at the standard value g_n\", \"SOURCE\": \"g_n = 9.80665 m s-2, exact by definition: 3rd CGPM (1901), declaration on the unit of mass and on the definition of weight\", \"PREREQUISITES\": [{\"SLOT\": \"MASS\", \"KIND\": \"CONSTANT\", \"DIMENSION\": \"M1\", \"MIN\": 1, \"MAX\": 1, \"LABEL\": \"the mass of the body\"}, {\"SLOT\": \"UP_VELOCITY\", \"KIND\": \"DOF\", \"DIMENSION\": \"L1 T-1\", \"MIN\": 1, \"MAX\": 1, \"LABEL\": \"the velocity component pointing up; its equation of motion receives the weight\"}, {\"SLOT\": \"HEIGHT\", \"KIND\": \"DOF\", \"DIMENSION\": \"L1\", \"MIN\": 1, \"MAX\": 1, \"LABEL\": \"the position along the same upward axis\"}], \"PARAMETERS\": [{\"NAME\": \"g_n\", \"DIMENSION\": \"L1 T-2\", \"SUPPLY\": \"DECLARED\", \"VALUE\": \"9.80665\", \"UNIT\": \"m s-2\", \"OVERRIDABLE\": \"NO\", \"LABEL\": \"the standard acceleration of gravity\"}, {\"NAME\": \"h_max\", \"DIMENSION\": \"L1\", \"SUPPLY\": \"AUTHOR\", \"LABEL\": \"the largest height, above or below the origin, over which the field is taken as uniform\"}], \"SUMS\": [], \"TERMS\": [{\"TARGET\": \"UP_VELOCITY\", \"SIGN\": \"-\", \"EXPR\": \"MASS*g_n\", \"LABEL\": \"the weight\"}], \"ASSUMPTIONS\": [{\"NAME\": \"gravity_uniform\", \"PROPOSITION\": \"the gravitational field is uniform over the region abs({HEIGHT}) < h_max\", \"REFS\": [\"HEIGHT\", \"h_max\"]}, {\"NAME\": \"gravity_standard\", \"PROPOSITION\": \"the local gravitational acceleration equals the conventional standard value g_n\", \"REFS\": [\"g_n\"]}, {\"NAME\": \"frame_inertial\", \"PROPOSITION\": \"the frame in which {HEIGHT} is measured is treated as inertial\", \"REFS\": [\"HEIGHT\"]}], \"BOUNDARIES\": [{\"NAME\": \"gravity_region\", \"PREDICATE\": \"abs({HEIGHT}) < h_max\", \"CONDITION\": \"abs(HEIGHT) < h_max\"}], \"NOT_CHOSEN\": \"No gravity: no weight acts on any DOF.\", \"NOT_INCLUDED\": [\"No variation of gravity with height or latitude beyond what g_n contains.\", \"No Earth rotation (Coriolis or centrifugal force) beyond what g_n contains.\", \"No gravity of bodies other than the Earth.\"], \"EXCLUDES\": [], \"INTERACTS_WITH\": [{\"WITH\": \"AIR-*\", \"QUESTION_ID\": \"BUOYANCY\", \"QUESTION\": \"Does the air's buoyancy (upthrust) act on the body in the system you mean?\", \"YES_LINE\": \"Buoyancy acts (your answer): no module adds it; it acts in this kernel only where one of your own laws states it.\", \"NO_LINE\": \"No buoyancy: the air's upthrust on the body is not included.\"}], \"TEST_BINDINGS\": [{\"NAME\": \"PROJECTILE_2D\", \"TPK\": {\"DOF\": [{\"NAME\": \"t\", \"DIMENSION\": \"T1\"}, {\"NAME\": \"x\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"z\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"v_x\", \"DIMENSION\": \"L1 T-1\"}, {\"NAME\": \"v_z\", \"DIMENSION\": \"L1 T-1\"}], \"CONSTANT\": [{\"NAME\": \"m\", \"DIMENSION\": \"M1\"}], \"LAW\": [{\"NAME\": \"KIN_X\", \"STATEMENT\": \"dx/dt = v_x\", \"REFS\": [\"t\", \"v_x\", \"x\"], \"ROLE\": \"EOM(x)\", \"EQUATION\": \"D(x,t)=v_x\"}, {\"NAME\": \"KIN_Z\", \"STATEMENT\": \"dz/dt = v_z\", \"REFS\": [\"t\", \"v_z\", \"z\"], \"ROLE\": \"EOM(z)\", \"EQUATION\": \"D(z,t)=v_z\"}, {\"NAME\": \"EOM_X\", \"STATEMENT\": \"m dv_x/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_x\"], \"ROLE\": \"EOM(v_x)\", \"EQUATION\": \"m*D(v_x,t)=0\"}, {\"NAME\": \"EOM_Z\", \"STATEMENT\": \"m dv_z/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_z\"], \"ROLE\": \"EOM(v_z)\", \"EQUATION\": \"m*D(v_z,t)=0\"}], \"ASSUMPTION\": [{\"NAME\": \"point_mass\", \"PROPOSITION\": \"the body is treated as a point mass\", \"REFS\": [\"m\"]}]}, \"BIND\": {\"HEIGHT\": [\"z\"], \"MASS\": [\"m\"], \"UP_VELOCITY\": [\"v_z\"]}, \"VALUES\": {\"h_max\": {\"VALUE\": \"100\", \"UNIT\": \"m\"}}, \"ANSWERS\": {}}, {\"NAME\": \"TABLE\", \"TPK\": {\"DOF\": [{\"NAME\": \"t\", \"DIMENSION\": \"T1\"}, {\"NAME\": \"x\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"z\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"v_x\", \"DIMENSION\": \"L1 T-1\"}, {\"NAME\": \"v_z\", \"DIMENSION\": \"L1 T-1\"}], \"CONSTANT\": [{\"NAME\": \"m\", \"DIMENSION\": \"M1\"}], \"LAW\": [{\"NAME\": \"KIN_X\", \"STATEMENT\": \"dx/dt = v_x\", \"REFS\": [\"t\", \"v_x\", \"x\"], \"ROLE\": \"EOM(x)\", \"EQUATION\": \"D(x,t)=v_x\"}, {\"NAME\": \"KIN_Z\", \"STATEMENT\": \"dz/dt = v_z\", \"REFS\": [\"t\", \"v_z\", \"z\"], \"ROLE\": \"CONSTRAINT\", \"EQUATION\": \"D(z,t)=v_z\"}, {\"NAME\": \"EOM_X\", \"STATEMENT\": \"m dv_x/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_x\"], \"ROLE\": \"EOM(v_x)\", \"EQUATION\": \"m*D(v_x,t)=0\"}], \"CONSTRAINT\": [{\"NAME\": \"C_Z\", \"TARGET\": \"z\", \"ACTION\": \"FIX\", \"VALUE\": \"0\", \"UNIT\": \"m\", \"STATEMENT\": \"the puck stays on the table top, z = 0\"}, {\"NAME\": \"C_VZ\", \"TARGET\": \"v_z\", \"ACTION\": \"FIX\", \"VALUE\": \"0\", \"UNIT\": \"m s-1\", \"STATEMENT\": \"the puck has no vertical velocity\"}]}, \"BIND\": {\"HEIGHT\": [\"z\"], \"MASS\": [\"m\"], \"UP_VELOCITY\": [\"v_z\"]}, \"VALUES\": {\"h_max\": {\"VALUE\": \"1\", \"UNIT\": \"m\"}}, \"ANSWERS\": {\"FIXED:v_z\": \"YES\"}}]}",
"{\"ID\": \"MATH\", \"VERSION\": \"1.0.0\", \"TITLE\": \"The mathematical constant pi, as the CONSTANT pi_c\", \"SOURCE\": \"pi to 16 significant digits, 3.141592653589793, the nearest IEEE 754 binary64 value\", \"PREREQUISITES\": [], \"PARAMETERS\": [{\"NAME\": \"pi_c\", \"DIMENSION\": \"1\", \"SUPPLY\": \"DECLARED\", \"VALUE\": \"3.141592653589793\", \"UNIT\": \"1\", \"OVERRIDABLE\": \"NO\", \"LABEL\": \"pi, to 16 significant digits\"}], \"SUMS\": [], \"TERMS\": [], \"ASSUMPTIONS\": [], \"BOUNDARIES\": [], \"NOT_CHOSEN\": \"No mathematical constant: pi exists only if you declare it.\", \"NOT_INCLUDED\": [\"pi_c is pi rounded to 16 significant digits; no other mathematical constant is declared.\"], \"EXCLUDES\": [], \"INTERACTS_WITH\": [], \"TEST_BINDINGS\": [{\"NAME\": \"PROJECTILE_2D\", \"TPK\": {\"DOF\": [{\"NAME\": \"t\", \"DIMENSION\": \"T1\"}, {\"NAME\": \"x\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"z\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"v_x\", \"DIMENSION\": \"L1 T-1\"}, {\"NAME\": \"v_z\", \"DIMENSION\": \"L1 T-1\"}], \"CONSTANT\": [{\"NAME\": \"m\", \"DIMENSION\": \"M1\"}], \"LAW\": [{\"NAME\": \"KIN_X\", \"STATEMENT\": \"dx/dt = v_x\", \"REFS\": [\"t\", \"v_x\", \"x\"], \"ROLE\": \"EOM(x)\", \"EQUATION\": \"D(x,t)=v_x\"}, {\"NAME\": \"KIN_Z\", \"STATEMENT\": \"dz/dt = v_z\", \"REFS\": [\"t\", \"v_z\", \"z\"], \"ROLE\": \"EOM(z)\", \"EQUATION\": \"D(z,t)=v_z\"}, {\"NAME\": \"EOM_X\", \"STATEMENT\": \"m dv_x/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_x\"], \"ROLE\": \"EOM(v_x)\", \"EQUATION\": \"m*D(v_x,t)=0\"}, {\"NAME\": \"EOM_Z\", \"STATEMENT\": \"m dv_z/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_z\"], \"ROLE\": \"EOM(v_z)\", \"EQUATION\": \"m*D(v_z,t)=0\"}], \"ASSUMPTION\": [{\"NAME\": \"point_mass\", \"PROPOSITION\": \"the body is treated as a point mass\", \"REFS\": [\"m\"]}]}, \"BIND\": {}, \"VALUES\": {}, \"ANSWERS\": {}}]}"
]
},
"expected": "[\"REFUSED\",\"CLAIM 1: VERSION is not a version\"]",
"fn": "module_expand",
"hand_checked": true,
"name": "X60 a claim VERSION that is not a version"
},
{
"args": {
"claims": [
{
"ANSWERS": {},
"BIND": {},
"DIGEST": "93d24797bd704b2bacfa234aaa2a6694114001c43e07f9e71c856405fa1de6a7",
"ID": "TEST-NOAIR",
"VALUES": {},
"VERSION": "1.0.0"
},
{
"ANSWERS": {},
"BIND": {
"VELOCITY": [
"v_x",
"v_z"
]
},
"DIGEST": "6fb53c3a6546151eead2bd6e72e9cf8334f3a2040ad0ee2f5b988ec96d6fc852",
"ID": "AIR-QUADRATIC",
"VALUES": {
"A_ref": {},
"C_d": {},
"L_ref": {}
},
"VERSION": "1.0.0"
}
],
"draft": {
"TPK": {
"ASSUMPTION": [
{
"NAME": "point_mass",
"PROPOSITION": "the body is treated as a point mass",
"REFS": [
"m"
]
}
],
"CONSTANT": [
{
"DIMENSION": "M1",
"NAME": "m"
}
],
"DOF": [
{
"DIMENSION": "T1",
"NAME": "t"
},
{
"DIMENSION": "L1",
"NAME": "x"
},
{
"DIMENSION": "L1",
"NAME": "z"
},
{
"DIMENSION": "L1 T-1",
"NAME": "v_x"
},
{
"DIMENSION": "L1 T-1",
"NAME": "v_z"
}
],
"LAW": [
{
"EQUATION": "D(x,t)=v_x",
"NAME": "KIN_X",
"REFS": [
"t",
"v_x",
"x"
],
"ROLE": "EOM(x)",
"STATEMENT": "dx/dt = v_x"
},
{
"EQUATION": "D(z,t)=v_z",
"NAME": "KIN_Z",
"REFS": [
"t",
"v_z",
"z"
],
"ROLE": "EOM(z)",
"STATEMENT": "dz/dt = v_z"
},
{
"EQUATION": "m*D(v_x,t)=0",
"NAME": "EOM_X",
"REFS": [
"m",
"t",
"v_x"
],
"ROLE": "EOM(v_x)",
"STATEMENT": "m dv_x/dt = 0"
},
{
"EQUATION": "m*D(v_z,t)=0",
"NAME": "EOM_Z",
"REFS": [
"m",
"t",
"v_z"
],
"ROLE": "EOM(v_z)",
"STATEMENT": "m dv_z/dt = 0"
}
]
}
},
"modules": [
"{\"ID\": \"AIR-LINEAR\", \"VERSION\": \"1.0.0\", \"TITLE\": \"Air resistance at sea level, linear in the speed (Stokes drag on a sphere)\", \"SOURCE\": \"ISO 2533:1975, Standard Atmosphere, sea-level values: density 1.225 kg m-3, dynamic viscosity 1.7894e-5 Pa s\", \"PREREQUISITES\": [{\"SLOT\": \"VELOCITY\", \"KIND\": \"DOF\", \"DIMENSION\": \"L1 T-1\", \"MIN\": 1, \"MAX\": 3, \"LABEL\": \"the velocity components of the body, one per axis\"}], \"PARAMETERS\": [{\"NAME\": \"rho_air\", \"DIMENSION\": \"L-3 M1\", \"SUPPLY\": \"DECLARED\", \"VALUE\": \"1.225\", \"UNIT\": \"kg m-3\", \"OVERRIDABLE\": \"NO\", \"LABEL\": \"the density of air at sea level\"}, {\"NAME\": \"mu_air\", \"DIMENSION\": \"L-1 M1 T-1\", \"SUPPLY\": \"DECLARED\", \"VALUE\": \"1.7894e-5\", \"UNIT\": \"Pa s\", \"OVERRIDABLE\": \"NO\", \"LABEL\": \"the dynamic viscosity of air at sea level\"}, {\"NAME\": \"pi_c\", \"DIMENSION\": \"1\", \"SUPPLY\": \"DECLARED\", \"VALUE\": \"3.141592653589793\", \"UNIT\": \"1\", \"OVERRIDABLE\": \"NO\", \"LABEL\": \"pi, to 16 significant digits\"}, {\"NAME\": \"R_s\", \"DIMENSION\": \"L1\", \"SUPPLY\": \"AUTHOR\", \"LABEL\": \"the radius of the sphere\"}], \"SUMS\": [{\"NAME\": \"SPEED2\", \"OVER\": \"VELOCITY\", \"EACH\": \"VELOCITY^2\"}], \"TERMS\": [{\"TARGET\": \"VELOCITY\", \"SIGN\": \"-\", \"EXPR\": \"6*pi_c*mu_air*R_s*VELOCITY\", \"LABEL\": \"the linear (Stokes) drag\"}], \"ASSUMPTIONS\": [{\"NAME\": \"air_still\", \"PROPOSITION\": \"the air is at rest in the frame of the body's velocity\", \"REFS\": [\"VELOCITY\"]}, {\"NAME\": \"air_uniform\", \"PROPOSITION\": \"the air density is uniform over the region of motion\", \"REFS\": [\"rho_air\"]}, {\"NAME\": \"drag_sphere\", \"PROPOSITION\": \"the body is a rigid sphere of radius R_s\", \"REFS\": [\"R_s\"]}], \"BOUNDARIES\": [{\"NAME\": \"drag_linear_regime\", \"PREDICATE\": \"2 rho_air |v| R_s / mu_air < 1: the regime of the linear law\", \"CONDITION\": \"mu_air != 0 and SPEED2 >= 0 and 2*rho_air*sqrt(SPEED2)*R_s/mu_air < 1\"}], \"NOT_CHOSEN\": \"No linear (Stokes) air resistance.\", \"NOT_INCLUDED\": [\"No wind: the air is at rest.\", \"No change of air density or viscosity with altitude or temperature.\", \"No drag outside the regime of the linear law.\"], \"EXCLUDES\": [], \"INTERACTS_WITH\": [], \"TEST_BINDINGS\": [{\"NAME\": \"PROJECTILE_2D\", \"TPK\": {\"DOF\": [{\"NAME\": \"t\", \"DIMENSION\": \"T1\"}, {\"NAME\": \"x\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"z\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"v_x\", \"DIMENSION\": \"L1 T-1\"}, {\"NAME\": \"v_z\", \"DIMENSION\": \"L1 T-1\"}], \"CONSTANT\": [{\"NAME\": \"m\", \"DIMENSION\": \"M1\"}], \"LAW\": [{\"NAME\": \"KIN_X\", \"STATEMENT\": \"dx/dt = v_x\", \"REFS\": [\"t\", \"v_x\", \"x\"], \"ROLE\": \"EOM(x)\", \"EQUATION\": \"D(x,t)=v_x\"}, {\"NAME\": \"KIN_Z\", \"STATEMENT\": \"dz/dt = v_z\", \"REFS\": [\"t\", \"v_z\", \"z\"], \"ROLE\": \"EOM(z)\", \"EQUATION\": \"D(z,t)=v_z\"}, {\"NAME\": \"EOM_X\", \"STATEMENT\": \"m dv_x/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_x\"], \"ROLE\": \"EOM(v_x)\", \"EQUATION\": \"m*D(v_x,t)=0\"}, {\"NAME\": \"EOM_Z\", \"STATEMENT\": \"m dv_z/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_z\"], \"ROLE\": \"EOM(v_z)\", \"EQUATION\": \"m*D(v_z,t)=0\"}], \"ASSUMPTION\": [{\"NAME\": \"point_mass\", \"PROPOSITION\": \"the body is treated as a point mass\", \"REFS\": [\"m\"]}]}, \"BIND\": {\"VELOCITY\": [\"v_x\", \"v_z\"]}, \"VALUES\": {\"R_s\": {}}, \"ANSWERS\": {}}]}",
"{\"ID\": \"AIR-QUADRATIC\", \"VERSION\": \"1.0.0\", \"TITLE\": \"Air resistance at sea level, quadratic in the speed\", \"SOURCE\": \"ISO 2533:1975, Standard Atmosphere, sea-level values: density 1.225 kg m-3, dynamic viscosity 1.7894e-5 Pa s\", \"PREREQUISITES\": [{\"SLOT\": \"VELOCITY\", \"KIND\": \"DOF\", \"DIMENSION\": \"L1 T-1\", \"MIN\": 1, \"MAX\": 3, \"LABEL\": \"the velocity components of the body, one per axis\"}], \"PARAMETERS\": [{\"NAME\": \"rho_air\", \"DIMENSION\": \"L-3 M1\", \"SUPPLY\": \"DECLARED\", \"VALUE\": \"1.225\", \"UNIT\": \"kg m-3\", \"OVERRIDABLE\": \"NO\", \"LABEL\": \"the density of air at sea level\"}, {\"NAME\": \"mu_air\", \"DIMENSION\": \"L-1 M1 T-1\", \"SUPPLY\": \"DECLARED\", \"VALUE\": \"1.7894e-5\", \"UNIT\": \"Pa s\", \"OVERRIDABLE\": \"NO\", \"LABEL\": \"the dynamic viscosity of air at sea level\"}, {\"NAME\": \"C_d\", \"DIMENSION\": \"1\", \"SUPPLY\": \"AUTHOR\", \"LABEL\": \"the drag coefficient of the body\"}, {\"NAME\": \"A_ref\", \"DIMENSION\": \"L2\", \"SUPPLY\": \"AUTHOR\", \"LABEL\": \"the reference area of the drag coefficient\"}, {\"NAME\": \"L_ref\", \"DIMENSION\": \"L1\", \"SUPPLY\": \"AUTHOR\", \"LABEL\": \"the reference length of the Reynolds number\"}], \"SUMS\": [{\"NAME\": \"SPEED2\", \"OVER\": \"VELOCITY\", \"EACH\": \"VELOCITY^2\"}], \"TERMS\": [{\"TARGET\": \"VELOCITY\", \"SIGN\": \"-\", \"EXPR\": \"0.5*rho_air*C_d*A_ref*sqrt(SPEED2)*VELOCITY\", \"LABEL\": \"the quadratic drag\"}], \"ASSUMPTIONS\": [{\"NAME\": \"air_still\", \"PROPOSITION\": \"the air is at rest in the frame of the body's velocity\", \"REFS\": [\"VELOCITY\"]}, {\"NAME\": \"air_uniform\", \"PROPOSITION\": \"the air density is uniform over the region of motion\", \"REFS\": [\"rho_air\"]}, {\"NAME\": \"drag_cd_constant\", \"PROPOSITION\": \"the drag coefficient C_d is constant over the motion\", \"REFS\": [\"C_d\"]}, {\"NAME\": \"drag_no_lift\", \"PROPOSITION\": \"the body experiences no lift force\", \"REFS\": [\"VELOCITY\"]}, {\"NAME\": \"drag_no_magnus\", \"PROPOSITION\": \"the body experiences no Magnus force\", \"REFS\": [\"VELOCITY\"]}], \"BOUNDARIES\": [{\"NAME\": \"drag_quadratic_regime\", \"PREDICATE\": \"1e3 < rho_air |v| L_ref / mu_air < 2e5: the Reynolds window of the quadratic law\", \"CONDITION\": \"mu_air != 0 and SPEED2 >= 0 and rho_air*sqrt(SPEED2)*L_ref/mu_air > 1000 and rho_air*sqrt(SPEED2)*L_ref/mu_air < 200000\"}], \"NOT_CHOSEN\": \"No quadratic air resistance.\", \"NOT_INCLUDED\": [\"No wind: the air is at rest.\", \"No change of air density or viscosity with altitude or temperature.\", \"No lift, Magnus or added-mass force.\", \"No drag outside the Reynolds window of the quadratic law.\"], \"EXCLUDES\": [\"AIR-LINEAR\"], \"INTERACTS_WITH\": [], \"TEST_BINDINGS\": [{\"NAME\": \"PROJECTILE_2D\", \"TPK\": {\"DOF\": [{\"NAME\": \"t\", \"DIMENSION\": \"T1\"}, {\"NAME\": \"x\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"z\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"v_x\", \"DIMENSION\": \"L1 T-1\"}, {\"NAME\": \"v_z\", \"DIMENSION\": \"L1 T-1\"}], \"CONSTANT\": [{\"NAME\": \"m\", \"DIMENSION\": \"M1\"}], \"LAW\": [{\"NAME\": \"KIN_X\", \"STATEMENT\": \"dx/dt = v_x\", \"REFS\": [\"t\", \"v_x\", \"x\"], \"ROLE\": \"EOM(x)\", \"EQUATION\": \"D(x,t)=v_x\"}, {\"NAME\": \"KIN_Z\", \"STATEMENT\": \"dz/dt = v_z\", \"REFS\": [\"t\", \"v_z\", \"z\"], \"ROLE\": \"EOM(z)\", \"EQUATION\": \"D(z,t)=v_z\"}, {\"NAME\": \"EOM_X\", \"STATEMENT\": \"m dv_x/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_x\"], \"ROLE\": \"EOM(v_x)\", \"EQUATION\": \"m*D(v_x,t)=0\"}, {\"NAME\": \"EOM_Z\", \"STATEMENT\": \"m dv_z/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_z\"], \"ROLE\": \"EOM(v_z)\", \"EQUATION\": \"m*D(v_z,t)=0\"}], \"ASSUMPTION\": [{\"NAME\": \"point_mass\", \"PROPOSITION\": \"the body is treated as a point mass\", \"REFS\": [\"m\"]}]}, \"BIND\": {\"VELOCITY\": [\"v_x\", \"v_z\"]}, \"VALUES\": {\"A_ref\": {}, \"C_d\": {}, \"L_ref\": {}}, \"ANSWERS\": {}}]}",
"{\"ID\": \"GRAV-UNIFORM\", \"VERSION\": \"1.0.0\", \"TITLE\": \"Uniform gravity at the standard value g_n\", \"SOURCE\": \"g_n = 9.80665 m s-2, exact by definition: 3rd CGPM (1901), declaration on the unit of mass and on the definition of weight\", \"PREREQUISITES\": [{\"SLOT\": \"MASS\", \"KIND\": \"CONSTANT\", \"DIMENSION\": \"M1\", \"MIN\": 1, \"MAX\": 1, \"LABEL\": \"the mass of the body\"}, {\"SLOT\": \"UP_VELOCITY\", \"KIND\": \"DOF\", \"DIMENSION\": \"L1 T-1\", \"MIN\": 1, \"MAX\": 1, \"LABEL\": \"the velocity component pointing up; its equation of motion receives the weight\"}, {\"SLOT\": \"HEIGHT\", \"KIND\": \"DOF\", \"DIMENSION\": \"L1\", \"MIN\": 1, \"MAX\": 1, \"LABEL\": \"the position along the same upward axis\"}], \"PARAMETERS\": [{\"NAME\": \"g_n\", \"DIMENSION\": \"L1 T-2\", \"SUPPLY\": \"DECLARED\", \"VALUE\": \"9.80665\", \"UNIT\": \"m s-2\", \"OVERRIDABLE\": \"NO\", \"LABEL\": \"the standard acceleration of gravity\"}, {\"NAME\": \"h_max\", \"DIMENSION\": \"L1\", \"SUPPLY\": \"AUTHOR\", \"LABEL\": \"the largest height, above or below the origin, over which the field is taken as uniform\"}], \"SUMS\": [], \"TERMS\": [{\"TARGET\": \"UP_VELOCITY\", \"SIGN\": \"-\", \"EXPR\": \"MASS*g_n\", \"LABEL\": \"the weight\"}], \"ASSUMPTIONS\": [{\"NAME\": \"gravity_uniform\", \"PROPOSITION\": \"the gravitational field is uniform over the region abs({HEIGHT}) < h_max\", \"REFS\": [\"HEIGHT\", \"h_max\"]}, {\"NAME\": \"gravity_standard\", \"PROPOSITION\": \"the local gravitational acceleration equals the conventional standard value g_n\", \"REFS\": [\"g_n\"]}, {\"NAME\": \"frame_inertial\", \"PROPOSITION\": \"the frame in which {HEIGHT} is measured is treated as inertial\", \"REFS\": [\"HEIGHT\"]}], \"BOUNDARIES\": [{\"NAME\": \"gravity_region\", \"PREDICATE\": \"abs({HEIGHT}) < h_max\", \"CONDITION\": \"abs(HEIGHT) < h_max\"}], \"NOT_CHOSEN\": \"No gravity: no weight acts on any DOF.\", \"NOT_INCLUDED\": [\"No variation of gravity with height or latitude beyond what g_n contains.\", \"No Earth rotation (Coriolis or centrifugal force) beyond what g_n contains.\", \"No gravity of bodies other than the Earth.\"], \"EXCLUDES\": [], \"INTERACTS_WITH\": [{\"WITH\": \"AIR-*\", \"QUESTION_ID\": \"BUOYANCY\", \"QUESTION\": \"Does the air's buoyancy (upthrust) act on the body in the system you mean?\", \"YES_LINE\": \"Buoyancy acts (your answer): no module adds it; it acts in this kernel only where one of your own laws states it.\", \"NO_LINE\": \"No buoyancy: the air's upthrust on the body is not included.\"}], \"TEST_BINDINGS\": [{\"NAME\": \"PROJECTILE_2D\", \"TPK\": {\"DOF\": [{\"NAME\": \"t\", \"DIMENSION\": \"T1\"}, {\"NAME\": \"x\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"z\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"v_x\", \"DIMENSION\": \"L1 T-1\"}, {\"NAME\": \"v_z\", \"DIMENSION\": \"L1 T-1\"}], \"CONSTANT\": [{\"NAME\": \"m\", \"DIMENSION\": \"M1\"}], \"LAW\": [{\"NAME\": \"KIN_X\", \"STATEMENT\": \"dx/dt = v_x\", \"REFS\": [\"t\", \"v_x\", \"x\"], \"ROLE\": \"EOM(x)\", \"EQUATION\": \"D(x,t)=v_x\"}, {\"NAME\": \"KIN_Z\", \"STATEMENT\": \"dz/dt = v_z\", \"REFS\": [\"t\", \"v_z\", \"z\"], \"ROLE\": \"EOM(z)\", \"EQUATION\": \"D(z,t)=v_z\"}, {\"NAME\": \"EOM_X\", \"STATEMENT\": \"m dv_x/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_x\"], \"ROLE\": \"EOM(v_x)\", \"EQUATION\": \"m*D(v_x,t)=0\"}, {\"NAME\": \"EOM_Z\", \"STATEMENT\": \"m dv_z/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_z\"], \"ROLE\": \"EOM(v_z)\", \"EQUATION\": \"m*D(v_z,t)=0\"}], \"ASSUMPTION\": [{\"NAME\": \"point_mass\", \"PROPOSITION\": \"the body is treated as a point mass\", \"REFS\": [\"m\"]}]}, \"BIND\": {\"HEIGHT\": [\"z\"], \"MASS\": [\"m\"], \"UP_VELOCITY\": [\"v_z\"]}, \"VALUES\": {\"h_max\": {\"VALUE\": \"100\", \"UNIT\": \"m\"}}, \"ANSWERS\": {}}, {\"NAME\": \"TABLE\", \"TPK\": {\"DOF\": [{\"NAME\": \"t\", \"DIMENSION\": \"T1\"}, {\"NAME\": \"x\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"z\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"v_x\", \"DIMENSION\": \"L1 T-1\"}, {\"NAME\": \"v_z\", \"DIMENSION\": \"L1 T-1\"}], \"CONSTANT\": [{\"NAME\": \"m\", \"DIMENSION\": \"M1\"}], \"LAW\": [{\"NAME\": \"KIN_X\", \"STATEMENT\": \"dx/dt = v_x\", \"REFS\": [\"t\", \"v_x\", \"x\"], \"ROLE\": \"EOM(x)\", \"EQUATION\": \"D(x,t)=v_x\"}, {\"NAME\": \"KIN_Z\", \"STATEMENT\": \"dz/dt = v_z\", \"REFS\": [\"t\", \"v_z\", \"z\"], \"ROLE\": \"CONSTRAINT\", \"EQUATION\": \"D(z,t)=v_z\"}, {\"NAME\": \"EOM_X\", \"STATEMENT\": \"m dv_x/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_x\"], \"ROLE\": \"EOM(v_x)\", \"EQUATION\": \"m*D(v_x,t)=0\"}], \"CONSTRAINT\": [{\"NAME\": \"C_Z\", \"TARGET\": \"z\", \"ACTION\": \"FIX\", \"VALUE\": \"0\", \"UNIT\": \"m\", \"STATEMENT\": \"the puck stays on the table top, z = 0\"}, {\"NAME\": \"C_VZ\", \"TARGET\": \"v_z\", \"ACTION\": \"FIX\", \"VALUE\": \"0\", \"UNIT\": \"m s-1\", \"STATEMENT\": \"the puck has no vertical velocity\"}]}, \"BIND\": {\"HEIGHT\": [\"z\"], \"MASS\": [\"m\"], \"UP_VELOCITY\": [\"v_z\"]}, \"VALUES\": {\"h_max\": {\"VALUE\": \"1\", \"UNIT\": \"m\"}}, \"ANSWERS\": {\"FIXED:v_z\": \"YES\"}}]}",
"{\"ID\": \"MATH\", \"VERSION\": \"1.0.0\", \"TITLE\": \"The mathematical constant pi, as the CONSTANT pi_c\", \"SOURCE\": \"pi to 16 significant digits, 3.141592653589793, the nearest IEEE 754 binary64 value\", \"PREREQUISITES\": [], \"PARAMETERS\": [{\"NAME\": \"pi_c\", \"DIMENSION\": \"1\", \"SUPPLY\": \"DECLARED\", \"VALUE\": \"3.141592653589793\", \"UNIT\": \"1\", \"OVERRIDABLE\": \"NO\", \"LABEL\": \"pi, to 16 significant digits\"}], \"SUMS\": [], \"TERMS\": [], \"ASSUMPTIONS\": [], \"BOUNDARIES\": [], \"NOT_CHOSEN\": \"No mathematical constant: pi exists only if you declare it.\", \"NOT_INCLUDED\": [\"pi_c is pi rounded to 16 significant digits; no other mathematical constant is declared.\"], \"EXCLUDES\": [], \"INTERACTS_WITH\": [], \"TEST_BINDINGS\": [{\"NAME\": \"PROJECTILE_2D\", \"TPK\": {\"DOF\": [{\"NAME\": \"t\", \"DIMENSION\": \"T1\"}, {\"NAME\": \"x\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"z\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"v_x\", \"DIMENSION\": \"L1 T-1\"}, {\"NAME\": \"v_z\", \"DIMENSION\": \"L1 T-1\"}], \"CONSTANT\": [{\"NAME\": \"m\", \"DIMENSION\": \"M1\"}], \"LAW\": [{\"NAME\": \"KIN_X\", \"STATEMENT\": \"dx/dt = v_x\", \"REFS\": [\"t\", \"v_x\", \"x\"], \"ROLE\": \"EOM(x)\", \"EQUATION\": \"D(x,t)=v_x\"}, {\"NAME\": \"KIN_Z\", \"STATEMENT\": \"dz/dt = v_z\", \"REFS\": [\"t\", \"v_z\", \"z\"], \"ROLE\": \"EOM(z)\", \"EQUATION\": \"D(z,t)=v_z\"}, {\"NAME\": \"EOM_X\", \"STATEMENT\": \"m dv_x/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_x\"], \"ROLE\": \"EOM(v_x)\", \"EQUATION\": \"m*D(v_x,t)=0\"}, {\"NAME\": \"EOM_Z\", \"STATEMENT\": \"m dv_z/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_z\"], \"ROLE\": \"EOM(v_z)\", \"EQUATION\": \"m*D(v_z,t)=0\"}], \"ASSUMPTION\": [{\"NAME\": \"point_mass\", \"PROPOSITION\": \"the body is treated as a point mass\", \"REFS\": [\"m\"]}]}, \"BIND\": {}, \"VALUES\": {}, \"ANSWERS\": {}}]}",
"{\"ID\": \"TEST-NOAIR\", \"VERSION\": \"1.0.0\", \"TITLE\": \"Test: excludes every AIR module\", \"SOURCE\": \"synthetic fixture\", \"PREREQUISITES\": [], \"PARAMETERS\": [], \"SUMS\": [], \"TERMS\": [], \"ASSUMPTIONS\": [], \"BOUNDARIES\": [], \"NOT_CHOSEN\": \"No pattern test.\", \"NOT_INCLUDED\": [], \"EXCLUDES\": [\"AIR-*\"], \"INTERACTS_WITH\": [], \"TEST_BINDINGS\": [{\"NAME\": \"PROJECTILE_2D\", \"TPK\": {\"DOF\": [{\"NAME\": \"t\", \"DIMENSION\": \"T1\"}, {\"NAME\": \"x\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"z\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"v_x\", \"DIMENSION\": \"L1 T-1\"}, {\"NAME\": \"v_z\", \"DIMENSION\": \"L1 T-1\"}], \"CONSTANT\": [{\"NAME\": \"m\", \"DIMENSION\": \"M1\"}], \"LAW\": [{\"NAME\": \"KIN_X\", \"STATEMENT\": \"dx/dt = v_x\", \"REFS\": [\"t\", \"v_x\", \"x\"], \"ROLE\": \"EOM(x)\", \"EQUATION\": \"D(x,t)=v_x\"}, {\"NAME\": \"KIN_Z\", \"STATEMENT\": \"dz/dt = v_z\", \"REFS\": [\"t\", \"v_z\", \"z\"], \"ROLE\": \"EOM(z)\", \"EQUATION\": \"D(z,t)=v_z\"}, {\"NAME\": \"EOM_X\", \"STATEMENT\": \"m dv_x/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_x\"], \"ROLE\": \"EOM(v_x)\", \"EQUATION\": \"m*D(v_x,t)=0\"}, {\"NAME\": \"EOM_Z\", \"STATEMENT\": \"m dv_z/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_z\"], \"ROLE\": \"EOM(v_z)\", \"EQUATION\": \"m*D(v_z,t)=0\"}], \"ASSUMPTION\": [{\"NAME\": \"point_mass\", \"PROPOSITION\": \"the body is treated as a point mass\", \"REFS\": [\"m\"]}]}, \"BIND\": {}, \"VALUES\": {}, \"ANSWERS\": {}}]}"
]
},
"expected": "[\"REFUSED\",\"CLAIMS: AIR-QUADRATIC 1.0.0 and TEST-NOAIR 1.0.0 exclude each other (EXCLUDES)\"]",
"fn": "module_expand",
"hand_checked": true,
"name": "X61 EXCLUDES by pattern (AIR-*)"
},
{
"args": {
"claims": [
{
"ANSWERS": {},
"BIND": {
"VELOCITY": [
"v_x",
"v_z"
]
},
"DIGEST": "d2c0eaf665eb165b5c7e311008011349e146564f0679f8ca32f5c98a5924bd8b",
"ID": "TEST-SUMP",
"VALUES": {
"k_q": {}
},
"VERSION": "1.0.0"
},
{
"ANSWERS": {},
"BIND": {},
"DIGEST": "9252524a73f9979d905a4b84ed2a5186d170d071f8a81f9cbd222c8e53da7b12",
"ID": "TEST-SHARE",
"VALUES": {
"k_q": {}
},
"VERSION": "1.0.0"
}
],
"draft": {
"TPK": {
"ASSUMPTION": [
{
"NAME": "point_mass",
"PROPOSITION": "the body is treated as a point mass",
"REFS": [
"m"
]
}
],
"CONSTANT": [
{
"DIMENSION": "M1",
"NAME": "m"
}
],
"DOF": [
{
"DIMENSION": "T1",
"NAME": "t"
},
{
"DIMENSION": "L1",
"NAME": "x"
},
{
"DIMENSION": "L1",
"NAME": "z"
},
{
"DIMENSION": "L1 T-1",
"NAME": "v_x"
},
{
"DIMENSION": "L1 T-1",
"NAME": "v_z"
}
],
"LAW": [
{
"EQUATION": "D(x,t)=v_x",
"NAME": "KIN_X",
"REFS": [
"t",
"v_x",
"x"
],
"ROLE": "EOM(x)",
"STATEMENT": "dx/dt = v_x"
},
{
"EQUATION": "D(z,t)=v_z",
"NAME": "KIN_Z",
"REFS": [
"t",
"v_z",
"z"
],
"ROLE": "EOM(z)",
"STATEMENT": "dz/dt = v_z"
},
{
"EQUATION": "m*D(v_x,t)=0",
"NAME": "EOM_X",
"REFS": [
"m",
"t",
"v_x"
],
"ROLE": "EOM(v_x)",
"STATEMENT": "m dv_x/dt = 0"
},
{
"EQUATION": "m*D(v_z,t)=0",
"NAME": "EOM_Z",
"REFS": [
"m",
"t",
"v_z"
],
"ROLE": "EOM(v_z)",
"STATEMENT": "m dv_z/dt = 0"
}
]
}
},
"modules": [
"{\"ID\": \"TEST-SUMP\", \"VERSION\": \"1.0.0\", \"TITLE\": \"Test: a sum inside a product\", \"SOURCE\": \"synthetic fixture\", \"PREREQUISITES\": [{\"SLOT\": \"VELOCITY\", \"KIND\": \"DOF\", \"DIMENSION\": \"L1 T-1\", \"MIN\": 1, \"MAX\": 3, \"LABEL\": \"the velocity components of the body, one per axis\"}], \"PARAMETERS\": [{\"NAME\": \"k_q\", \"DIMENSION\": \"L-1 M1\", \"SUPPLY\": \"AUTHOR\", \"LABEL\": \"a quadratic coefficient\"}], \"SUMS\": [{\"NAME\": \"SPEED2\", \"OVER\": \"VELOCITY\", \"EACH\": \"VELOCITY^2\"}], \"TERMS\": [{\"TARGET\": \"VELOCITY\", \"SIGN\": \"-\", \"EXPR\": \"k_q*SPEED2\", \"LABEL\": \"the test force\"}], \"ASSUMPTIONS\": [], \"BOUNDARIES\": [], \"NOT_CHOSEN\": \"No sum test.\", \"NOT_INCLUDED\": [], \"EXCLUDES\": [], \"INTERACTS_WITH\": [], \"TEST_BINDINGS\": [{\"NAME\": \"PROJECTILE_2D\", \"TPK\": {\"DOF\": [{\"NAME\": \"t\", \"DIMENSION\": \"T1\"}, {\"NAME\": \"x\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"z\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"v_x\", \"DIMENSION\": \"L1 T-1\"}, {\"NAME\": \"v_z\", \"DIMENSION\": \"L1 T-1\"}], \"CONSTANT\": [{\"NAME\": \"m\", \"DIMENSION\": \"M1\"}], \"LAW\": [{\"NAME\": \"KIN_X\", \"STATEMENT\": \"dx/dt = v_x\", \"REFS\": [\"t\", \"v_x\", \"x\"], \"ROLE\": \"EOM(x)\", \"EQUATION\": \"D(x,t)=v_x\"}, {\"NAME\": \"KIN_Z\", \"STATEMENT\": \"dz/dt = v_z\", \"REFS\": [\"t\", \"v_z\", \"z\"], \"ROLE\": \"EOM(z)\", \"EQUATION\": \"D(z,t)=v_z\"}, {\"NAME\": \"EOM_X\", \"STATEMENT\": \"m dv_x/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_x\"], \"ROLE\": \"EOM(v_x)\", \"EQUATION\": \"m*D(v_x,t)=0\"}, {\"NAME\": \"EOM_Z\", \"STATEMENT\": \"m dv_z/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_z\"], \"ROLE\": \"EOM(v_z)\", \"EQUATION\": \"m*D(v_z,t)=0\"}], \"ASSUMPTION\": [{\"NAME\": \"point_mass\", \"PROPOSITION\": \"the body is treated as a point mass\", \"REFS\": [\"m\"]}]}, \"BIND\": {\"VELOCITY\": [\"v_x\", \"v_z\"]}, \"VALUES\": {\"k_q\": {}}, \"ANSWERS\": {}}]}",
"{\"ID\": \"TEST-SHARE\", \"VERSION\": \"1.0.0\", \"TITLE\": \"Test: an author parameter shared by name\", \"SOURCE\": \"synthetic fixture\", \"PREREQUISITES\": [], \"PARAMETERS\": [{\"NAME\": \"k_q\", \"DIMENSION\": \"L-1 M1\", \"SUPPLY\": \"AUTHOR\", \"LABEL\": \"a quadratic coefficient, named by another module too\"}], \"SUMS\": [], \"TERMS\": [], \"ASSUMPTIONS\": [], \"BOUNDARIES\": [], \"NOT_CHOSEN\": \"No shared-name test.\", \"NOT_INCLUDED\": [], \"EXCLUDES\": [], \"INTERACTS_WITH\": [], \"TEST_BINDINGS\": [{\"NAME\": \"PROJECTILE_2D\", \"TPK\": {\"DOF\": [{\"NAME\": \"t\", \"DIMENSION\": \"T1\"}, {\"NAME\": \"x\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"z\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"v_x\", \"DIMENSION\": \"L1 T-1\"}, {\"NAME\": \"v_z\", \"DIMENSION\": \"L1 T-1\"}], \"CONSTANT\": [{\"NAME\": \"m\", \"DIMENSION\": \"M1\"}], \"LAW\": [{\"NAME\": \"KIN_X\", \"STATEMENT\": \"dx/dt = v_x\", \"REFS\": [\"t\", \"v_x\", \"x\"], \"ROLE\": \"EOM(x)\", \"EQUATION\": \"D(x,t)=v_x\"}, {\"NAME\": \"KIN_Z\", \"STATEMENT\": \"dz/dt = v_z\", \"REFS\": [\"t\", \"v_z\", \"z\"], \"ROLE\": \"EOM(z)\", \"EQUATION\": \"D(z,t)=v_z\"}, {\"NAME\": \"EOM_X\", \"STATEMENT\": \"m dv_x/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_x\"], \"ROLE\": \"EOM(v_x)\", \"EQUATION\": \"m*D(v_x,t)=0\"}, {\"NAME\": \"EOM_Z\", \"STATEMENT\": \"m dv_z/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_z\"], \"ROLE\": \"EOM(v_z)\", \"EQUATION\": \"m*D(v_z,t)=0\"}], \"ASSUMPTION\": [{\"NAME\": \"point_mass\", \"PROPOSITION\": \"the body is treated as a point mass\", \"REFS\": [\"m\"]}]}, \"BIND\": {}, \"VALUES\": {\"k_q\": {}}, \"ANSWERS\": {}}]}"
]
},
"computed": "digests by existing TPC-PY functions over literal data",
"expected": "[\"OK\",[\"D(TPK)\",\"e1cff39ece3129f139b8b74d9e94d7e33718d2a94920165f2f5b6cd471acf187\"],[\"COMPOSED\",[[\"EOM_X\",\"m*D(v_x,t)=-k_q*(v_x^2+v_z^2)\"],[\"EOM_Z\",\"m*D(v_z,t)=-k_q*(v_x^2+v_z^2)\"]]],[\"EMITTED\",[[\"CONSTANT\",\"k_q\",[\"TEST-SHARE 1.0.0\",\"TEST-SUMP 1.0.0\"]]]],[\"DROPPED\",[]]]",
"fn": "module_expand",
"hand_checked": false,
"name": "X62 two same-named AUTHOR parameters left symbolic: one CONSTANT (S51)"
},
{
"args": {
"claims": [
{
"ANSWERS": {},
"BIND": {
"VELOCITY": [
"v_x",
"v_z"
]
},
"DIGEST": "d2c0eaf665eb165b5c7e311008011349e146564f0679f8ca32f5c98a5924bd8b",
"ID": "TEST-SUMP",
"VALUES": {
"k_q": {}
},
"VERSION": "1.0.0"
},
{
"ANSWERS": {},
"BIND": {},
"DIGEST": "9252524a73f9979d905a4b84ed2a5186d170d071f8a81f9cbd222c8e53da7b12",
"ID": "TEST-SHARE",
"VALUES": {
"k_q": {
"UNIT": "kg m-1",
"VALUE": "2"
}
},
"VERSION": "1.0.0"
}
],
"draft": {
"TPK": {
"ASSUMPTION": [
{
"NAME": "point_mass",
"PROPOSITION": "the body is treated as a point mass",
"REFS": [
"m"
]
}
],
"CONSTANT": [
{
"DIMENSION": "M1",
"NAME": "m"
}
],
"DOF": [
{
"DIMENSION": "T1",
"NAME": "t"
},
{
"DIMENSION": "L1",
"NAME": "x"
},
{
"DIMENSION": "L1",
"NAME": "z"
},
{
"DIMENSION": "L1 T-1",
"NAME": "v_x"
},
{
"DIMENSION": "L1 T-1",
"NAME": "v_z"
}
],
"LAW": [
{
"EQUATION": "D(x,t)=v_x",
"NAME": "KIN_X",
"REFS": [
"t",
"v_x",
"x"
],
"ROLE": "EOM(x)",
"STATEMENT": "dx/dt = v_x"
},
{
"EQUATION": "D(z,t)=v_z",
"NAME": "KIN_Z",
"REFS": [
"t",
"v_z",
"z"
],
"ROLE": "EOM(z)",
"STATEMENT": "dz/dt = v_z"
},
{
"EQUATION": "m*D(v_x,t)=0",
"NAME": "EOM_X",
"REFS": [
"m",
"t",
"v_x"
],
"ROLE": "EOM(v_x)",
"STATEMENT": "m dv_x/dt = 0"
},
{
"EQUATION": "m*D(v_z,t)=0",
"NAME": "EOM_Z",
"REFS": [
"m",
"t",
"v_z"
],
"ROLE": "EOM(v_z)",
"STATEMENT": "m dv_z/dt = 0"
}
]
}
},
"modules": [
"{\"ID\": \"TEST-SUMP\", \"VERSION\": \"1.0.0\", \"TITLE\": \"Test: a sum inside a product\", \"SOURCE\": \"synthetic fixture\", \"PREREQUISITES\": [{\"SLOT\": \"VELOCITY\", \"KIND\": \"DOF\", \"DIMENSION\": \"L1 T-1\", \"MIN\": 1, \"MAX\": 3, \"LABEL\": \"the velocity components of the body, one per axis\"}], \"PARAMETERS\": [{\"NAME\": \"k_q\", \"DIMENSION\": \"L-1 M1\", \"SUPPLY\": \"AUTHOR\", \"LABEL\": \"a quadratic coefficient\"}], \"SUMS\": [{\"NAME\": \"SPEED2\", \"OVER\": \"VELOCITY\", \"EACH\": \"VELOCITY^2\"}], \"TERMS\": [{\"TARGET\": \"VELOCITY\", \"SIGN\": \"-\", \"EXPR\": \"k_q*SPEED2\", \"LABEL\": \"the test force\"}], \"ASSUMPTIONS\": [], \"BOUNDARIES\": [], \"NOT_CHOSEN\": \"No sum test.\", \"NOT_INCLUDED\": [], \"EXCLUDES\": [], \"INTERACTS_WITH\": [], \"TEST_BINDINGS\": [{\"NAME\": \"PROJECTILE_2D\", \"TPK\": {\"DOF\": [{\"NAME\": \"t\", \"DIMENSION\": \"T1\"}, {\"NAME\": \"x\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"z\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"v_x\", \"DIMENSION\": \"L1 T-1\"}, {\"NAME\": \"v_z\", \"DIMENSION\": \"L1 T-1\"}], \"CONSTANT\": [{\"NAME\": \"m\", \"DIMENSION\": \"M1\"}], \"LAW\": [{\"NAME\": \"KIN_X\", \"STATEMENT\": \"dx/dt = v_x\", \"REFS\": [\"t\", \"v_x\", \"x\"], \"ROLE\": \"EOM(x)\", \"EQUATION\": \"D(x,t)=v_x\"}, {\"NAME\": \"KIN_Z\", \"STATEMENT\": \"dz/dt = v_z\", \"REFS\": [\"t\", \"v_z\", \"z\"], \"ROLE\": \"EOM(z)\", \"EQUATION\": \"D(z,t)=v_z\"}, {\"NAME\": \"EOM_X\", \"STATEMENT\": \"m dv_x/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_x\"], \"ROLE\": \"EOM(v_x)\", \"EQUATION\": \"m*D(v_x,t)=0\"}, {\"NAME\": \"EOM_Z\", \"STATEMENT\": \"m dv_z/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_z\"], \"ROLE\": \"EOM(v_z)\", \"EQUATION\": \"m*D(v_z,t)=0\"}], \"ASSUMPTION\": [{\"NAME\": \"point_mass\", \"PROPOSITION\": \"the body is treated as a point mass\", \"REFS\": [\"m\"]}]}, \"BIND\": {\"VELOCITY\": [\"v_x\", \"v_z\"]}, \"VALUES\": {\"k_q\": {}}, \"ANSWERS\": {}}]}",
"{\"ID\": \"TEST-SHARE\", \"VERSION\": \"1.0.0\", \"TITLE\": \"Test: an author parameter shared by name\", \"SOURCE\": \"synthetic fixture\", \"PREREQUISITES\": [], \"PARAMETERS\": [{\"NAME\": \"k_q\", \"DIMENSION\": \"L-1 M1\", \"SUPPLY\": \"AUTHOR\", \"LABEL\": \"a quadratic coefficient, named by another module too\"}], \"SUMS\": [], \"TERMS\": [], \"ASSUMPTIONS\": [], \"BOUNDARIES\": [], \"NOT_CHOSEN\": \"No shared-name test.\", \"NOT_INCLUDED\": [], \"EXCLUDES\": [], \"INTERACTS_WITH\": [], \"TEST_BINDINGS\": [{\"NAME\": \"PROJECTILE_2D\", \"TPK\": {\"DOF\": [{\"NAME\": \"t\", \"DIMENSION\": \"T1\"}, {\"NAME\": \"x\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"z\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"v_x\", \"DIMENSION\": \"L1 T-1\"}, {\"NAME\": \"v_z\", \"DIMENSION\": \"L1 T-1\"}], \"CONSTANT\": [{\"NAME\": \"m\", \"DIMENSION\": \"M1\"}], \"LAW\": [{\"NAME\": \"KIN_X\", \"STATEMENT\": \"dx/dt = v_x\", \"REFS\": [\"t\", \"v_x\", \"x\"], \"ROLE\": \"EOM(x)\", \"EQUATION\": \"D(x,t)=v_x\"}, {\"NAME\": \"KIN_Z\", \"STATEMENT\": \"dz/dt = v_z\", \"REFS\": [\"t\", \"v_z\", \"z\"], \"ROLE\": \"EOM(z)\", \"EQUATION\": \"D(z,t)=v_z\"}, {\"NAME\": \"EOM_X\", \"STATEMENT\": \"m dv_x/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_x\"], \"ROLE\": \"EOM(v_x)\", \"EQUATION\": \"m*D(v_x,t)=0\"}, {\"NAME\": \"EOM_Z\", \"STATEMENT\": \"m dv_z/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_z\"], \"ROLE\": \"EOM(v_z)\", \"EQUATION\": \"m*D(v_z,t)=0\"}], \"ASSUMPTION\": [{\"NAME\": \"point_mass\", \"PROPOSITION\": \"the body is treated as a point mass\", \"REFS\": [\"m\"]}]}, \"BIND\": {}, \"VALUES\": {\"k_q\": {}}, \"ANSWERS\": {}}]}"
]
},
"expected": "[\"REFUSED\",\"EXPAND: TEST-SHARE 1.0.0 and TEST-SUMP 1.0.0 both emit k_q, differently\"]",
"fn": "module_expand",
"hand_checked": true,
"name": "X63 the same, one given a value: they differ, refused"
},
{
"args": {
"lines": []
},
"expected": "[\"OK\",[\"VERSIONS\",[]],[\"OFFERED\",[]],[\"STATES\",[]]]",
"fn": "catalogue_state",
"hand_checked": true,
"name": "S01 no line: an empty catalogue"
},
{
"args": {
"lines": [
{
"ACT": "MODULE ADD",
"DATE": "2026-10-01",
"DIGEST": "5f3fe27b42378bce0830b0d0959f892f4a8e73b12b540ae877e39e6439d08b4d",
"ID": "AIR-LINEAR",
"VERSION": "1.0.0"
},
{
"ACT": "MODULE ADD",
"DATE": "2026-10-01",
"DIGEST": "6fb53c3a6546151eead2bd6e72e9cf8334f3a2040ad0ee2f5b988ec96d6fc852",
"ID": "AIR-QUADRATIC",
"VERSION": "1.0.0"
},
{
"ACT": "MODULE ADD",
"DATE": "2026-10-01",
"DIGEST": "24877ccb5c8ec300d29ed82ce6650592f35cf8899a3d878ccce9c08d4c72c025",
"ID": "GRAV-UNIFORM",
"VERSION": "1.0.0"
},
{
"ACT": "MODULE ADD",
"DATE": "2026-10-01",
"DIGEST": "8f39a356f35527b901fcee012764590f0819c8ffdeccad4bc05195ce3d2e0bcf",
"ID": "MATH",
"VERSION": "1.0.0"
}
]
},
"computed": "digests by existing TPC-PY functions over literal data",
"expected": "[\"OK\",[\"VERSIONS\",[[\"AIR-LINEAR\",\"1.0.0\",\"5f3fe27b42378bce0830b0d0959f892f4a8e73b12b540ae877e39e6439d08b4d\",\"OFFERED\",\"2026-10-01\",\"\"],[\"AIR-QUADRATIC\",\"1.0.0\",\"6fb53c3a6546151eead2bd6e72e9cf8334f3a2040ad0ee2f5b988ec96d6fc852\",\"OFFERED\",\"2026-10-01\",\"\"],[\"GRAV-UNIFORM\",\"1.0.0\",\"24877ccb5c8ec300d29ed82ce6650592f35cf8899a3d878ccce9c08d4c72c025\",\"OFFERED\",\"2026-10-01\",\"\"],[\"MATH\",\"1.0.0\",\"8f39a356f35527b901fcee012764590f0819c8ffdeccad4bc05195ce3d2e0bcf\",\"OFFERED\",\"2026-10-01\",\"\"]]],[\"OFFERED\",[[\"AIR-LINEAR\",\"1.0.0\",\"5f3fe27b42378bce0830b0d0959f892f4a8e73b12b540ae877e39e6439d08b4d\"],[\"AIR-QUADRATIC\",\"1.0.0\",\"6fb53c3a6546151eead2bd6e72e9cf8334f3a2040ad0ee2f5b988ec96d6fc852\"],[\"GRAV-UNIFORM\",\"1.0.0\",\"24877ccb5c8ec300d29ed82ce6650592f35cf8899a3d878ccce9c08d4c72c025\"],[\"MATH\",\"1.0.0\",\"8f39a356f35527b901fcee012764590f0819c8ffdeccad4bc05195ce3d2e0bcf\"]]],[\"STATES\",[[1,\"6b762dee9c4eebd4d4a733cf23563ec5cf00597d2c9218661394acef4d73f92a\"],[2,\"45504804366ccda13432d9a6f611443c9a9471d56e14c3dc5c20a907841f8397\"],[3,\"05585887057d5127e313f19d2da51b5ff845f7ade54ba47718f81995258be87e\"],[4,\"e6daa136c61c09471760b8d472c93bab9639752b8c22180b445918ac759e3852\"]]]]",
"fn": "catalogue_state",
"hand_checked": false,
"name": "S02 the first catalogue: four MODULE ADD lines"
},
{
"args": {
"lines": [
{
"ACT": "MODULE ADD",
"DATE": "2026-10-01",
"DIGEST": "5f3fe27b42378bce0830b0d0959f892f4a8e73b12b540ae877e39e6439d08b4d",
"ID": "AIR-LINEAR",
"VERSION": "1.0.0"
},
{
"ACT": "MODULE ADD",
"DATE": "2026-10-01",
"DIGEST": "6fb53c3a6546151eead2bd6e72e9cf8334f3a2040ad0ee2f5b988ec96d6fc852",
"ID": "AIR-QUADRATIC",
"VERSION": "1.0.0"
},
{
"ACT": "MODULE ADD",
"DATE": "2026-10-01",
"DIGEST": "24877ccb5c8ec300d29ed82ce6650592f35cf8899a3d878ccce9c08d4c72c025",
"ID": "GRAV-UNIFORM",
"VERSION": "1.0.0"
},
{
"ACT": "MODULE ADD",
"DATE": "2026-10-01",
"DIGEST": "8f39a356f35527b901fcee012764590f0819c8ffdeccad4bc05195ce3d2e0bcf",
"ID": "MATH",
"VERSION": "1.0.0"
},
{
"ACT": "MODULE VERSION",
"DATE": "2026-10-02",
"DIGEST": "5be3923c28dc8f8ff910b033c2d17154f267f2a20fdb32c74a07293a37dfe338",
"ID": "GRAV-UNIFORM",
"VERSION": "1.1.0"
}
]
},
"computed": "digests by existing TPC-PY functions over literal data",
"expected": "[\"OK\",[\"VERSIONS\",[[\"AIR-LINEAR\",\"1.0.0\",\"5f3fe27b42378bce0830b0d0959f892f4a8e73b12b540ae877e39e6439d08b4d\",\"OFFERED\",\"2026-10-01\",\"\"],[\"AIR-QUADRATIC\",\"1.0.0\",\"6fb53c3a6546151eead2bd6e72e9cf8334f3a2040ad0ee2f5b988ec96d6fc852\",\"OFFERED\",\"2026-10-01\",\"\"],[\"GRAV-UNIFORM\",\"1.0.0\",\"24877ccb5c8ec300d29ed82ce6650592f35cf8899a3d878ccce9c08d4c72c025\",\"SUPERSEDED\",\"2026-10-02\",\"\"],[\"GRAV-UNIFORM\",\"1.1.0\",\"5be3923c28dc8f8ff910b033c2d17154f267f2a20fdb32c74a07293a37dfe338\",\"OFFERED\",\"2026-10-02\",\"\"],[\"MATH\",\"1.0.0\",\"8f39a356f35527b901fcee012764590f0819c8ffdeccad4bc05195ce3d2e0bcf\",\"OFFERED\",\"2026-10-01\",\"\"]]],[\"OFFERED\",[[\"AIR-LINEAR\",\"1.0.0\",\"5f3fe27b42378bce0830b0d0959f892f4a8e73b12b540ae877e39e6439d08b4d\"],[\"AIR-QUADRATIC\",\"1.0.0\",\"6fb53c3a6546151eead2bd6e72e9cf8334f3a2040ad0ee2f5b988ec96d6fc852\"],[\"GRAV-UNIFORM\",\"1.1.0\",\"5be3923c28dc8f8ff910b033c2d17154f267f2a20fdb32c74a07293a37dfe338\"],[\"MATH\",\"1.0.0\",\"8f39a356f35527b901fcee012764590f0819c8ffdeccad4bc05195ce3d2e0bcf\"]]],[\"STATES\",[[1,\"6b762dee9c4eebd4d4a733cf23563ec5cf00597d2c9218661394acef4d73f92a\"],[2,\"45504804366ccda13432d9a6f611443c9a9471d56e14c3dc5c20a907841f8397\"],[3,\"05585887057d5127e313f19d2da51b5ff845f7ade54ba47718f81995258be87e\"],[4,\"e6daa136c61c09471760b8d472c93bab9639752b8c22180b445918ac759e3852\"],[5,\"2989c1ae13adeef9729cc94954eb12048901a5a92b2db340df65c901d8320433\"]]]]",
"fn": "catalogue_state",
"hand_checked": false,
"name": "S03 MODULE VERSION: the previous version SUPERSEDED in the same act"
},
{
"args": {
"lines": [
{
"ACT": "MODULE ADD",
"DATE": "2026-10-01",
"DIGEST": "5f3fe27b42378bce0830b0d0959f892f4a8e73b12b540ae877e39e6439d08b4d",
"ID": "AIR-LINEAR",
"VERSION": "1.0.0"
},
{
"ACT": "MODULE ADD",
"DATE": "2026-10-01",
"DIGEST": "6fb53c3a6546151eead2bd6e72e9cf8334f3a2040ad0ee2f5b988ec96d6fc852",
"ID": "AIR-QUADRATIC",
"VERSION": "1.0.0"
},
{
"ACT": "MODULE ADD",
"DATE": "2026-10-01",
"DIGEST": "24877ccb5c8ec300d29ed82ce6650592f35cf8899a3d878ccce9c08d4c72c025",
"ID": "GRAV-UNIFORM",
"VERSION": "1.0.0"
},
{
"ACT": "MODULE ADD",
"DATE": "2026-10-01",
"DIGEST": "8f39a356f35527b901fcee012764590f0819c8ffdeccad4bc05195ce3d2e0bcf",
"ID": "MATH",
"VERSION": "1.0.0"
},
{
"ACT": "MODULE RETIRE",
"DATE": "2026-10-02",
"ID": "MATH",
"VERSION": "1.0.0"
}
]
},
"computed": "digests by existing TPC-PY functions over literal data",
"expected": "[\"OK\",[\"VERSIONS\",[[\"AIR-LINEAR\",\"1.0.0\",\"5f3fe27b42378bce0830b0d0959f892f4a8e73b12b540ae877e39e6439d08b4d\",\"OFFERED\",\"2026-10-01\",\"\"],[\"AIR-QUADRATIC\",\"1.0.0\",\"6fb53c3a6546151eead2bd6e72e9cf8334f3a2040ad0ee2f5b988ec96d6fc852\",\"OFFERED\",\"2026-10-01\",\"\"],[\"GRAV-UNIFORM\",\"1.0.0\",\"24877ccb5c8ec300d29ed82ce6650592f35cf8899a3d878ccce9c08d4c72c025\",\"OFFERED\",\"2026-10-01\",\"\"],[\"MATH\",\"1.0.0\",\"8f39a356f35527b901fcee012764590f0819c8ffdeccad4bc05195ce3d2e0bcf\",\"RETIRED\",\"2026-10-02\",\"\"]]],[\"OFFERED\",[[\"AIR-LINEAR\",\"1.0.0\",\"5f3fe27b42378bce0830b0d0959f892f4a8e73b12b540ae877e39e6439d08b4d\"],[\"AIR-QUADRATIC\",\"1.0.0\",\"6fb53c3a6546151eead2bd6e72e9cf8334f3a2040ad0ee2f5b988ec96d6fc852\"],[\"GRAV-UNIFORM\",\"1.0.0\",\"24877ccb5c8ec300d29ed82ce6650592f35cf8899a3d878ccce9c08d4c72c025\"]]],[\"STATES\",[[1,\"6b762dee9c4eebd4d4a733cf23563ec5cf00597d2c9218661394acef4d73f92a\"],[2,\"45504804366ccda13432d9a6f611443c9a9471d56e14c3dc5c20a907841f8397\"],[3,\"05585887057d5127e313f19d2da51b5ff845f7ade54ba47718f81995258be87e\"],[4,\"e6daa136c61c09471760b8d472c93bab9639752b8c22180b445918ac759e3852\"],[5,\"05585887057d5127e313f19d2da51b5ff845f7ade54ba47718f81995258be87e\"]]]]",
"fn": "catalogue_state",
"hand_checked": false,
"name": "S04 MODULE RETIRE"
},
{
"args": {
"lines": [
{
"ACT": "MODULE ADD",
"DATE": "2026-10-01",
"DIGEST": "5f3fe27b42378bce0830b0d0959f892f4a8e73b12b540ae877e39e6439d08b4d",
"ID": "AIR-LINEAR",
"VERSION": "1.0.0"
},
{
"ACT": "MODULE ADD",
"DATE": "2026-10-01",
"DIGEST": "6fb53c3a6546151eead2bd6e72e9cf8334f3a2040ad0ee2f5b988ec96d6fc852",
"ID": "AIR-QUADRATIC",
"VERSION": "1.0.0"
},
{
"ACT": "MODULE ADD",
"DATE": "2026-10-01",
"DIGEST": "24877ccb5c8ec300d29ed82ce6650592f35cf8899a3d878ccce9c08d4c72c025",
"ID": "GRAV-UNIFORM",
"VERSION": "1.0.0"
},
{
"ACT": "MODULE ADD",
"DATE": "2026-10-01",
"DIGEST": "8f39a356f35527b901fcee012764590f0819c8ffdeccad4bc05195ce3d2e0bcf",
"ID": "MATH",
"VERSION": "1.0.0"
},
{
"ACT": "MODULE RETIRE",
"DATE": "2026-10-02",
"ID": "MATH",
"VERSION": "1.0.0"
},
{
"ACT": "MODULE REINSTATE",
"DATE": "2026-10-03",
"ID": "MATH",
"VERSION": "1.0.0"
}
]
},
"computed": "digests by existing TPC-PY functions over literal data",
"expected": "[\"OK\",[\"VERSIONS\",[[\"AIR-LINEAR\",\"1.0.0\",\"5f3fe27b42378bce0830b0d0959f892f4a8e73b12b540ae877e39e6439d08b4d\",\"OFFERED\",\"2026-10-01\",\"\"],[\"AIR-QUADRATIC\",\"1.0.0\",\"6fb53c3a6546151eead2bd6e72e9cf8334f3a2040ad0ee2f5b988ec96d6fc852\",\"OFFERED\",\"2026-10-01\",\"\"],[\"GRAV-UNIFORM\",\"1.0.0\",\"24877ccb5c8ec300d29ed82ce6650592f35cf8899a3d878ccce9c08d4c72c025\",\"OFFERED\",\"2026-10-01\",\"\"],[\"MATH\",\"1.0.0\",\"8f39a356f35527b901fcee012764590f0819c8ffdeccad4bc05195ce3d2e0bcf\",\"OFFERED\",\"2026-10-03\",\"\"]]],[\"OFFERED\",[[\"AIR-LINEAR\",\"1.0.0\",\"5f3fe27b42378bce0830b0d0959f892f4a8e73b12b540ae877e39e6439d08b4d\"],[\"AIR-QUADRATIC\",\"1.0.0\",\"6fb53c3a6546151eead2bd6e72e9cf8334f3a2040ad0ee2f5b988ec96d6fc852\"],[\"GRAV-UNIFORM\",\"1.0.0\",\"24877ccb5c8ec300d29ed82ce6650592f35cf8899a3d878ccce9c08d4c72c025\"],[\"MATH\",\"1.0.0\",\"8f39a356f35527b901fcee012764590f0819c8ffdeccad4bc05195ce3d2e0bcf\"]]],[\"STATES\",[[1,\"6b762dee9c4eebd4d4a733cf23563ec5cf00597d2c9218661394acef4d73f92a\"],[2,\"45504804366ccda13432d9a6f611443c9a9471d56e14c3dc5c20a907841f8397\"],[3,\"05585887057d5127e313f19d2da51b5ff845f7ade54ba47718f81995258be87e\"],[4,\"e6daa136c61c09471760b8d472c93bab9639752b8c22180b445918ac759e3852\"],[5,\"05585887057d5127e313f19d2da51b5ff845f7ade54ba47718f81995258be87e\"],[6,\"e6daa136c61c09471760b8d472c93bab9639752b8c22180b445918ac759e3852\"]]]]",
"fn": "catalogue_state",
"hand_checked": false,
"name": "S05 MODULE REINSTATE of a RETIRED version; equal offers, equal state digests"
},
{
"args": {
"lines": [
{
"ACT": "MODULE ADD",
"DATE": "2026-10-01",
"DIGEST": "5f3fe27b42378bce0830b0d0959f892f4a8e73b12b540ae877e39e6439d08b4d",
"ID": "AIR-LINEAR",
"VERSION": "1.0.0"
},
{
"ACT": "MODULE ADD",
"DATE": "2026-10-01",
"DIGEST": "6fb53c3a6546151eead2bd6e72e9cf8334f3a2040ad0ee2f5b988ec96d6fc852",
"ID": "AIR-QUADRATIC",
"VERSION": "1.0.0"
},
{
"ACT": "MODULE ADD",
"DATE": "2026-10-01",
"DIGEST": "24877ccb5c8ec300d29ed82ce6650592f35cf8899a3d878ccce9c08d4c72c025",
"ID": "GRAV-UNIFORM",
"VERSION": "1.0.0"
},
{
"ACT": "MODULE ADD",
"DATE": "2026-10-01",
"DIGEST": "8f39a356f35527b901fcee012764590f0819c8ffdeccad4bc05195ce3d2e0bcf",
"ID": "MATH",
"VERSION": "1.0.0"
},
{
"ACT": "MODULE VERSION",
"DATE": "2026-10-02",
"DIGEST": "5be3923c28dc8f8ff910b033c2d17154f267f2a20fdb32c74a07293a37dfe338",
"ID": "GRAV-UNIFORM",
"VERSION": "1.1.0"
},
{
"ACT": "MODULE REINSTATE",
"DATE": "2026-10-03",
"ID": "GRAV-UNIFORM",
"VERSION": "1.0.0"
}
]
},
"computed": "digests by existing TPC-PY functions over literal data",
"expected": "[\"OK\",[\"VERSIONS\",[[\"AIR-LINEAR\",\"1.0.0\",\"5f3fe27b42378bce0830b0d0959f892f4a8e73b12b540ae877e39e6439d08b4d\",\"OFFERED\",\"2026-10-01\",\"\"],[\"AIR-QUADRATIC\",\"1.0.0\",\"6fb53c3a6546151eead2bd6e72e9cf8334f3a2040ad0ee2f5b988ec96d6fc852\",\"OFFERED\",\"2026-10-01\",\"\"],[\"GRAV-UNIFORM\",\"1.0.0\",\"24877ccb5c8ec300d29ed82ce6650592f35cf8899a3d878ccce9c08d4c72c025\",\"OFFERED\",\"2026-10-03\",\"\"],[\"GRAV-UNIFORM\",\"1.1.0\",\"5be3923c28dc8f8ff910b033c2d17154f267f2a20fdb32c74a07293a37dfe338\",\"SUPERSEDED\",\"2026-10-03\",\"\"],[\"MATH\",\"1.0.0\",\"8f39a356f35527b901fcee012764590f0819c8ffdeccad4bc05195ce3d2e0bcf\",\"OFFERED\",\"2026-10-01\",\"\"]]],[\"OFFERED\",[[\"AIR-LINEAR\",\"1.0.0\",\"5f3fe27b42378bce0830b0d0959f892f4a8e73b12b540ae877e39e6439d08b4d\"],[\"AIR-QUADRATIC\",\"1.0.0\",\"6fb53c3a6546151eead2bd6e72e9cf8334f3a2040ad0ee2f5b988ec96d6fc852\"],[\"GRAV-UNIFORM\",\"1.0.0\",\"24877ccb5c8ec300d29ed82ce6650592f35cf8899a3d878ccce9c08d4c72c025\"],[\"MATH\",\"1.0.0\",\"8f39a356f35527b901fcee012764590f0819c8ffdeccad4bc05195ce3d2e0bcf\"]]],[\"STATES\",[[1,\"6b762dee9c4eebd4d4a733cf23563ec5cf00597d2c9218661394acef4d73f92a\"],[2,\"45504804366ccda13432d9a6f611443c9a9471d56e14c3dc5c20a907841f8397\"],[3,\"05585887057d5127e313f19d2da51b5ff845f7ade54ba47718f81995258be87e\"],[4,\"e6daa136c61c09471760b8d472c93bab9639752b8c22180b445918ac759e3852\"],[5,\"2989c1ae13adeef9729cc94954eb12048901a5a92b2db340df65c901d8320433\"],[6,\"e6daa136c61c09471760b8d472c93bab9639752b8c22180b445918ac759e3852\"]]]]",
"fn": "catalogue_state",
"hand_checked": false,
"name": "S06 MODULE REINSTATE of a SUPERSEDED version: the OFFERED one SUPERSEDED"
},
{
"args": {
"lines": [
{
"ACT": "MODULE ADD",
"DATE": "2026-10-01",
"DIGEST": "5f3fe27b42378bce0830b0d0959f892f4a8e73b12b540ae877e39e6439d08b4d",
"ID": "AIR-LINEAR",
"VERSION": "1.0.0"
},
{
"ACT": "MODULE ADD",
"DATE": "2026-10-01",
"DIGEST": "6fb53c3a6546151eead2bd6e72e9cf8334f3a2040ad0ee2f5b988ec96d6fc852",
"ID": "AIR-QUADRATIC",
"VERSION": "1.0.0"
},
{
"ACT": "MODULE ADD",
"DATE": "2026-10-01",
"DIGEST": "24877ccb5c8ec300d29ed82ce6650592f35cf8899a3d878ccce9c08d4c72c025",
"ID": "GRAV-UNIFORM",
"VERSION": "1.0.0"
},
{
"ACT": "MODULE ADD",
"DATE": "2026-10-01",
"DIGEST": "8f39a356f35527b901fcee012764590f0819c8ffdeccad4bc05195ce3d2e0bcf",
"ID": "MATH",
"VERSION": "1.0.0"
},
{
"ACT": "MODULE WITHDRAW",
"DATE": "2026-10-02",
"ID": "GRAV-UNIFORM",
"REASON": "the weight's sign was reversed in the binding page's preview",
"VERSION": "1.0.0"
}
]
},
"computed": "digests by existing TPC-PY functions over literal data",
"expected": "[\"OK\",[\"VERSIONS\",[[\"AIR-LINEAR\",\"1.0.0\",\"5f3fe27b42378bce0830b0d0959f892f4a8e73b12b540ae877e39e6439d08b4d\",\"OFFERED\",\"2026-10-01\",\"\"],[\"AIR-QUADRATIC\",\"1.0.0\",\"6fb53c3a6546151eead2bd6e72e9cf8334f3a2040ad0ee2f5b988ec96d6fc852\",\"OFFERED\",\"2026-10-01\",\"\"],[\"GRAV-UNIFORM\",\"1.0.0\",\"24877ccb5c8ec300d29ed82ce6650592f35cf8899a3d878ccce9c08d4c72c025\",\"WITHDRAWN\",\"2026-10-02\",\"the weight's sign was reversed in the binding page's preview\"],[\"MATH\",\"1.0.0\",\"8f39a356f35527b901fcee012764590f0819c8ffdeccad4bc05195ce3d2e0bcf\",\"OFFERED\",\"2026-10-01\",\"\"]]],[\"OFFERED\",[[\"AIR-LINEAR\",\"1.0.0\",\"5f3fe27b42378bce0830b0d0959f892f4a8e73b12b540ae877e39e6439d08b4d\"],[\"AIR-QUADRATIC\",\"1.0.0\",\"6fb53c3a6546151eead2bd6e72e9cf8334f3a2040ad0ee2f5b988ec96d6fc852\"],[\"MATH\",\"1.0.0\",\"8f39a356f35527b901fcee012764590f0819c8ffdeccad4bc05195ce3d2e0bcf\"]]],[\"STATES\",[[1,\"6b762dee9c4eebd4d4a733cf23563ec5cf00597d2c9218661394acef4d73f92a\"],[2,\"45504804366ccda13432d9a6f611443c9a9471d56e14c3dc5c20a907841f8397\"],[3,\"05585887057d5127e313f19d2da51b5ff845f7ade54ba47718f81995258be87e\"],[4,\"e6daa136c61c09471760b8d472c93bab9639752b8c22180b445918ac759e3852\"],[5,\"d4330326363217b053f4341478ecc22c8f817696fa10cf3214574cfcf54730ea\"]]]]",
"fn": "catalogue_state",
"hand_checked": false,
"name": "S07 MODULE WITHDRAW of the OFFERED version: the ID offers nothing"
},
{
"args": {
"lines": [
{
"ACT": "MODULE ADD",
"DATE": "2026-10-01",
"DIGEST": "5f3fe27b42378bce0830b0d0959f892f4a8e73b12b540ae877e39e6439d08b4d",
"ID": "AIR-LINEAR",
"VERSION": "1.0.0"
},
{
"ACT": "MODULE ADD",
"DATE": "2026-10-01",
"DIGEST": "6fb53c3a6546151eead2bd6e72e9cf8334f3a2040ad0ee2f5b988ec96d6fc852",
"ID": "AIR-QUADRATIC",
"VERSION": "1.0.0"
},
{
"ACT": "MODULE ADD",
"DATE": "2026-10-01",
"DIGEST": "24877ccb5c8ec300d29ed82ce6650592f35cf8899a3d878ccce9c08d4c72c025",
"ID": "GRAV-UNIFORM",
"VERSION": "1.0.0"
},
{
"ACT": "MODULE ADD",
"DATE": "2026-10-01",
"DIGEST": "8f39a356f35527b901fcee012764590f0819c8ffdeccad4bc05195ce3d2e0bcf",
"ID": "MATH",
"VERSION": "1.0.0"
},
{
"ACT": "MODULE VERSION",
"DATE": "2026-10-02",
"DIGEST": "5be3923c28dc8f8ff910b033c2d17154f267f2a20fdb32c74a07293a37dfe338",
"ID": "GRAV-UNIFORM",
"VERSION": "1.1.0"
},
{
"ACT": "MODULE WITHDRAW",
"DATE": "2026-10-03",
"ID": "GRAV-UNIFORM",
"REASON": "the weight's sign was reversed in the binding page's preview",
"VERSION": "1.0.0"
}
]
},
"computed": "digests by existing TPC-PY functions over literal data",
"expected": "[\"OK\",[\"VERSIONS\",[[\"AIR-LINEAR\",\"1.0.0\",\"5f3fe27b42378bce0830b0d0959f892f4a8e73b12b540ae877e39e6439d08b4d\",\"OFFERED\",\"2026-10-01\",\"\"],[\"AIR-QUADRATIC\",\"1.0.0\",\"6fb53c3a6546151eead2bd6e72e9cf8334f3a2040ad0ee2f5b988ec96d6fc852\",\"OFFERED\",\"2026-10-01\",\"\"],[\"GRAV-UNIFORM\",\"1.0.0\",\"24877ccb5c8ec300d29ed82ce6650592f35cf8899a3d878ccce9c08d4c72c025\",\"WITHDRAWN\",\"2026-10-03\",\"the weight's sign was reversed in the binding page's preview\"],[\"GRAV-UNIFORM\",\"1.1.0\",\"5be3923c28dc8f8ff910b033c2d17154f267f2a20fdb32c74a07293a37dfe338\",\"OFFERED\",\"2026-10-02\",\"\"],[\"MATH\",\"1.0.0\",\"8f39a356f35527b901fcee012764590f0819c8ffdeccad4bc05195ce3d2e0bcf\",\"OFFERED\",\"2026-10-01\",\"\"]]],[\"OFFERED\",[[\"AIR-LINEAR\",\"1.0.0\",\"5f3fe27b42378bce0830b0d0959f892f4a8e73b12b540ae877e39e6439d08b4d\"],[\"AIR-QUADRATIC\",\"1.0.0\",\"6fb53c3a6546151eead2bd6e72e9cf8334f3a2040ad0ee2f5b988ec96d6fc852\"],[\"GRAV-UNIFORM\",\"1.1.0\",\"5be3923c28dc8f8ff910b033c2d17154f267f2a20fdb32c74a07293a37dfe338\"],[\"MATH\",\"1.0.0\",\"8f39a356f35527b901fcee012764590f0819c8ffdeccad4bc05195ce3d2e0bcf\"]]],[\"STATES\",[[1,\"6b762dee9c4eebd4d4a733cf23563ec5cf00597d2c9218661394acef4d73f92a\"],[2,\"45504804366ccda13432d9a6f611443c9a9471d56e14c3dc5c20a907841f8397\"],[3,\"05585887057d5127e313f19d2da51b5ff845f7ade54ba47718f81995258be87e\"],[4,\"e6daa136c61c09471760b8d472c93bab9639752b8c22180b445918ac759e3852\"],[5,\"2989c1ae13adeef9729cc94954eb12048901a5a92b2db340df65c901d8320433\"],[6,\"2989c1ae13adeef9729cc94954eb12048901a5a92b2db340df65c901d8320433\"]]]]",
"fn": "catalogue_state",
"hand_checked": false,
"name": "S08 MODULE WITHDRAW of a SUPERSEDED version"
},
{
"args": {
"lines": [
{
"ACT": "MODULE ADD",
"DATE": "2026-10-01",
"DIGEST": "5f3fe27b42378bce0830b0d0959f892f4a8e73b12b540ae877e39e6439d08b4d",
"ID": "AIR-LINEAR",
"VERSION": "1.0.0"
},
{
"ACT": "MODULE ADD",
"DATE": "2026-10-01",
"DIGEST": "6fb53c3a6546151eead2bd6e72e9cf8334f3a2040ad0ee2f5b988ec96d6fc852",
"ID": "AIR-QUADRATIC",
"VERSION": "1.0.0"
},
{
"ACT": "MODULE ADD",
"DATE": "2026-10-01",
"DIGEST": "24877ccb5c8ec300d29ed82ce6650592f35cf8899a3d878ccce9c08d4c72c025",
"ID": "GRAV-UNIFORM",
"VERSION": "1.0.0"
},
{
"ACT": "MODULE ADD",
"DATE": "2026-10-01",
"DIGEST": "8f39a356f35527b901fcee012764590f0819c8ffdeccad4bc05195ce3d2e0bcf",
"ID": "MATH",
"VERSION": "1.0.0"
},
{
"ACT": "MODULE VERSION",
"DATE": "2026-10-02",
"DIGEST": "5be3923c28dc8f8ff910b033c2d17154f267f2a20fdb32c74a07293a37dfe338",
"ID": "GRAV-UNIFORM",
"VERSION": "1.1.0"
},
{
"ACT": "MODULE WITHDRAW",
"DATE": "2026-10-03",
"ID": "GRAV-UNIFORM",
"REASON": "the weight's sign was reversed in the binding page's preview",
"REPLACED_BY": "1.0.0",
"VERSION": "1.1.0"
}
]
},
"computed": "digests by existing TPC-PY functions over literal data",
"expected": "[\"OK\",[\"VERSIONS\",[[\"AIR-LINEAR\",\"1.0.0\",\"5f3fe27b42378bce0830b0d0959f892f4a8e73b12b540ae877e39e6439d08b4d\",\"OFFERED\",\"2026-10-01\",\"\"],[\"AIR-QUADRATIC\",\"1.0.0\",\"6fb53c3a6546151eead2bd6e72e9cf8334f3a2040ad0ee2f5b988ec96d6fc852\",\"OFFERED\",\"2026-10-01\",\"\"],[\"GRAV-UNIFORM\",\"1.0.0\",\"24877ccb5c8ec300d29ed82ce6650592f35cf8899a3d878ccce9c08d4c72c025\",\"OFFERED\",\"2026-10-03\",\"\"],[\"GRAV-UNIFORM\",\"1.1.0\",\"5be3923c28dc8f8ff910b033c2d17154f267f2a20fdb32c74a07293a37dfe338\",\"WITHDRAWN\",\"2026-10-03\",\"the weight's sign was reversed in the binding page's preview\"],[\"MATH\",\"1.0.0\",\"8f39a356f35527b901fcee012764590f0819c8ffdeccad4bc05195ce3d2e0bcf\",\"OFFERED\",\"2026-10-01\",\"\"]]],[\"OFFERED\",[[\"AIR-LINEAR\",\"1.0.0\",\"5f3fe27b42378bce0830b0d0959f892f4a8e73b12b540ae877e39e6439d08b4d\"],[\"AIR-QUADRATIC\",\"1.0.0\",\"6fb53c3a6546151eead2bd6e72e9cf8334f3a2040ad0ee2f5b988ec96d6fc852\"],[\"GRAV-UNIFORM\",\"1.0.0\",\"24877ccb5c8ec300d29ed82ce6650592f35cf8899a3d878ccce9c08d4c72c025\"],[\"MATH\",\"1.0.0\",\"8f39a356f35527b901fcee012764590f0819c8ffdeccad4bc05195ce3d2e0bcf\"]]],[\"STATES\",[[1,\"6b762dee9c4eebd4d4a733cf23563ec5cf00597d2c9218661394acef4d73f92a\"],[2,\"45504804366ccda13432d9a6f611443c9a9471d56e14c3dc5c20a907841f8397\"],[3,\"05585887057d5127e313f19d2da51b5ff845f7ade54ba47718f81995258be87e\"],[4,\"e6daa136c61c09471760b8d472c93bab9639752b8c22180b445918ac759e3852\"],[5,\"2989c1ae13adeef9729cc94954eb12048901a5a92b2db340df65c901d8320433\"],[6,\"e6daa136c61c09471760b8d472c93bab9639752b8c22180b445918ac759e3852\"]]]]",
"fn": "catalogue_state",
"hand_checked": false,
"name": "S09 MODULE WITHDRAW naming REPLACED_BY a SUPERSEDED version"
},
{
"args": {
"lines": [
{
"ACT": "MODULE ADD",
"DATE": "2026-10-01",
"DIGEST": "5f3fe27b42378bce0830b0d0959f892f4a8e73b12b540ae877e39e6439d08b4d",
"ID": "AIR-LINEAR",
"VERSION": "1.0.0"
},
{
"ACT": "MODULE ADD",
"DATE": "2026-10-01",
"DIGEST": "6fb53c3a6546151eead2bd6e72e9cf8334f3a2040ad0ee2f5b988ec96d6fc852",
"ID": "AIR-QUADRATIC",
"VERSION": "1.0.0"
},
{
"ACT": "MODULE ADD",
"DATE": "2026-10-01",
"DIGEST": "24877ccb5c8ec300d29ed82ce6650592f35cf8899a3d878ccce9c08d4c72c025",
"ID": "GRAV-UNIFORM",
"VERSION": "1.0.0"
},
{
"ACT": "MODULE ADD",
"DATE": "2026-10-01",
"DIGEST": "8f39a356f35527b901fcee012764590f0819c8ffdeccad4bc05195ce3d2e0bcf",
"ID": "MATH",
"VERSION": "1.0.0"
},
{
"ACT": "MODULE RETIRE",
"DATE": "2026-10-02",
"ID": "GRAV-UNIFORM",
"VERSION": "1.0.0"
},
{
"ACT": "MODULE VERSION",
"DATE": "2026-10-03",
"DIGEST": "5be3923c28dc8f8ff910b033c2d17154f267f2a20fdb32c74a07293a37dfe338",
"ID": "GRAV-UNIFORM",
"VERSION": "1.1.0"
}
]
},
"computed": "digests by existing TPC-PY functions over literal data",
"expected": "[\"OK\",[\"VERSIONS\",[[\"AIR-LINEAR\",\"1.0.0\",\"5f3fe27b42378bce0830b0d0959f892f4a8e73b12b540ae877e39e6439d08b4d\",\"OFFERED\",\"2026-10-01\",\"\"],[\"AIR-QUADRATIC\",\"1.0.0\",\"6fb53c3a6546151eead2bd6e72e9cf8334f3a2040ad0ee2f5b988ec96d6fc852\",\"OFFERED\",\"2026-10-01\",\"\"],[\"GRAV-UNIFORM\",\"1.0.0\",\"24877ccb5c8ec300d29ed82ce6650592f35cf8899a3d878ccce9c08d4c72c025\",\"RETIRED\",\"2026-10-02\",\"\"],[\"GRAV-UNIFORM\",\"1.1.0\",\"5be3923c28dc8f8ff910b033c2d17154f267f2a20fdb32c74a07293a37dfe338\",\"OFFERED\",\"2026-10-03\",\"\"],[\"MATH\",\"1.0.0\",\"8f39a356f35527b901fcee012764590f0819c8ffdeccad4bc05195ce3d2e0bcf\",\"OFFERED\",\"2026-10-01\",\"\"]]],[\"OFFERED\",[[\"AIR-LINEAR\",\"1.0.0\",\"5f3fe27b42378bce0830b0d0959f892f4a8e73b12b540ae877e39e6439d08b4d\"],[\"AIR-QUADRATIC\",\"1.0.0\",\"6fb53c3a6546151eead2bd6e72e9cf8334f3a2040ad0ee2f5b988ec96d6fc852\"],[\"GRAV-UNIFORM\",\"1.1.0\",\"5be3923c28dc8f8ff910b033c2d17154f267f2a20fdb32c74a07293a37dfe338\"],[\"MATH\",\"1.0.0\",\"8f39a356f35527b901fcee012764590f0819c8ffdeccad4bc05195ce3d2e0bcf\"]]],[\"STATES\",[[1,\"6b762dee9c4eebd4d4a733cf23563ec5cf00597d2c9218661394acef4d73f92a\"],[2,\"45504804366ccda13432d9a6f611443c9a9471d56e14c3dc5c20a907841f8397\"],[3,\"05585887057d5127e313f19d2da51b5ff845f7ade54ba47718f81995258be87e\"],[4,\"e6daa136c61c09471760b8d472c93bab9639752b8c22180b445918ac759e3852\"],[5,\"d4330326363217b053f4341478ecc22c8f817696fa10cf3214574cfcf54730ea\"],[6,\"2989c1ae13adeef9729cc94954eb12048901a5a92b2db340df65c901d8320433\"]]]]",
"fn": "catalogue_state",
"hand_checked": false,
"name": "S10 MODULE VERSION of an ID whose versions are all RETIRED"
},
{
"args": {
"lines": [
{
"ACT": "MODULE ADD",
"DATE": "2026-10-01",
"DIGEST": "5f3fe27b42378bce0830b0d0959f892f4a8e73b12b540ae877e39e6439d08b4d",
"ID": "AIR-LINEAR",
"VERSION": "1.0.0"
},
{
"ACT": "MODULE ADD",
"DATE": "2026-10-01",
"DIGEST": "6fb53c3a6546151eead2bd6e72e9cf8334f3a2040ad0ee2f5b988ec96d6fc852",
"ID": "AIR-QUADRATIC",
"VERSION": "1.0.0"
},
{
"ACT": "MODULE ADD",
"DATE": "2026-10-01",
"DIGEST": "24877ccb5c8ec300d29ed82ce6650592f35cf8899a3d878ccce9c08d4c72c025",
"ID": "GRAV-UNIFORM",
"VERSION": "1.0.0"
},
{
"ACT": "MODULE ADD",
"DATE": "2026-10-01",
"DIGEST": "8f39a356f35527b901fcee012764590f0819c8ffdeccad4bc05195ce3d2e0bcf",
"ID": "MATH",
"VERSION": "1.0.0"
},
{
"ACT": "MODULE VERSION",
"DATE": "2026-10-02",
"DIGEST": "5be3923c28dc8f8ff910b033c2d17154f267f2a20fdb32c74a07293a37dfe338",
"ID": "GRAV-UNIFORM",
"VERSION": "1.1.0"
},
{
"ACT": "MODULE RETIRE",
"DATE": "2026-10-03",
"ID": "GRAV-UNIFORM",
"VERSION": "1.1.0"
},
{
"ACT": "MODULE REINSTATE",
"DATE": "2026-10-04",
"ID": "GRAV-UNIFORM",
"VERSION": "1.0.0"
},
{
"ACT": "MODULE WITHDRAW",
"DATE": "2026-10-05",
"ID": "GRAV-UNIFORM",
"REASON": "the weight's sign was reversed in the binding page's preview",
"REPLACED_BY": "1.1.0",
"VERSION": "1.0.0"
}
]
},
"computed": "digests by existing TPC-PY functions over literal data",
"expected": "[\"OK\",[\"VERSIONS\",[[\"AIR-LINEAR\",\"1.0.0\",\"5f3fe27b42378bce0830b0d0959f892f4a8e73b12b540ae877e39e6439d08b4d\",\"OFFERED\",\"2026-10-01\",\"\"],[\"AIR-QUADRATIC\",\"1.0.0\",\"6fb53c3a6546151eead2bd6e72e9cf8334f3a2040ad0ee2f5b988ec96d6fc852\",\"OFFERED\",\"2026-10-01\",\"\"],[\"GRAV-UNIFORM\",\"1.0.0\",\"24877ccb5c8ec300d29ed82ce6650592f35cf8899a3d878ccce9c08d4c72c025\",\"WITHDRAWN\",\"2026-10-05\",\"the weight's sign was reversed in the binding page's preview\"],[\"GRAV-UNIFORM\",\"1.1.0\",\"5be3923c28dc8f8ff910b033c2d17154f267f2a20fdb32c74a07293a37dfe338\",\"OFFERED\",\"2026-10-05\",\"\"],[\"MATH\",\"1.0.0\",\"8f39a356f35527b901fcee012764590f0819c8ffdeccad4bc05195ce3d2e0bcf\",\"OFFERED\",\"2026-10-01\",\"\"]]],[\"OFFERED\",[[\"AIR-LINEAR\",\"1.0.0\",\"5f3fe27b42378bce0830b0d0959f892f4a8e73b12b540ae877e39e6439d08b4d\"],[\"AIR-QUADRATIC\",\"1.0.0\",\"6fb53c3a6546151eead2bd6e72e9cf8334f3a2040ad0ee2f5b988ec96d6fc852\"],[\"GRAV-UNIFORM\",\"1.1.0\",\"5be3923c28dc8f8ff910b033c2d17154f267f2a20fdb32c74a07293a37dfe338\"],[\"MATH\",\"1.0.0\",\"8f39a356f35527b901fcee012764590f0819c8ffdeccad4bc05195ce3d2e0bcf\"]]],[\"STATES\",[[1,\"6b762dee9c4eebd4d4a733cf23563ec5cf00597d2c9218661394acef4d73f92a\"],[2,\"45504804366ccda13432d9a6f611443c9a9471d56e14c3dc5c20a907841f8397\"],[3,\"05585887057d5127e313f19d2da51b5ff845f7ade54ba47718f81995258be87e\"],[4,\"e6daa136c61c09471760b8d472c93bab9639752b8c22180b445918ac759e3852\"],[5,\"2989c1ae13adeef9729cc94954eb12048901a5a92b2db340df65c901d8320433\"],[6,\"d4330326363217b053f4341478ecc22c8f817696fa10cf3214574cfcf54730ea\"],[7,\"e6daa136c61c09471760b8d472c93bab9639752b8c22180b445918ac759e3852\"],[8,\"2989c1ae13adeef9729cc94954eb12048901a5a92b2db340df65c901d8320433\"]]]]",
"fn": "catalogue_state",
"hand_checked": false,
"name": "S11 REPLACED_BY a RETIRED version"
},
{
"args": {
"lines": [
{
"ACT": "MODULE ADD",
"DATE": "2026-10-01",
"DIGEST": "5f3fe27b42378bce0830b0d0959f892f4a8e73b12b540ae877e39e6439d08b4d",
"ID": "AIR-LINEAR",
"VERSION": "1.0.0"
},
{
"ACT": "MODULE ADD",
"DATE": "2026-10-01",
"DIGEST": "6fb53c3a6546151eead2bd6e72e9cf8334f3a2040ad0ee2f5b988ec96d6fc852",
"ID": "AIR-QUADRATIC",
"VERSION": "1.0.0"
},
{
"ACT": "MODULE ADD",
"DATE": "2026-10-01",
"DIGEST": "24877ccb5c8ec300d29ed82ce6650592f35cf8899a3d878ccce9c08d4c72c025",
"ID": "GRAV-UNIFORM",
"VERSION": "1.0.0"
},
{
"ACT": "MODULE ADD",
"DATE": "2026-10-01",
"DIGEST": "8f39a356f35527b901fcee012764590f0819c8ffdeccad4bc05195ce3d2e0bcf",
"ID": "MATH",
"VERSION": "1.0.0"
},
{
"ACT": "MODULE ADD",
"DATE": "2026-10-02",
"DIGEST": "ca978112ca1bbdcafac231b39a23dc4da786eff8147c4e72b9807785afee48bb",
"ID": "GRAV-UNIFORM",
"VERSION": "2.0.0"
}
]
},
"expected": "[\"REFUSED\",\"LINE 5: MODULE ADD of GRAV-UNIFORM, an ID already declared (no ID is reissued)\"]",
"fn": "catalogue_state",
"hand_checked": true,
"name": "S12 MODULE ADD of an ID already declared"
},
{
"args": {
"lines": [
{
"ACT": "MODULE ADD",
"DATE": "2026-10-01",
"DIGEST": "5f3fe27b42378bce0830b0d0959f892f4a8e73b12b540ae877e39e6439d08b4d",
"ID": "AIR-LINEAR",
"VERSION": "1.0.0"
},
{
"ACT": "MODULE ADD",
"DATE": "2026-10-01",
"DIGEST": "6fb53c3a6546151eead2bd6e72e9cf8334f3a2040ad0ee2f5b988ec96d6fc852",
"ID": "AIR-QUADRATIC",
"VERSION": "1.0.0"
},
{
"ACT": "MODULE ADD",
"DATE": "2026-10-01",
"DIGEST": "24877ccb5c8ec300d29ed82ce6650592f35cf8899a3d878ccce9c08d4c72c025",
"ID": "GRAV-UNIFORM",
"VERSION": "1.0.0"
},
{
"ACT": "MODULE ADD",
"DATE": "2026-10-01",
"DIGEST": "8f39a356f35527b901fcee012764590f0819c8ffdeccad4bc05195ce3d2e0bcf",
"ID": "MATH",
"VERSION": "1.0.0"
},
{
"ACT": "MODULE RETIRE",
"DATE": "2026-10-02",
"ID": "GRAV-UNIFORM",
"VERSION": "1.0.0"
},
{
"ACT": "MODULE ADD",
"DATE": "2026-10-03",
"DIGEST": "3e23e8160039594a33894f6564e1b1348bbd7a0088d42c4acb73eeaed59c009d",
"ID": "GRAV-UNIFORM",
"VERSION": "1.0.0"
}
]
},
"expected": "[\"REFUSED\",\"LINE 6: MODULE ADD of GRAV-UNIFORM, an ID already declared (no ID is reissued)\"]",
"fn": "catalogue_state",
"hand_checked": true,
"name": "S13 MODULE ADD of an ID whose only version is RETIRED"
},
{
"args": {
"lines": [
{
"ACT": "MODULE VERSION",
"DATE": "2026-10-01",
"DIGEST": "2e7d2c03a9507ae265ecf5b5356885a53393a2029d241394997265a1a25aefc6",
"ID": "GRAV-UNIFORM",
"VERSION": "1.0.0"
}
]
},
"expected": "[\"REFUSED\",\"LINE 1: MODULE VERSION of GRAV-UNIFORM, an ID never added\"]",
"fn": "catalogue_state",
"hand_checked": true,
"name": "S14 MODULE VERSION of an ID never added"
},
{
"args": {
"lines": [
{
"ACT": "MODULE ADD",
"DATE": "2026-10-01",
"DIGEST": "5f3fe27b42378bce0830b0d0959f892f4a8e73b12b540ae877e39e6439d08b4d",
"ID": "AIR-LINEAR",
"VERSION": "1.0.0"
},
{
"ACT": "MODULE ADD",
"DATE": "2026-10-01",
"DIGEST": "6fb53c3a6546151eead2bd6e72e9cf8334f3a2040ad0ee2f5b988ec96d6fc852",
"ID": "AIR-QUADRATIC",
"VERSION": "1.0.0"
},
{
"ACT": "MODULE ADD",
"DATE": "2026-10-01",
"DIGEST": "24877ccb5c8ec300d29ed82ce6650592f35cf8899a3d878ccce9c08d4c72c025",
"ID": "GRAV-UNIFORM",
"VERSION": "1.0.0"
},
{
"ACT": "MODULE ADD",
"DATE": "2026-10-01",
"DIGEST": "8f39a356f35527b901fcee012764590f0819c8ffdeccad4bc05195ce3d2e0bcf",
"ID": "MATH",
"VERSION": "1.0.0"
},
{
"ACT": "MODULE VERSION",
"DATE": "2026-10-02",
"DIGEST": "18ac3e7343f016890c510e93f935261169d9e3f565436429830faf0934f4f8e4",
"ID": "GRAV-UNIFORM",
"VERSION": "1.0.0"
}
]
},
"expected": "[\"REFUSED\",\"LINE 5: GRAV-UNIFORM 1.0.0 is already declared (no version is reissued)\"]",
"fn": "catalogue_state",
"hand_checked": true,
"name": "S15 MODULE VERSION reissuing a version"
},
{
"args": {
"lines": [
{
"ACT": "MODULE ADD",
"DATE": "2026-10-01",
"DIGEST": "5f3fe27b42378bce0830b0d0959f892f4a8e73b12b540ae877e39e6439d08b4d",
"ID": "AIR-LINEAR",
"VERSION": "1.0.0"
},
{
"ACT": "MODULE ADD",
"DATE": "2026-10-01",
"DIGEST": "6fb53c3a6546151eead2bd6e72e9cf8334f3a2040ad0ee2f5b988ec96d6fc852",
"ID": "AIR-QUADRATIC",
"VERSION": "1.0.0"
},
{
"ACT": "MODULE ADD",
"DATE": "2026-10-01",
"DIGEST": "24877ccb5c8ec300d29ed82ce6650592f35cf8899a3d878ccce9c08d4c72c025",
"ID": "GRAV-UNIFORM",
"VERSION": "1.0.0"
},
{
"ACT": "MODULE ADD",
"DATE": "2026-10-01",
"DIGEST": "8f39a356f35527b901fcee012764590f0819c8ffdeccad4bc05195ce3d2e0bcf",
"ID": "MATH",
"VERSION": "1.0.0"
},
{
"ACT": "MODULE VERSION",
"DATE": "2026-10-02",
"DIGEST": "3f79bb7b435b05321651daefd374cdc681dc06faa65e374e38337b88ca046dea",
"ID": "GRAV-UNIFORM",
"VERSION": "0.9.0"
}
]
},
"expected": "[\"REFUSED\",\"LINE 5: GRAV-UNIFORM 0.9.0 is not greater than GRAV-UNIFORM 1.0.0\"]",
"fn": "catalogue_state",
"hand_checked": true,
"name": "S16 MODULE VERSION not greater"
},
{
"args": {
"lines": [
{
"ACT": "MODULE ADD",
"DATE": "2026-10-01",
"DIGEST": "88662ab87ecb5884e6688116bd0fb4f9e049672582ff1bf8816767869882581a",
"ID": "TEST-V",
"VERSION": "1.9.0"
},
{
"ACT": "MODULE VERSION",
"DATE": "2026-10-02",
"DIGEST": "65e0e2ab9e080526e02b36b563481a9524714fb892344305ed1331d4ef97da20",
"ID": "TEST-V",
"VERSION": "1.10.0"
}
]
},
"computed": "digests by existing TPC-PY functions over literal data",
"expected": "[\"OK\",[\"VERSIONS\",[[\"TEST-V\",\"1.10.0\",\"65e0e2ab9e080526e02b36b563481a9524714fb892344305ed1331d4ef97da20\",\"OFFERED\",\"2026-10-02\",\"\"],[\"TEST-V\",\"1.9.0\",\"88662ab87ecb5884e6688116bd0fb4f9e049672582ff1bf8816767869882581a\",\"SUPERSEDED\",\"2026-10-02\",\"\"]]],[\"OFFERED\",[[\"TEST-V\",\"1.10.0\",\"65e0e2ab9e080526e02b36b563481a9524714fb892344305ed1331d4ef97da20\"]]],[\"STATES\",[[1,\"6922672f6cfef50462d41b55ca9b8243f45aa9e8dc515651fa894b6db8ef2bb0\"],[2,\"4eec9f8c10bbddc4ec2ee1c4a6167609b7a36b90447222a04733ad7d37e897bd\"]]]]",
"fn": "catalogue_state",
"hand_checked": false,
"name": "S17 greater as integers: 1.10.0 after 1.9.0"
},
{
"args": {
"lines": [
{
"ACT": "MODULE ADD",
"DATE": "2026-10-01",
"DIGEST": "5f3fe27b42378bce0830b0d0959f892f4a8e73b12b540ae877e39e6439d08b4d",
"ID": "AIR-LINEAR",
"VERSION": "1.0.0"
},
{
"ACT": "MODULE ADD",
"DATE": "2026-10-01",
"DIGEST": "6fb53c3a6546151eead2bd6e72e9cf8334f3a2040ad0ee2f5b988ec96d6fc852",
"ID": "AIR-QUADRATIC",
"VERSION": "1.0.0"
},
{
"ACT": "MODULE ADD",
"DATE": "2026-10-01",
"DIGEST": "24877ccb5c8ec300d29ed82ce6650592f35cf8899a3d878ccce9c08d4c72c025",
"ID": "GRAV-UNIFORM",
"VERSION": "1.0.0"
},
{
"ACT": "MODULE ADD",
"DATE": "2026-10-01",
"DIGEST": "8f39a356f35527b901fcee012764590f0819c8ffdeccad4bc05195ce3d2e0bcf",
"ID": "MATH",
"VERSION": "1.0.0"
},
{
"ACT": "MODULE WITHDRAW",
"DATE": "2026-10-02",
"ID": "GRAV-UNIFORM",
"REASON": "the weight's sign was reversed in the binding page's preview",
"VERSION": "1.0.0"
},
{
"ACT": "MODULE REINSTATE",
"DATE": "2026-10-03",
"ID": "GRAV-UNIFORM",
"VERSION": "1.0.0"
}
]
},
"expected": "[\"REFUSED\",\"LINE 6: MODULE REINSTATE of GRAV-UNIFORM 1.0.0, which is WITHDRAWN (WITHDRAWN is final)\"]",
"fn": "catalogue_state",
"hand_checked": true,
"name": "S18 MODULE REINSTATE of a WITHDRAWN version"
},
{
"args": {
"lines": [
{
"ACT": "MODULE ADD",
"DATE": "2026-10-01",
"DIGEST": "5f3fe27b42378bce0830b0d0959f892f4a8e73b12b540ae877e39e6439d08b4d",
"ID": "AIR-LINEAR",
"VERSION": "1.0.0"
},
{
"ACT": "MODULE ADD",
"DATE": "2026-10-01",
"DIGEST": "6fb53c3a6546151eead2bd6e72e9cf8334f3a2040ad0ee2f5b988ec96d6fc852",
"ID": "AIR-QUADRATIC",
"VERSION": "1.0.0"
},
{
"ACT": "MODULE ADD",
"DATE": "2026-10-01",
"DIGEST": "24877ccb5c8ec300d29ed82ce6650592f35cf8899a3d878ccce9c08d4c72c025",
"ID": "GRAV-UNIFORM",
"VERSION": "1.0.0"
},
{
"ACT": "MODULE ADD",
"DATE": "2026-10-01",
"DIGEST": "8f39a356f35527b901fcee012764590f0819c8ffdeccad4bc05195ce3d2e0bcf",
"ID": "MATH",
"VERSION": "1.0.0"
},
{
"ACT": "MODULE REINSTATE",
"DATE": "2026-10-02",
"ID": "GRAV-UNIFORM",
"VERSION": "1.0.0"
}
]
},
"expected": "[\"REFUSED\",\"LINE 5: MODULE REINSTATE of GRAV-UNIFORM 1.0.0, which is already OFFERED\"]",
"fn": "catalogue_state",
"hand_checked": true,
"name": "S19 MODULE REINSTATE of the OFFERED version"
},
{
"args": {
"lines": [
{
"ACT": "MODULE ADD",
"DATE": "2026-10-01",
"DIGEST": "5f3fe27b42378bce0830b0d0959f892f4a8e73b12b540ae877e39e6439d08b4d",
"ID": "AIR-LINEAR",
"VERSION": "1.0.0"
},
{
"ACT": "MODULE ADD",
"DATE": "2026-10-01",
"DIGEST": "6fb53c3a6546151eead2bd6e72e9cf8334f3a2040ad0ee2f5b988ec96d6fc852",
"ID": "AIR-QUADRATIC",
"VERSION": "1.0.0"
},
{
"ACT": "MODULE ADD",
"DATE": "2026-10-01",
"DIGEST": "24877ccb5c8ec300d29ed82ce6650592f35cf8899a3d878ccce9c08d4c72c025",
"ID": "GRAV-UNIFORM",
"VERSION": "1.0.0"
},
{
"ACT": "MODULE ADD",
"DATE": "2026-10-01",
"DIGEST": "8f39a356f35527b901fcee012764590f0819c8ffdeccad4bc05195ce3d2e0bcf",
"ID": "MATH",
"VERSION": "1.0.0"
},
{
"ACT": "MODULE VERSION",
"DATE": "2026-10-02",
"DIGEST": "5be3923c28dc8f8ff910b033c2d17154f267f2a20fdb32c74a07293a37dfe338",
"ID": "GRAV-UNIFORM",
"VERSION": "1.1.0"
},
{
"ACT": "MODULE RETIRE",
"DATE": "2026-10-03",
"ID": "GRAV-UNIFORM",
"VERSION": "1.0.0"
}
]
},
"expected": "[\"REFUSED\",\"LINE 6: MODULE RETIRE of GRAV-UNIFORM 1.0.0, which is SUPERSEDED, not OFFERED\"]",
"fn": "catalogue_state",
"hand_checked": true,
"name": "S20 MODULE RETIRE of a SUPERSEDED version"
},
{
"args": {
"lines": [
{
"ACT": "MODULE ADD",
"DATE": "2026-10-01",
"DIGEST": "5f3fe27b42378bce0830b0d0959f892f4a8e73b12b540ae877e39e6439d08b4d",
"ID": "AIR-LINEAR",
"VERSION": "1.0.0"
},
{
"ACT": "MODULE ADD",
"DATE": "2026-10-01",
"DIGEST": "6fb53c3a6546151eead2bd6e72e9cf8334f3a2040ad0ee2f5b988ec96d6fc852",
"ID": "AIR-QUADRATIC",
"VERSION": "1.0.0"
},
{
"ACT": "MODULE ADD",
"DATE": "2026-10-01",
"DIGEST": "24877ccb5c8ec300d29ed82ce6650592f35cf8899a3d878ccce9c08d4c72c025",
"ID": "GRAV-UNIFORM",
"VERSION": "1.0.0"
},
{
"ACT": "MODULE ADD",
"DATE": "2026-10-01",
"DIGEST": "8f39a356f35527b901fcee012764590f0819c8ffdeccad4bc05195ce3d2e0bcf",
"ID": "MATH",
"VERSION": "1.0.0"
},
{
"ACT": "MODULE RETIRE",
"DATE": "2026-10-02",
"ID": "GRAV-UNIFORM",
"VERSION": "3.0.0"
}
]
},
"expected": "[\"REFUSED\",\"LINE 5: GRAV-UNIFORM 3.0.0 is not declared\"]",
"fn": "catalogue_state",
"hand_checked": true,
"name": "S21 MODULE RETIRE of a version never declared"
},
{
"args": {
"lines": [
{
"ACT": "MODULE ADD",
"DATE": "2026-10-01",
"DIGEST": "5f3fe27b42378bce0830b0d0959f892f4a8e73b12b540ae877e39e6439d08b4d",
"ID": "AIR-LINEAR",
"VERSION": "1.0.0"
},
{
"ACT": "MODULE ADD",
"DATE": "2026-10-01",
"DIGEST": "6fb53c3a6546151eead2bd6e72e9cf8334f3a2040ad0ee2f5b988ec96d6fc852",
"ID": "AIR-QUADRATIC",
"VERSION": "1.0.0"
},
{
"ACT": "MODULE ADD",
"DATE": "2026-10-01",
"DIGEST": "24877ccb5c8ec300d29ed82ce6650592f35cf8899a3d878ccce9c08d4c72c025",
"ID": "GRAV-UNIFORM",
"VERSION": "1.0.0"
},
{
"ACT": "MODULE ADD",
"DATE": "2026-10-01",
"DIGEST": "8f39a356f35527b901fcee012764590f0819c8ffdeccad4bc05195ce3d2e0bcf",
"ID": "MATH",
"VERSION": "1.0.0"
},
{
"ACT": "MODULE WITHDRAW",
"DATE": "2026-10-02",
"ID": "GRAV-UNIFORM",
"VERSION": "1.0.0"
}
]
},
"expected": "[\"REFUSED\",\"LINE 5: MODULE WITHDRAW without a reason\"]",
"fn": "catalogue_state",
"hand_checked": true,
"name": "S22 MODULE WITHDRAW without a reason"
},
{
"args": {
"lines": [
{
"ACT": "MODULE ADD",
"DATE": "2026-10-01",
"DIGEST": "5f3fe27b42378bce0830b0d0959f892f4a8e73b12b540ae877e39e6439d08b4d",
"ID": "AIR-LINEAR",
"VERSION": "1.0.0"
},
{
"ACT": "MODULE ADD",
"DATE": "2026-10-01",
"DIGEST": "6fb53c3a6546151eead2bd6e72e9cf8334f3a2040ad0ee2f5b988ec96d6fc852",
"ID": "AIR-QUADRATIC",
"VERSION": "1.0.0"
},
{
"ACT": "MODULE ADD",
"DATE": "2026-10-01",
"DIGEST": "24877ccb5c8ec300d29ed82ce6650592f35cf8899a3d878ccce9c08d4c72c025",
"ID": "GRAV-UNIFORM",
"VERSION": "1.0.0"
},
{
"ACT": "MODULE ADD",
"DATE": "2026-10-01",
"DIGEST": "8f39a356f35527b901fcee012764590f0819c8ffdeccad4bc05195ce3d2e0bcf",
"ID": "MATH",
"VERSION": "1.0.0"
},
{
"ACT": "MODULE WITHDRAW",
"DATE": "2026-10-02",
"ID": "GRAV-UNIFORM",
"REASON": " ",
"VERSION": "1.0.0"
}
]
},
"expected": "[\"REFUSED\",\"LINE 5: MODULE WITHDRAW without a reason\"]",
"fn": "catalogue_state",
"hand_checked": true,
"name": "S23 MODULE WITHDRAW with a blank reason"
},
{
"args": {
"lines": [
{
"ACT": "MODULE ADD",
"DATE": "2026-10-01",
"DIGEST": "5f3fe27b42378bce0830b0d0959f892f4a8e73b12b540ae877e39e6439d08b4d",
"ID": "AIR-LINEAR",
"VERSION": "1.0.0"
},
{
"ACT": "MODULE ADD",
"DATE": "2026-10-01",
"DIGEST": "6fb53c3a6546151eead2bd6e72e9cf8334f3a2040ad0ee2f5b988ec96d6fc852",
"ID": "AIR-QUADRATIC",
"VERSION": "1.0.0"
},
{
"ACT": "MODULE ADD",
"DATE": "2026-10-01",
"DIGEST": "24877ccb5c8ec300d29ed82ce6650592f35cf8899a3d878ccce9c08d4c72c025",
"ID": "GRAV-UNIFORM",
"VERSION": "1.0.0"
},
{
"ACT": "MODULE ADD",
"DATE": "2026-10-01",
"DIGEST": "8f39a356f35527b901fcee012764590f0819c8ffdeccad4bc05195ce3d2e0bcf",
"ID": "MATH",
"VERSION": "1.0.0"
},
{
"ACT": "MODULE WITHDRAW",
"DATE": "2026-10-02",
"ID": "GRAV-UNIFORM",
"REASON": "the weight's sign was reversed in the binding page's preview",
"VERSION": "1.0.0"
},
{
"ACT": "MODULE WITHDRAW",
"DATE": "2026-10-03",
"ID": "GRAV-UNIFORM",
"REASON": "the weight's sign was reversed in the binding page's preview",
"VERSION": "1.0.0"
}
]
},
"expected": "[\"REFUSED\",\"LINE 6: GRAV-UNIFORM 1.0.0 is already WITHDRAWN (WITHDRAWN is final)\"]",
"fn": "catalogue_state",
"hand_checked": true,
"name": "S24 WITHDRAWN is final: withdrawn twice"
},
{
"args": {
"lines": [
{
"ACT": "MODULE ADD",
"DATE": "2026-10-01",
"DIGEST": "5f3fe27b42378bce0830b0d0959f892f4a8e73b12b540ae877e39e6439d08b4d",
"ID": "AIR-LINEAR",
"VERSION": "1.0.0"
},
{
"ACT": "MODULE ADD",
"DATE": "2026-10-01",
"DIGEST": "6fb53c3a6546151eead2bd6e72e9cf8334f3a2040ad0ee2f5b988ec96d6fc852",
"ID": "AIR-QUADRATIC",
"VERSION": "1.0.0"
},
{
"ACT": "MODULE ADD",
"DATE": "2026-10-01",
"DIGEST": "24877ccb5c8ec300d29ed82ce6650592f35cf8899a3d878ccce9c08d4c72c025",
"ID": "GRAV-UNIFORM",
"VERSION": "1.0.0"
},
{
"ACT": "MODULE ADD",
"DATE": "2026-10-01",
"DIGEST": "8f39a356f35527b901fcee012764590f0819c8ffdeccad4bc05195ce3d2e0bcf",
"ID": "MATH",
"VERSION": "1.0.0"
},
{
"ACT": "MODULE VERSION",
"DATE": "2026-10-02",
"DIGEST": "5be3923c28dc8f8ff910b033c2d17154f267f2a20fdb32c74a07293a37dfe338",
"ID": "GRAV-UNIFORM",
"VERSION": "1.1.0"
},
{
"ACT": "MODULE WITHDRAW",
"DATE": "2026-10-03",
"ID": "GRAV-UNIFORM",
"REASON": "the weight's sign was reversed in the binding page's preview",
"REPLACED_BY": "1.1.0",
"VERSION": "1.0.0"
}
]
},
"expected": "[\"REFUSED\",\"LINE 6: REPLACED_BY needs GRAV-UNIFORM 1.0.0 OFFERED; it is SUPERSEDED\"]",
"fn": "catalogue_state",
"hand_checked": true,
"name": "S25 REPLACED_BY when the withdrawn version is not OFFERED"
},
{
"args": {
"lines": [
{
"ACT": "MODULE ADD",
"DATE": "2026-10-01",
"DIGEST": "5f3fe27b42378bce0830b0d0959f892f4a8e73b12b540ae877e39e6439d08b4d",
"ID": "AIR-LINEAR",
"VERSION": "1.0.0"
},
{
"ACT": "MODULE ADD",
"DATE": "2026-10-01",
"DIGEST": "6fb53c3a6546151eead2bd6e72e9cf8334f3a2040ad0ee2f5b988ec96d6fc852",
"ID": "AIR-QUADRATIC",
"VERSION": "1.0.0"
},
{
"ACT": "MODULE ADD",
"DATE": "2026-10-01",
"DIGEST": "24877ccb5c8ec300d29ed82ce6650592f35cf8899a3d878ccce9c08d4c72c025",
"ID": "GRAV-UNIFORM",
"VERSION": "1.0.0"
},
{
"ACT": "MODULE ADD",
"DATE": "2026-10-01",
"DIGEST": "8f39a356f35527b901fcee012764590f0819c8ffdeccad4bc05195ce3d2e0bcf",
"ID": "MATH",
"VERSION": "1.0.0"
},
{
"ACT": "MODULE WITHDRAW",
"DATE": "2026-10-02",
"ID": "GRAV-UNIFORM",
"REASON": "the weight's sign was reversed in the binding page's preview",
"REPLACED_BY": "0.5.0",
"VERSION": "1.0.0"
}
]
},
"expected": "[\"REFUSED\",\"LINE 5: REPLACED_BY GRAV-UNIFORM 0.5.0 is not declared\"]",
"fn": "catalogue_state",
"hand_checked": true,
"name": "S26 REPLACED_BY a version never declared"
},
{
"args": {
"lines": [
{
"ACT": "MODULE ADD",
"DATE": "2026-10-01",
"DIGEST": "5f3fe27b42378bce0830b0d0959f892f4a8e73b12b540ae877e39e6439d08b4d",
"ID": "AIR-LINEAR",
"VERSION": "1.0.0"
},
{
"ACT": "MODULE ADD",
"DATE": "2026-10-01",
"DIGEST": "6fb53c3a6546151eead2bd6e72e9cf8334f3a2040ad0ee2f5b988ec96d6fc852",
"ID": "AIR-QUADRATIC",
"VERSION": "1.0.0"
},
{
"ACT": "MODULE ADD",
"DATE": "2026-10-01",
"DIGEST": "24877ccb5c8ec300d29ed82ce6650592f35cf8899a3d878ccce9c08d4c72c025",
"ID": "GRAV-UNIFORM",
"VERSION": "1.0.0"
},
{
"ACT": "MODULE ADD",
"DATE": "2026-10-01",
"DIGEST": "8f39a356f35527b901fcee012764590f0819c8ffdeccad4bc05195ce3d2e0bcf",
"ID": "MATH",
"VERSION": "1.0.0"
},
{
"ACT": "MODULE VERSION",
"DATE": "2026-10-02",
"DIGEST": "5be3923c28dc8f8ff910b033c2d17154f267f2a20fdb32c74a07293a37dfe338",
"ID": "GRAV-UNIFORM",
"VERSION": "1.1.0"
},
{
"ACT": "MODULE WITHDRAW",
"DATE": "2026-10-03",
"ID": "GRAV-UNIFORM",
"REASON": "the weight's sign was reversed in the binding page's preview",
"VERSION": "1.0.0"
},
{
"ACT": "MODULE WITHDRAW",
"DATE": "2026-10-04",
"ID": "GRAV-UNIFORM",
"REASON": "the weight's sign was reversed in the binding page's preview",
"REPLACED_BY": "1.0.0",
"VERSION": "1.1.0"
}
]
},
"expected": "[\"REFUSED\",\"LINE 7: REPLACED_BY GRAV-UNIFORM 1.0.0 is WITHDRAWN, not SUPERSEDED or RETIRED\"]",
"fn": "catalogue_state",
"hand_checked": true,
"name": "S27 REPLACED_BY a WITHDRAWN version"
},
{
"args": {
"lines": [
{
"ACT": "MODULE DELETE",
"DATE": "2026-10-01",
"ID": "GRAV-UNIFORM",
"VERSION": "1.0.0"
}
]
},
"expected": "[\"REFUSED\",\"LINE 1: ACT MODULE DELETE is not a module act\"]",
"fn": "catalogue_state",
"hand_checked": true,
"name": "S28 an act that is not a module act"
},
{
"args": {
"lines": [
{
"ACT": "MODULE ADD",
"DATE": "2026-10-01",
"DIGEST": "24877ccb5c8ec300d29ed82ce6650592f35cf8899a3d878ccce9c08d4c72c025",
"ID": "GRAV-UNIFORM",
"NOTE": "x",
"VERSION": "1.0.0"
}
]
},
"expected": "[\"REFUSED\",\"LINE 1: unknown field NOTE\"]",
"fn": "catalogue_state",
"hand_checked": true,
"name": "S29 an unknown field"
},
{
"args": {
"lines": [
{
"ACT": "MODULE ADD",
"DATE": "2026-10-01",
"DIGEST": "5f3fe27b42378bce0830b0d0959f892f4a8e73b12b540ae877e39e6439d08b4d",
"ID": "AIR-LINEAR",
"VERSION": "1.0.0"
},
{
"ACT": "MODULE ADD",
"DATE": "2026-10-01",
"DIGEST": "6fb53c3a6546151eead2bd6e72e9cf8334f3a2040ad0ee2f5b988ec96d6fc852",
"ID": "AIR-QUADRATIC",
"VERSION": "1.0.0"
},
{
"ACT": "MODULE ADD",
"DATE": "2026-10-01",
"DIGEST": "24877ccb5c8ec300d29ed82ce6650592f35cf8899a3d878ccce9c08d4c72c025",
"ID": "GRAV-UNIFORM",
"VERSION": "1.0.0"
},
{
"ACT": "MODULE ADD",
"DATE": "2026-10-01",
"DIGEST": "8f39a356f35527b901fcee012764590f0819c8ffdeccad4bc05195ce3d2e0bcf",
"ID": "MATH",
"VERSION": "1.0.0"
},
{
"ACT": "MODULE RETIRE",
"DATE": "2026-10-02",
"DIGEST": "24877ccb5c8ec300d29ed82ce6650592f35cf8899a3d878ccce9c08d4c72c025",
"ID": "GRAV-UNIFORM",
"VERSION": "1.0.0"
}
]
},
"expected": "[\"REFUSED\",\"LINE 5: unknown field DIGEST\"]",
"fn": "catalogue_state",
"hand_checked": true,
"name": "S30 a field of another act: DIGEST on RETIRE"
},
{
"args": {
"lines": [
{
"DATE": "2026-10-01",
"ID": "GRAV-UNIFORM",
"VERSION": "1.0.0"
}
]
},
"expected": "[\"REFUSED\",\"LINE 1: missing field ACT\"]",
"fn": "catalogue_state",
"hand_checked": true,
"name": "S31 no ACT"
},
{
"args": {
"lines": [
{
"ACT": 1,
"ID": "GRAV-UNIFORM"
}
]
},
"expected": "[\"REFUSED\",\"LINE 1: field ACT has the wrong type\"]",
"fn": "catalogue_state",
"hand_checked": true,
"name": "S32 ACT not a string"
},
{
"args": {
"lines": [
{
"ACT": "MODULE ADD",
"DATE": "2026-10-01",
"ID": "GRAV-UNIFORM",
"VERSION": "1.0.0"
}
]
},
"expected": "[\"REFUSED\",\"LINE 1: missing field DIGEST\"]",
"fn": "catalogue_state",
"hand_checked": true,
"name": "S33 MODULE ADD without DIGEST"
},
{
"args": {
"lines": [
{
"ACT": "MODULE ADD",
"DATE": "2026-10-01",
"DIGEST": "24877CCB5C8EC300D29ED82CE6650592F35CF8899A3D878CCCE9C08D4C72C025",
"ID": "GRAV-UNIFORM",
"VERSION": "1.0.0"
}
]
},
"expected": "[\"REFUSED\",\"LINE 1: DIGEST is not a digest\"]",
"fn": "catalogue_state",
"hand_checked": true,
"name": "S34 a DIGEST in upper case"
},
{
"args": {
"lines": [
{
"ACT": "MODULE ADD",
"DATE": "2026-10-01",
"DIGEST": "5f3fe27b42378bce0830b0d0959f892f4a8e73b12b540ae877e39e6439d08b4d",
"ID": "AIR-LINEAR",
"VERSION": "1.0.0"
},
{
"ACT": "MODULE ADD",
"DATE": "2026-10-01",
"DIGEST": "5f3fe27b42378bce0830b0d0959f892f4a8e73b12b540ae877e39e6439d08b4d",
"ID": "AIR-QUADRATIC",
"VERSION": "1.0.0"
}
]
},
"expected": "[\"REFUSED\",\"LINE 2: DIGEST already declared for AIR-LINEAR 1.0.0\"]",
"fn": "catalogue_state",
"hand_checked": true,
"name": "S35 a DIGEST already declared"
},
{
"args": {
"lines": [
{
"ACT": "MODULE ADD",
"DATE": "2026-13-01",
"DIGEST": "24877ccb5c8ec300d29ed82ce6650592f35cf8899a3d878ccce9c08d4c72c025",
"ID": "GRAV-UNIFORM",
"VERSION": "1.0.0"
}
]
},
"expected": "[\"REFUSED\",\"LINE 1: DATE 2026-13-01 is not a date\"]",
"fn": "catalogue_state",
"hand_checked": true,
"name": "S36 a month 13"
},
{
"args": {
"lines": [
{
"ACT": "MODULE ADD",
"DATE": "2026-02-29",
"DIGEST": "24877ccb5c8ec300d29ed82ce6650592f35cf8899a3d878ccce9c08d4c72c025",
"ID": "GRAV-UNIFORM",
"VERSION": "1.0.0"
}
]
},
"expected": "[\"REFUSED\",\"LINE 1: DATE 2026-02-29 is not a date\"]",
"fn": "catalogue_state",
"hand_checked": true,
"name": "S37 29 February of a common year"
},
{
"args": {
"lines": [
{
"ACT": "MODULE ADD",
"DATE": "2028-02-29",
"DIGEST": "24877ccb5c8ec300d29ed82ce6650592f35cf8899a3d878ccce9c08d4c72c025",
"ID": "GRAV-UNIFORM",
"VERSION": "1.0.0"
}
]
},
"computed": "digests by existing TPC-PY functions over literal data",
"expected": "[\"OK\",[\"VERSIONS\",[[\"GRAV-UNIFORM\",\"1.0.0\",\"24877ccb5c8ec300d29ed82ce6650592f35cf8899a3d878ccce9c08d4c72c025\",\"OFFERED\",\"2028-02-29\",\"\"]]],[\"OFFERED\",[[\"GRAV-UNIFORM\",\"1.0.0\",\"24877ccb5c8ec300d29ed82ce6650592f35cf8899a3d878ccce9c08d4c72c025\"]]],[\"STATES\",[[1,\"c7268827a13c0aa766c9002aca875174f9c0fc868db6fb553107a944bbe391bb\"]]]]",
"fn": "catalogue_state",
"hand_checked": false,
"name": "S38 29 February of a leap year"
},
{
"args": {
"lines": [
{
"ACT": "MODULE ADD",
"DATE": "2026-10-02",
"DIGEST": "5f3fe27b42378bce0830b0d0959f892f4a8e73b12b540ae877e39e6439d08b4d",
"ID": "AIR-LINEAR",
"VERSION": "1.0.0"
},
{
"ACT": "MODULE ADD",
"DATE": "2026-10-01",
"DIGEST": "6fb53c3a6546151eead2bd6e72e9cf8334f3a2040ad0ee2f5b988ec96d6fc852",
"ID": "AIR-QUADRATIC",
"VERSION": "1.0.0"
}
]
},
"expected": "[\"REFUSED\",\"LINE 2: DATE 2026-10-01 is before the previous line's\"]",
"fn": "catalogue_state",
"hand_checked": true,
"name": "S39 a line dated before the previous one"
},
{
"args": {
"lines": [
{
"ACT": "MODULE ADD",
"DATE": "2026-10-01",
"DIGEST": "24877ccb5c8ec300d29ed82ce6650592f35cf8899a3d878ccce9c08d4c72c025",
"ID": "GRAV-UNIFORM",
"VERSION": "1.0"
}
]
},
"expected": "[\"REFUSED\",\"LINE 1: VERSION 1.0 is not a version\"]",
"fn": "catalogue_state",
"hand_checked": true,
"name": "S40 a VERSION of two parts"
},
{
"args": {
"lines": [
{
"ACT": "MODULE ADD",
"DATE": "2026-10-01",
"DIGEST": "24877ccb5c8ec300d29ed82ce6650592f35cf8899a3d878ccce9c08d4c72c025",
"ID": "grav",
"VERSION": "1.0.0"
}
]
},
"expected": "[\"REFUSED\",\"LINE 1: ID grav is not a module ID\"]",
"fn": "catalogue_state",
"hand_checked": true,
"name": "S41 an ID in lower case"
},
{
"args": {
"lines": {
"ACT": "MODULE ADD"
}
},
"expected": "[\"REFUSED\",\"LINES: not a list\"]",
"fn": "catalogue_state",
"hand_checked": true,
"name": "S42 lines not a list"
},
{
"args": {
"lines": [
[
"MODULE ADD"
]
]
},
"expected": "[\"REFUSED\",\"LINE 1: not an object\"]",
"fn": "catalogue_state",
"hand_checked": true,
"name": "S43 a line not an object"
},
{
"args": {
"lines": [
{
"ACT": "MODULE ADD",
"DATE": "2026-10-01",
"DIGEST": "24877ccb5c8ec300d29ed82ce6650592f35cf8899a3d878ccce9c08d4c72c025",
"ID": "GRAV-UNIFORM",
"VERSION": 1
}
]
},
"expected": "[\"REFUSED\",\"LINE 1: field VERSION has the wrong type\"]",
"fn": "catalogue_state",
"hand_checked": true,
"name": "S44 a VERSION given as a number"
},
{
"args": {
"lines": [
{
"ACT": "MODULE ADD",
"DATE": "2026-10-01",
"DIGEST": "5f3fe27b42378bce0830b0d0959f892f4a8e73b12b540ae877e39e6439d08b4d",
"ID": "AIR-LINEAR",
"VERSION": "1.0.0"
},
{
"ACT": "MODULE ADD",
"DATE": "2026-10-01",
"DIGEST": "6fb53c3a6546151eead2bd6e72e9cf8334f3a2040ad0ee2f5b988ec96d6fc852",
"ID": "AIR-QUADRATIC",
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},
{
"ACT": "MODULE ADD",
"DATE": "2026-10-01",
"DIGEST": "24877ccb5c8ec300d29ed82ce6650592f35cf8899a3d878ccce9c08d4c72c025",
"ID": "GRAV-UNIFORM",
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},
{
"ACT": "MODULE ADD",
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"DIGEST": "8f39a356f35527b901fcee012764590f0819c8ffdeccad4bc05195ce3d2e0bcf",
"ID": "MATH",
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},
{
"ACT": "MODULE WITHDRAW",
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"ID": "GRAV-UNIFORM",
"REASON": "bad \u202e sign",
"VERSION": "1.0.0"
}
]
},
"expected": "[\"REFUSED\",\"LINE 5: field REASON contains disallowed character U+202E\"]",
"fn": "catalogue_state",
"hand_checked": true,
"name": "S45 a REASON with a bidi override"
},
{
"args": {
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{
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},
{
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},
{
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},
{
"ACT": "MODULE ADD",
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"DIGEST": "8f39a356f35527b901fcee012764590f0819c8ffdeccad4bc05195ce3d2e0bcf",
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},
{
"ACT": "MODULE WITHDRAW",
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"ID": "GRAV-UNIFORM",
"REASON": "the weight's sign was reversed in the binding page's preview",
"REPLACED_BY": "one",
"VERSION": "1.0.0"
}
]
},
"expected": "[\"REFUSED\",\"LINE 5: REPLACED_BY one is not a version\"]",
"fn": "catalogue_state",
"hand_checked": true,
"name": "S46 a REPLACED_BY that is not a version"
},
{
"args": {
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{
"ACT": "MODULE ADD",
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{
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},
{
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},
{
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},
{
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},
{
"ACT": "MODULE WITHDRAW",
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"ID": "MATH",
"REASON": "the weight's sign was reversed in the binding page's preview",
"VERSION": "1.0.0"
}
]
},
"computed": "digests by existing TPC-PY functions over literal data",
"expected": "[\"OK\",[\"VERSIONS\",[[\"AIR-LINEAR\",\"1.0.0\",\"5f3fe27b42378bce0830b0d0959f892f4a8e73b12b540ae877e39e6439d08b4d\",\"OFFERED\",\"2026-10-01\",\"\"],[\"AIR-QUADRATIC\",\"1.0.0\",\"6fb53c3a6546151eead2bd6e72e9cf8334f3a2040ad0ee2f5b988ec96d6fc852\",\"OFFERED\",\"2026-10-01\",\"\"],[\"GRAV-UNIFORM\",\"1.0.0\",\"24877ccb5c8ec300d29ed82ce6650592f35cf8899a3d878ccce9c08d4c72c025\",\"OFFERED\",\"2026-10-01\",\"\"],[\"MATH\",\"1.0.0\",\"8f39a356f35527b901fcee012764590f0819c8ffdeccad4bc05195ce3d2e0bcf\",\"WITHDRAWN\",\"2026-10-03\",\"the weight's sign was reversed in the binding page's preview\"]]],[\"OFFERED\",[[\"AIR-LINEAR\",\"1.0.0\",\"5f3fe27b42378bce0830b0d0959f892f4a8e73b12b540ae877e39e6439d08b4d\"],[\"AIR-QUADRATIC\",\"1.0.0\",\"6fb53c3a6546151eead2bd6e72e9cf8334f3a2040ad0ee2f5b988ec96d6fc852\"],[\"GRAV-UNIFORM\",\"1.0.0\",\"24877ccb5c8ec300d29ed82ce6650592f35cf8899a3d878ccce9c08d4c72c025\"]]],[\"STATES\",[[1,\"6b762dee9c4eebd4d4a733cf23563ec5cf00597d2c9218661394acef4d73f92a\"],[2,\"45504804366ccda13432d9a6f611443c9a9471d56e14c3dc5c20a907841f8397\"],[3,\"05585887057d5127e313f19d2da51b5ff845f7ade54ba47718f81995258be87e\"],[4,\"e6daa136c61c09471760b8d472c93bab9639752b8c22180b445918ac759e3852\"],[5,\"05585887057d5127e313f19d2da51b5ff845f7ade54ba47718f81995258be87e\"],[6,\"05585887057d5127e313f19d2da51b5ff845f7ade54ba47718f81995258be87e\"]]]]",
"fn": "catalogue_state",
"hand_checked": false,
"name": "S47 MODULE WITHDRAW of a RETIRED version"
},
{
"args": {
"lines": [
{
"ACT": "MODULE ADD",
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},
{
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{
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},
{
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"DIGEST": "8f39a356f35527b901fcee012764590f0819c8ffdeccad4bc05195ce3d2e0bcf",
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},
{
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"ID": "GRAV-UNIFORM",
"REASON": "the weight's sign was reversed in the binding page's preview",
"VERSION": "1.0.0"
},
{
"ACT": "MODULE VERSION",
"DATE": "2026-10-03",
"DIGEST": "5be3923c28dc8f8ff910b033c2d17154f267f2a20fdb32c74a07293a37dfe338",
"ID": "GRAV-UNIFORM",
"VERSION": "1.1.0"
}
]
},
"computed": "digests by existing TPC-PY functions over literal data",
"expected": "[\"OK\",[\"VERSIONS\",[[\"AIR-LINEAR\",\"1.0.0\",\"5f3fe27b42378bce0830b0d0959f892f4a8e73b12b540ae877e39e6439d08b4d\",\"OFFERED\",\"2026-10-01\",\"\"],[\"AIR-QUADRATIC\",\"1.0.0\",\"6fb53c3a6546151eead2bd6e72e9cf8334f3a2040ad0ee2f5b988ec96d6fc852\",\"OFFERED\",\"2026-10-01\",\"\"],[\"GRAV-UNIFORM\",\"1.0.0\",\"24877ccb5c8ec300d29ed82ce6650592f35cf8899a3d878ccce9c08d4c72c025\",\"WITHDRAWN\",\"2026-10-02\",\"the weight's sign was reversed in the binding page's preview\"],[\"GRAV-UNIFORM\",\"1.1.0\",\"5be3923c28dc8f8ff910b033c2d17154f267f2a20fdb32c74a07293a37dfe338\",\"OFFERED\",\"2026-10-03\",\"\"],[\"MATH\",\"1.0.0\",\"8f39a356f35527b901fcee012764590f0819c8ffdeccad4bc05195ce3d2e0bcf\",\"OFFERED\",\"2026-10-01\",\"\"]]],[\"OFFERED\",[[\"AIR-LINEAR\",\"1.0.0\",\"5f3fe27b42378bce0830b0d0959f892f4a8e73b12b540ae877e39e6439d08b4d\"],[\"AIR-QUADRATIC\",\"1.0.0\",\"6fb53c3a6546151eead2bd6e72e9cf8334f3a2040ad0ee2f5b988ec96d6fc852\"],[\"GRAV-UNIFORM\",\"1.1.0\",\"5be3923c28dc8f8ff910b033c2d17154f267f2a20fdb32c74a07293a37dfe338\"],[\"MATH\",\"1.0.0\",\"8f39a356f35527b901fcee012764590f0819c8ffdeccad4bc05195ce3d2e0bcf\"]]],[\"STATES\",[[1,\"6b762dee9c4eebd4d4a733cf23563ec5cf00597d2c9218661394acef4d73f92a\"],[2,\"45504804366ccda13432d9a6f611443c9a9471d56e14c3dc5c20a907841f8397\"],[3,\"05585887057d5127e313f19d2da51b5ff845f7ade54ba47718f81995258be87e\"],[4,\"e6daa136c61c09471760b8d472c93bab9639752b8c22180b445918ac759e3852\"],[5,\"d4330326363217b053f4341478ecc22c8f817696fa10cf3214574cfcf54730ea\"],[6,\"2989c1ae13adeef9729cc94954eb12048901a5a92b2db340df65c901d8320433\"]]]]",
"fn": "catalogue_state",
"hand_checked": false,
"name": "S48 MODULE VERSION after the OFFERED version was WITHDRAWN (J F-4's repair)"
},
{
"args": {
"lines": [
{
"ACT": "MODULE ADD",
"DATE": "2026-10-01",
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{
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},
{
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},
{
"ACT": "MODULE ADD",
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"DIGEST": "8f39a356f35527b901fcee012764590f0819c8ffdeccad4bc05195ce3d2e0bcf",
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},
{
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"ID": "GRAV-UNIFORM",
"REASON": "the weight's sign was reversed in the binding page's preview",
"VERSION": "3.0.0"
}
]
},
"expected": "[\"REFUSED\",\"LINE 5: GRAV-UNIFORM 3.0.0 is not declared\"]",
"fn": "catalogue_state",
"hand_checked": true,
"name": "S49 MODULE WITHDRAW of a version never declared"
},
{
"args": {
"lines": [
{
"ACT": "MODULE ADD",
"DATE": "2026-10-01",
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},
{
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{
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},
{
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"VERSION": "1.0.0"
},
{
"ACT": "MODULE REINSTATE",
"DATE": "2026-10-02",
"ID": "MATH",
"VERSION": "2.0.0"
}
]
},
"expected": "[\"REFUSED\",\"LINE 5: MATH 2.0.0 is not declared\"]",
"fn": "catalogue_state",
"hand_checked": true,
"name": "S50 MODULE REINSTATE of a version never declared"
},
{
"args": {
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{
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},
{
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{
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},
{
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},
{
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"ID": "GRAV-UNIFORM",
"VERSION": "1.1.0"
}
]
},
"expected": "[\"REFUSED\",\"LINE 5: DIGEST already declared for GRAV-UNIFORM 1.0.0\"]",
"fn": "catalogue_state",
"hand_checked": true,
"name": "S51 MODULE VERSION whose DIGEST is already declared"
},
{
"args": {
"lines": [
{
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"DATE": "2026-10-01",
"DIGEST": "5f3fe27b42378bce0830b0d0959f892f4a8e73b12b540ae877e39e6439d08b4d",
"ID": "AIR-LINEAR",
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},
{
"ACT": "MODULE ADD",
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"DIGEST": "6fb53c3a6546151eead2bd6e72e9cf8334f3a2040ad0ee2f5b988ec96d6fc852",
"ID": "AIR-QUADRATIC",
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},
{
"ACT": "MODULE ADD",
"DATE": "2026-10-01",
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"ID": "GRAV-UNIFORM",
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},
{
"ACT": "MODULE ADD",
"DATE": "2026-10-01",
"DIGEST": "8f39a356f35527b901fcee012764590f0819c8ffdeccad4bc05195ce3d2e0bcf",
"ID": "MATH",
"VERSION": "1.0.0"
},
{
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"ID": "GRAV-UNIFORM",
"REASON": "the weight's sign was reversed in the binding page's preview",
"REPLACED_BY": "1.0.0",
"VERSION": "1.0.0"
}
]
},
"expected": "[\"REFUSED\",\"LINE 5: REPLACED_BY GRAV-UNIFORM 1.0.0 is OFFERED, not SUPERSEDED or RETIRED\"]",
"fn": "catalogue_state",
"hand_checked": true,
"name": "S52 REPLACED_BY naming the withdrawn version itself"
},
{
"args": {
"answer": [
{
"AT": 4,
"CHOSEN": "NONE",
"COVERED": [
[
"AIR-LINEAR",
"1.0.0",
"5f3fe27b42378bce0830b0d0959f892f4a8e73b12b540ae877e39e6439d08b4d"
],
[
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"6fb53c3a6546151eead2bd6e72e9cf8334f3a2040ad0ee2f5b988ec96d6fc852"
],
[
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"1.0.0",
"24877ccb5c8ec300d29ed82ce6650592f35cf8899a3d878ccce9c08d4c72c025"
],
[
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"1.0.0",
"8f39a356f35527b901fcee012764590f0819c8ffdeccad4bc05195ce3d2e0bcf"
]
]
}
],
"carried": [],
"claims": [],
"lines": [
{
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},
{
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"ID": "AIR-QUADRATIC",
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},
{
"ACT": "MODULE ADD",
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"DIGEST": "24877ccb5c8ec300d29ed82ce6650592f35cf8899a3d878ccce9c08d4c72c025",
"ID": "GRAV-UNIFORM",
"VERSION": "1.0.0"
},
{
"ACT": "MODULE ADD",
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"DIGEST": "8f39a356f35527b901fcee012764590f0819c8ffdeccad4bc05195ce3d2e0bcf",
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}
],
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"modules": [
"{\"ID\": \"AIR-LINEAR\", \"VERSION\": \"1.0.0\", \"TITLE\": \"Air resistance at sea level, linear in the speed (Stokes drag on a sphere)\", \"SOURCE\": \"ISO 2533:1975, Standard Atmosphere, sea-level values: density 1.225 kg m-3, dynamic viscosity 1.7894e-5 Pa s\", \"PREREQUISITES\": [{\"SLOT\": \"VELOCITY\", \"KIND\": \"DOF\", \"DIMENSION\": \"L1 T-1\", \"MIN\": 1, \"MAX\": 3, \"LABEL\": \"the velocity components of the body, one per axis\"}], \"PARAMETERS\": [{\"NAME\": \"rho_air\", \"DIMENSION\": \"L-3 M1\", \"SUPPLY\": \"DECLARED\", \"VALUE\": \"1.225\", \"UNIT\": \"kg m-3\", \"OVERRIDABLE\": \"NO\", \"LABEL\": \"the density of air at sea level\"}, {\"NAME\": \"mu_air\", \"DIMENSION\": \"L-1 M1 T-1\", \"SUPPLY\": \"DECLARED\", \"VALUE\": \"1.7894e-5\", \"UNIT\": \"Pa s\", \"OVERRIDABLE\": \"NO\", \"LABEL\": \"the dynamic viscosity of air at sea level\"}, {\"NAME\": \"pi_c\", \"DIMENSION\": \"1\", \"SUPPLY\": \"DECLARED\", \"VALUE\": \"3.141592653589793\", \"UNIT\": \"1\", \"OVERRIDABLE\": \"NO\", \"LABEL\": \"pi, to 16 significant digits\"}, {\"NAME\": \"R_s\", \"DIMENSION\": \"L1\", \"SUPPLY\": \"AUTHOR\", \"LABEL\": \"the radius of the sphere\"}], \"SUMS\": [{\"NAME\": \"SPEED2\", \"OVER\": \"VELOCITY\", \"EACH\": \"VELOCITY^2\"}], \"TERMS\": [{\"TARGET\": \"VELOCITY\", \"SIGN\": \"-\", \"EXPR\": \"6*pi_c*mu_air*R_s*VELOCITY\", \"LABEL\": \"the linear (Stokes) drag\"}], \"ASSUMPTIONS\": [{\"NAME\": \"air_still\", \"PROPOSITION\": \"the air is at rest in the frame of the body's velocity\", \"REFS\": [\"VELOCITY\"]}, {\"NAME\": \"air_uniform\", \"PROPOSITION\": \"the air density is uniform over the region of motion\", \"REFS\": [\"rho_air\"]}, {\"NAME\": \"drag_sphere\", \"PROPOSITION\": \"the body is a rigid sphere of radius R_s\", \"REFS\": [\"R_s\"]}], \"BOUNDARIES\": [{\"NAME\": \"drag_linear_regime\", \"PREDICATE\": \"2 rho_air |v| R_s / mu_air < 1: the regime of the linear law\", \"CONDITION\": \"mu_air != 0 and SPEED2 >= 0 and 2*rho_air*sqrt(SPEED2)*R_s/mu_air < 1\"}], \"NOT_CHOSEN\": \"No linear (Stokes) air resistance.\", \"NOT_INCLUDED\": [\"No wind: the air is at rest.\", \"No change of air density or viscosity with altitude or temperature.\", \"No drag outside the regime of the linear law.\"], \"EXCLUDES\": [], \"INTERACTS_WITH\": [], \"TEST_BINDINGS\": [{\"NAME\": \"PROJECTILE_2D\", \"TPK\": {\"DOF\": [{\"NAME\": \"t\", \"DIMENSION\": \"T1\"}, {\"NAME\": \"x\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"z\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"v_x\", \"DIMENSION\": \"L1 T-1\"}, {\"NAME\": \"v_z\", \"DIMENSION\": \"L1 T-1\"}], \"CONSTANT\": [{\"NAME\": \"m\", \"DIMENSION\": \"M1\"}], \"LAW\": [{\"NAME\": \"KIN_X\", \"STATEMENT\": \"dx/dt = v_x\", \"REFS\": [\"t\", \"v_x\", \"x\"], \"ROLE\": \"EOM(x)\", \"EQUATION\": \"D(x,t)=v_x\"}, {\"NAME\": \"KIN_Z\", \"STATEMENT\": \"dz/dt = v_z\", \"REFS\": [\"t\", \"v_z\", \"z\"], \"ROLE\": \"EOM(z)\", \"EQUATION\": \"D(z,t)=v_z\"}, {\"NAME\": \"EOM_X\", \"STATEMENT\": \"m dv_x/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_x\"], \"ROLE\": \"EOM(v_x)\", \"EQUATION\": \"m*D(v_x,t)=0\"}, {\"NAME\": \"EOM_Z\", \"STATEMENT\": \"m dv_z/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_z\"], \"ROLE\": \"EOM(v_z)\", \"EQUATION\": \"m*D(v_z,t)=0\"}], \"ASSUMPTION\": [{\"NAME\": \"point_mass\", \"PROPOSITION\": \"the body is treated as a point mass\", \"REFS\": [\"m\"]}]}, \"BIND\": {\"VELOCITY\": [\"v_x\", \"v_z\"]}, \"VALUES\": {\"R_s\": {}}, \"ANSWERS\": {}}]}",
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it acts in this kernel only where one of your own laws states it.\", \"NO_LINE\": \"No buoyancy: the air's upthrust on the body is not included.\"}], \"TEST_BINDINGS\": [{\"NAME\": \"PROJECTILE_2D\", \"TPK\": {\"DOF\": [{\"NAME\": \"t\", \"DIMENSION\": \"T1\"}, {\"NAME\": \"x\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"z\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"v_x\", \"DIMENSION\": \"L1 T-1\"}, {\"NAME\": \"v_z\", \"DIMENSION\": \"L1 T-1\"}], \"CONSTANT\": [{\"NAME\": \"m\", \"DIMENSION\": \"M1\"}], \"LAW\": [{\"NAME\": \"KIN_X\", \"STATEMENT\": \"dx/dt = v_x\", \"REFS\": [\"t\", \"v_x\", \"x\"], \"ROLE\": \"EOM(x)\", \"EQUATION\": \"D(x,t)=v_x\"}, {\"NAME\": \"KIN_Z\", \"STATEMENT\": \"dz/dt = v_z\", \"REFS\": [\"t\", \"v_z\", \"z\"], \"ROLE\": \"EOM(z)\", \"EQUATION\": \"D(z,t)=v_z\"}, {\"NAME\": \"EOM_X\", \"STATEMENT\": \"m dv_x/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_x\"], \"ROLE\": \"EOM(v_x)\", \"EQUATION\": \"m*D(v_x,t)=0\"}, {\"NAME\": \"EOM_Z\", \"STATEMENT\": \"m dv_z/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_z\"], \"ROLE\": \"EOM(v_z)\", \"EQUATION\": \"m*D(v_z,t)=0\"}], \"ASSUMPTION\": [{\"NAME\": \"point_mass\", \"PROPOSITION\": \"the body is treated as a point mass\", \"REFS\": [\"m\"]}]}, \"BIND\": {\"HEIGHT\": [\"z\"], \"MASS\": [\"m\"], \"UP_VELOCITY\": [\"v_z\"]}, \"VALUES\": {\"h_max\": {\"VALUE\": \"100\", \"UNIT\": \"m\"}}, \"ANSWERS\": {}}, {\"NAME\": \"TABLE\", \"TPK\": {\"DOF\": [{\"NAME\": \"t\", \"DIMENSION\": \"T1\"}, {\"NAME\": \"x\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"z\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"v_x\", \"DIMENSION\": \"L1 T-1\"}, {\"NAME\": \"v_z\", \"DIMENSION\": \"L1 T-1\"}], \"CONSTANT\": [{\"NAME\": \"m\", \"DIMENSION\": \"M1\"}], \"LAW\": [{\"NAME\": \"KIN_X\", \"STATEMENT\": \"dx/dt = v_x\", \"REFS\": [\"t\", \"v_x\", \"x\"], \"ROLE\": \"EOM(x)\", \"EQUATION\": \"D(x,t)=v_x\"}, {\"NAME\": \"KIN_Z\", \"STATEMENT\": \"dz/dt = v_z\", \"REFS\": [\"t\", \"v_z\", \"z\"], \"ROLE\": \"CONSTRAINT\", \"EQUATION\": \"D(z,t)=v_z\"}, {\"NAME\": \"EOM_X\", \"STATEMENT\": \"m dv_x/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_x\"], \"ROLE\": \"EOM(v_x)\", \"EQUATION\": \"m*D(v_x,t)=0\"}], \"CONSTRAINT\": [{\"NAME\": \"C_Z\", \"TARGET\": \"z\", \"ACTION\": \"FIX\", \"VALUE\": \"0\", \"UNIT\": \"m\", \"STATEMENT\": \"the puck stays on the table top, z = 0\"}, {\"NAME\": \"C_VZ\", \"TARGET\": \"v_z\", \"ACTION\": \"FIX\", \"VALUE\": \"0\", \"UNIT\": \"m s-1\", \"STATEMENT\": \"the puck has no vertical velocity\"}]}, \"BIND\": {\"HEIGHT\": [\"z\"], \"MASS\": [\"m\"], \"UP_VELOCITY\": [\"v_z\"]}, \"VALUES\": {\"h_max\": {\"VALUE\": \"1\", \"UNIT\": \"m\"}}, \"ANSWERS\": {\"FIXED:v_z\": \"YES\"}}]}",
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"name": "I01 NONE over the first catalogue"
},
{
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{
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"lines": [
{
"ACT": "MODULE ADD",
"DATE": "2026-10-01",
"DIGEST": "5f3fe27b42378bce0830b0d0959f892f4a8e73b12b540ae877e39e6439d08b4d",
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{
"ACT": "MODULE ADD",
"DATE": "2026-10-01",
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{
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"modules": [
"{\"ID\": \"AIR-LINEAR\", \"VERSION\": \"1.0.0\", \"TITLE\": \"Air resistance at sea level, linear in the speed (Stokes drag on a sphere)\", \"SOURCE\": \"ISO 2533:1975, Standard Atmosphere, sea-level values: density 1.225 kg m-3, dynamic viscosity 1.7894e-5 Pa s\", \"PREREQUISITES\": [{\"SLOT\": \"VELOCITY\", \"KIND\": \"DOF\", \"DIMENSION\": \"L1 T-1\", \"MIN\": 1, \"MAX\": 3, \"LABEL\": \"the velocity components of the body, one per axis\"}], \"PARAMETERS\": [{\"NAME\": \"rho_air\", \"DIMENSION\": \"L-3 M1\", \"SUPPLY\": \"DECLARED\", \"VALUE\": \"1.225\", \"UNIT\": \"kg m-3\", \"OVERRIDABLE\": \"NO\", \"LABEL\": \"the density of air at sea level\"}, {\"NAME\": \"mu_air\", \"DIMENSION\": \"L-1 M1 T-1\", \"SUPPLY\": \"DECLARED\", \"VALUE\": \"1.7894e-5\", \"UNIT\": \"Pa s\", \"OVERRIDABLE\": \"NO\", \"LABEL\": \"the dynamic viscosity of air at sea level\"}, {\"NAME\": \"pi_c\", \"DIMENSION\": \"1\", \"SUPPLY\": \"DECLARED\", \"VALUE\": \"3.141592653589793\", \"UNIT\": \"1\", \"OVERRIDABLE\": \"NO\", \"LABEL\": \"pi, to 16 significant digits\"}, {\"NAME\": \"R_s\", \"DIMENSION\": \"L1\", \"SUPPLY\": \"AUTHOR\", \"LABEL\": \"the radius of the sphere\"}], \"SUMS\": [{\"NAME\": \"SPEED2\", \"OVER\": \"VELOCITY\", \"EACH\": \"VELOCITY^2\"}], \"TERMS\": [{\"TARGET\": \"VELOCITY\", \"SIGN\": \"-\", \"EXPR\": \"6*pi_c*mu_air*R_s*VELOCITY\", \"LABEL\": \"the linear (Stokes) drag\"}], \"ASSUMPTIONS\": [{\"NAME\": \"air_still\", \"PROPOSITION\": \"the air is at rest in the frame of the body's velocity\", \"REFS\": [\"VELOCITY\"]}, {\"NAME\": \"air_uniform\", \"PROPOSITION\": \"the air density is uniform over the region of motion\", \"REFS\": [\"rho_air\"]}, {\"NAME\": \"drag_sphere\", \"PROPOSITION\": \"the body is a rigid sphere of radius R_s\", \"REFS\": [\"R_s\"]}], \"BOUNDARIES\": [{\"NAME\": \"drag_linear_regime\", \"PREDICATE\": \"2 rho_air |v| R_s / mu_air < 1: the regime of the linear law\", \"CONDITION\": \"mu_air != 0 and SPEED2 >= 0 and 2*rho_air*sqrt(SPEED2)*R_s/mu_air < 1\"}], \"NOT_CHOSEN\": \"No linear (Stokes) air resistance.\", \"NOT_INCLUDED\": [\"No wind: the air is at rest.\", \"No change of air density or viscosity with altitude or temperature.\", \"No drag outside the regime of the linear law.\"], \"EXCLUDES\": [], \"INTERACTS_WITH\": [], \"TEST_BINDINGS\": [{\"NAME\": \"PROJECTILE_2D\", \"TPK\": {\"DOF\": [{\"NAME\": \"t\", \"DIMENSION\": \"T1\"}, {\"NAME\": \"x\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"z\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"v_x\", \"DIMENSION\": \"L1 T-1\"}, {\"NAME\": \"v_z\", \"DIMENSION\": \"L1 T-1\"}], \"CONSTANT\": [{\"NAME\": \"m\", \"DIMENSION\": \"M1\"}], \"LAW\": [{\"NAME\": \"KIN_X\", \"STATEMENT\": \"dx/dt = v_x\", \"REFS\": [\"t\", \"v_x\", \"x\"], \"ROLE\": \"EOM(x)\", \"EQUATION\": \"D(x,t)=v_x\"}, {\"NAME\": \"KIN_Z\", \"STATEMENT\": \"dz/dt = v_z\", \"REFS\": [\"t\", \"v_z\", \"z\"], \"ROLE\": \"EOM(z)\", \"EQUATION\": \"D(z,t)=v_z\"}, {\"NAME\": \"EOM_X\", \"STATEMENT\": \"m dv_x/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_x\"], \"ROLE\": \"EOM(v_x)\", \"EQUATION\": \"m*D(v_x,t)=0\"}, {\"NAME\": \"EOM_Z\", \"STATEMENT\": \"m dv_z/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_z\"], \"ROLE\": \"EOM(v_z)\", \"EQUATION\": \"m*D(v_z,t)=0\"}], \"ASSUMPTION\": [{\"NAME\": \"point_mass\", \"PROPOSITION\": \"the body is treated as a point mass\", \"REFS\": [\"m\"]}]}, \"BIND\": {\"VELOCITY\": [\"v_x\", \"v_z\"]}, \"VALUES\": {\"R_s\": {}}, \"ANSWERS\": {}}]}",
"{\"ID\": \"AIR-QUADRATIC\", \"VERSION\": \"1.0.0\", \"TITLE\": \"Air resistance at sea level, quadratic in the speed\", \"SOURCE\": \"ISO 2533:1975, Standard Atmosphere, sea-level values: density 1.225 kg m-3, dynamic viscosity 1.7894e-5 Pa s\", \"PREREQUISITES\": [{\"SLOT\": \"VELOCITY\", \"KIND\": \"DOF\", \"DIMENSION\": \"L1 T-1\", \"MIN\": 1, \"MAX\": 3, \"LABEL\": \"the velocity components of the body, one per axis\"}], \"PARAMETERS\": [{\"NAME\": \"rho_air\", \"DIMENSION\": \"L-3 M1\", \"SUPPLY\": \"DECLARED\", \"VALUE\": \"1.225\", \"UNIT\": \"kg m-3\", \"OVERRIDABLE\": \"NO\", \"LABEL\": \"the density of air at sea level\"}, {\"NAME\": \"mu_air\", \"DIMENSION\": \"L-1 M1 T-1\", \"SUPPLY\": \"DECLARED\", \"VALUE\": \"1.7894e-5\", \"UNIT\": \"Pa s\", \"OVERRIDABLE\": \"NO\", \"LABEL\": \"the dynamic viscosity of air at sea level\"}, {\"NAME\": \"C_d\", \"DIMENSION\": \"1\", \"SUPPLY\": \"AUTHOR\", \"LABEL\": \"the drag coefficient of the body\"}, {\"NAME\": \"A_ref\", \"DIMENSION\": \"L2\", \"SUPPLY\": \"AUTHOR\", \"LABEL\": \"the reference area of the drag coefficient\"}, {\"NAME\": \"L_ref\", \"DIMENSION\": \"L1\", \"SUPPLY\": \"AUTHOR\", \"LABEL\": \"the reference length of the Reynolds number\"}], \"SUMS\": [{\"NAME\": \"SPEED2\", \"OVER\": \"VELOCITY\", \"EACH\": \"VELOCITY^2\"}], \"TERMS\": [{\"TARGET\": \"VELOCITY\", \"SIGN\": \"-\", \"EXPR\": \"0.5*rho_air*C_d*A_ref*sqrt(SPEED2)*VELOCITY\", \"LABEL\": \"the quadratic drag\"}], \"ASSUMPTIONS\": [{\"NAME\": \"air_still\", \"PROPOSITION\": \"the air is at rest in the frame of the body's velocity\", \"REFS\": [\"VELOCITY\"]}, {\"NAME\": \"air_uniform\", \"PROPOSITION\": \"the air density is uniform over the region of motion\", \"REFS\": [\"rho_air\"]}, {\"NAME\": \"drag_cd_constant\", \"PROPOSITION\": \"the drag coefficient C_d is constant over the motion\", \"REFS\": [\"C_d\"]}, {\"NAME\": \"drag_no_lift\", \"PROPOSITION\": \"the body experiences no lift force\", \"REFS\": [\"VELOCITY\"]}, {\"NAME\": \"drag_no_magnus\", \"PROPOSITION\": \"the body experiences no Magnus force\", \"REFS\": [\"VELOCITY\"]}], \"BOUNDARIES\": [{\"NAME\": \"drag_quadratic_regime\", \"PREDICATE\": \"1e3 < rho_air |v| L_ref / mu_air < 2e5: the Reynolds window of the quadratic law\", \"CONDITION\": \"mu_air != 0 and SPEED2 >= 0 and rho_air*sqrt(SPEED2)*L_ref/mu_air > 1000 and rho_air*sqrt(SPEED2)*L_ref/mu_air < 200000\"}], \"NOT_CHOSEN\": \"No quadratic air resistance.\", \"NOT_INCLUDED\": [\"No wind: the air is at rest.\", \"No change of air density or viscosity with altitude or temperature.\", \"No lift, Magnus or added-mass force.\", \"No drag outside the Reynolds window of the quadratic law.\"], \"EXCLUDES\": [\"AIR-LINEAR\"], \"INTERACTS_WITH\": [], \"TEST_BINDINGS\": [{\"NAME\": \"PROJECTILE_2D\", \"TPK\": {\"DOF\": [{\"NAME\": \"t\", \"DIMENSION\": \"T1\"}, {\"NAME\": \"x\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"z\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"v_x\", \"DIMENSION\": \"L1 T-1\"}, {\"NAME\": \"v_z\", \"DIMENSION\": \"L1 T-1\"}], \"CONSTANT\": [{\"NAME\": \"m\", \"DIMENSION\": \"M1\"}], \"LAW\": [{\"NAME\": \"KIN_X\", \"STATEMENT\": \"dx/dt = v_x\", \"REFS\": [\"t\", \"v_x\", \"x\"], \"ROLE\": \"EOM(x)\", \"EQUATION\": \"D(x,t)=v_x\"}, {\"NAME\": \"KIN_Z\", \"STATEMENT\": \"dz/dt = v_z\", \"REFS\": [\"t\", \"v_z\", \"z\"], \"ROLE\": \"EOM(z)\", \"EQUATION\": \"D(z,t)=v_z\"}, {\"NAME\": \"EOM_X\", \"STATEMENT\": \"m dv_x/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_x\"], \"ROLE\": \"EOM(v_x)\", \"EQUATION\": \"m*D(v_x,t)=0\"}, {\"NAME\": \"EOM_Z\", \"STATEMENT\": \"m dv_z/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_z\"], \"ROLE\": \"EOM(v_z)\", \"EQUATION\": \"m*D(v_z,t)=0\"}], \"ASSUMPTION\": [{\"NAME\": \"point_mass\", \"PROPOSITION\": \"the body is treated as a point mass\", \"REFS\": [\"m\"]}]}, \"BIND\": {\"VELOCITY\": [\"v_x\", \"v_z\"]}, \"VALUES\": {\"A_ref\": {}, \"C_d\": {}, \"L_ref\": {}}, \"ANSWERS\": {}}]}",
"{\"ID\": \"GRAV-UNIFORM\", \"VERSION\": \"1.0.0\", \"TITLE\": \"Uniform gravity at the standard value g_n\", \"SOURCE\": \"g_n = 9.80665 m s-2, exact by definition: 3rd CGPM (1901), declaration on the unit of mass and on the definition of weight\", \"PREREQUISITES\": [{\"SLOT\": \"MASS\", \"KIND\": \"CONSTANT\", \"DIMENSION\": \"M1\", \"MIN\": 1, \"MAX\": 1, \"LABEL\": \"the mass of the body\"}, {\"SLOT\": \"UP_VELOCITY\", \"KIND\": \"DOF\", \"DIMENSION\": \"L1 T-1\", \"MIN\": 1, \"MAX\": 1, \"LABEL\": \"the velocity component pointing up; its equation of motion receives the weight\"}, {\"SLOT\": \"HEIGHT\", \"KIND\": \"DOF\", \"DIMENSION\": \"L1\", \"MIN\": 1, \"MAX\": 1, \"LABEL\": \"the position along the same upward axis\"}], \"PARAMETERS\": [{\"NAME\": \"g_n\", \"DIMENSION\": \"L1 T-2\", \"SUPPLY\": \"DECLARED\", \"VALUE\": \"9.80665\", \"UNIT\": \"m s-2\", \"OVERRIDABLE\": \"NO\", \"LABEL\": \"the standard acceleration of gravity\"}, {\"NAME\": \"h_max\", \"DIMENSION\": \"L1\", \"SUPPLY\": \"AUTHOR\", \"LABEL\": \"the largest height, above or below the origin, over which the field is taken as uniform\"}], \"SUMS\": [], \"TERMS\": [{\"TARGET\": \"UP_VELOCITY\", \"SIGN\": \"-\", \"EXPR\": \"MASS*g_n\", \"LABEL\": \"the weight\"}], \"ASSUMPTIONS\": [{\"NAME\": \"gravity_uniform\", \"PROPOSITION\": \"the gravitational field is uniform over the region abs({HEIGHT}) < h_max\", \"REFS\": [\"HEIGHT\", \"h_max\"]}, {\"NAME\": \"gravity_standard\", \"PROPOSITION\": \"the local gravitational acceleration equals the conventional standard value g_n\", \"REFS\": [\"g_n\"]}, {\"NAME\": \"frame_inertial\", \"PROPOSITION\": \"the frame in which {HEIGHT} is measured is treated as inertial\", \"REFS\": [\"HEIGHT\"]}], \"BOUNDARIES\": [{\"NAME\": \"gravity_region\", \"PREDICATE\": \"abs({HEIGHT}) < h_max\", \"CONDITION\": \"abs(HEIGHT) < h_max\"}], \"NOT_CHOSEN\": \"No gravity: no weight acts on any DOF.\", \"NOT_INCLUDED\": [\"No variation of gravity with height or latitude beyond what g_n contains.\", \"No Earth rotation (Coriolis or centrifugal force) beyond what g_n contains.\", \"No gravity of bodies other than the Earth.\"], \"EXCLUDES\": [], \"INTERACTS_WITH\": [{\"WITH\": \"AIR-*\", \"QUESTION_ID\": \"BUOYANCY\", \"QUESTION\": \"Does the air's buoyancy (upthrust) act on the body in the system you mean?\", \"YES_LINE\": \"Buoyancy acts (your answer): no module adds it; it acts in this kernel only where one of your own laws states it.\", \"NO_LINE\": \"No buoyancy: the air's upthrust on the body is not included.\"}], \"TEST_BINDINGS\": [{\"NAME\": \"PROJECTILE_2D\", \"TPK\": {\"DOF\": [{\"NAME\": \"t\", \"DIMENSION\": \"T1\"}, {\"NAME\": \"x\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"z\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"v_x\", \"DIMENSION\": \"L1 T-1\"}, {\"NAME\": \"v_z\", \"DIMENSION\": \"L1 T-1\"}], \"CONSTANT\": [{\"NAME\": \"m\", \"DIMENSION\": \"M1\"}], \"LAW\": [{\"NAME\": \"KIN_X\", \"STATEMENT\": \"dx/dt = v_x\", \"REFS\": [\"t\", \"v_x\", \"x\"], \"ROLE\": \"EOM(x)\", \"EQUATION\": \"D(x,t)=v_x\"}, {\"NAME\": \"KIN_Z\", \"STATEMENT\": \"dz/dt = v_z\", \"REFS\": [\"t\", \"v_z\", \"z\"], \"ROLE\": \"EOM(z)\", \"EQUATION\": \"D(z,t)=v_z\"}, {\"NAME\": \"EOM_X\", \"STATEMENT\": \"m dv_x/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_x\"], \"ROLE\": \"EOM(v_x)\", \"EQUATION\": \"m*D(v_x,t)=0\"}, {\"NAME\": \"EOM_Z\", \"STATEMENT\": \"m dv_z/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_z\"], \"ROLE\": \"EOM(v_z)\", \"EQUATION\": \"m*D(v_z,t)=0\"}], \"ASSUMPTION\": [{\"NAME\": \"point_mass\", \"PROPOSITION\": \"the body is treated as a point mass\", \"REFS\": [\"m\"]}]}, \"BIND\": {\"HEIGHT\": [\"z\"], \"MASS\": [\"m\"], \"UP_VELOCITY\": [\"v_z\"]}, \"VALUES\": {\"h_max\": {\"VALUE\": \"100\", \"UNIT\": \"m\"}}, \"ANSWERS\": {}}, {\"NAME\": \"TABLE\", \"TPK\": {\"DOF\": [{\"NAME\": \"t\", \"DIMENSION\": \"T1\"}, {\"NAME\": \"x\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"z\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"v_x\", \"DIMENSION\": \"L1 T-1\"}, {\"NAME\": \"v_z\", \"DIMENSION\": \"L1 T-1\"}], \"CONSTANT\": [{\"NAME\": \"m\", \"DIMENSION\": \"M1\"}], \"LAW\": [{\"NAME\": \"KIN_X\", \"STATEMENT\": \"dx/dt = v_x\", \"REFS\": [\"t\", \"v_x\", \"x\"], \"ROLE\": \"EOM(x)\", \"EQUATION\": \"D(x,t)=v_x\"}, {\"NAME\": \"KIN_Z\", \"STATEMENT\": \"dz/dt = v_z\", \"REFS\": [\"t\", \"v_z\", \"z\"], \"ROLE\": \"CONSTRAINT\", \"EQUATION\": \"D(z,t)=v_z\"}, {\"NAME\": \"EOM_X\", \"STATEMENT\": \"m dv_x/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_x\"], \"ROLE\": \"EOM(v_x)\", \"EQUATION\": \"m*D(v_x,t)=0\"}], \"CONSTRAINT\": [{\"NAME\": \"C_Z\", \"TARGET\": \"z\", \"ACTION\": \"FIX\", \"VALUE\": \"0\", \"UNIT\": \"m\", \"STATEMENT\": \"the puck stays on the table top, z = 0\"}, {\"NAME\": \"C_VZ\", \"TARGET\": \"v_z\", \"ACTION\": \"FIX\", \"VALUE\": \"0\", \"UNIT\": \"m s-1\", \"STATEMENT\": \"the puck has no vertical velocity\"}]}, \"BIND\": {\"HEIGHT\": [\"z\"], \"MASS\": [\"m\"], \"UP_VELOCITY\": [\"v_z\"]}, \"VALUES\": {\"h_max\": {\"VALUE\": \"1\", \"UNIT\": \"m\"}}, \"ANSWERS\": {\"FIXED:v_z\": \"YES\"}}]}",
"{\"ID\": \"MATH\", \"VERSION\": \"1.0.0\", \"TITLE\": \"The mathematical constant pi, as the CONSTANT pi_c\", \"SOURCE\": \"pi to 16 significant digits, 3.141592653589793, the nearest IEEE 754 binary64 value\", \"PREREQUISITES\": [], \"PARAMETERS\": [{\"NAME\": \"pi_c\", \"DIMENSION\": \"1\", \"SUPPLY\": \"DECLARED\", \"VALUE\": \"3.141592653589793\", \"UNIT\": \"1\", \"OVERRIDABLE\": \"NO\", \"LABEL\": \"pi, to 16 significant digits\"}], \"SUMS\": [], \"TERMS\": [], \"ASSUMPTIONS\": [], \"BOUNDARIES\": [], \"NOT_CHOSEN\": \"No mathematical constant: pi exists only if you declare it.\", \"NOT_INCLUDED\": [\"pi_c is pi rounded to 16 significant digits; no other mathematical constant is declared.\"], \"EXCLUDES\": [], \"INTERACTS_WITH\": [], \"TEST_BINDINGS\": [{\"NAME\": \"PROJECTILE_2D\", \"TPK\": {\"DOF\": [{\"NAME\": \"t\", \"DIMENSION\": \"T1\"}, {\"NAME\": \"x\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"z\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"v_x\", \"DIMENSION\": \"L1 T-1\"}, {\"NAME\": \"v_z\", \"DIMENSION\": \"L1 T-1\"}], \"CONSTANT\": [{\"NAME\": \"m\", \"DIMENSION\": \"M1\"}], \"LAW\": [{\"NAME\": \"KIN_X\", \"STATEMENT\": \"dx/dt = v_x\", \"REFS\": [\"t\", \"v_x\", \"x\"], \"ROLE\": \"EOM(x)\", \"EQUATION\": \"D(x,t)=v_x\"}, {\"NAME\": \"KIN_Z\", \"STATEMENT\": \"dz/dt = v_z\", \"REFS\": [\"t\", \"v_z\", \"z\"], \"ROLE\": \"EOM(z)\", \"EQUATION\": \"D(z,t)=v_z\"}, {\"NAME\": \"EOM_X\", \"STATEMENT\": \"m dv_x/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_x\"], \"ROLE\": \"EOM(v_x)\", \"EQUATION\": \"m*D(v_x,t)=0\"}, {\"NAME\": \"EOM_Z\", \"STATEMENT\": \"m dv_z/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_z\"], \"ROLE\": \"EOM(v_z)\", \"EQUATION\": \"m*D(v_z,t)=0\"}], \"ASSUMPTION\": [{\"NAME\": \"point_mass\", \"PROPOSITION\": \"the body is treated as a point mass\", \"REFS\": [\"m\"]}]}, \"BIND\": {}, \"VALUES\": {}, \"ANSWERS\": {}}]}"
]
},
"expected": "[\"OK\",[\"ASK\",[]],[\"CLAIMS\",[[\"GRAV-UNIFORM\",\"1.0.0\",\"PINNED\"]]]]",
"fn": "interview_check",
"hand_checked": true,
"name": "I02 GRAV-UNIFORM chosen and claimed: PINNED"
},
{
"args": {
"answer": [
{
"AT": 4,
"CHOSEN": [
"AIR-QUADRATIC",
"GRAV-UNIFORM"
],
"COVERED": [
[
"AIR-LINEAR",
"1.0.0",
"5f3fe27b42378bce0830b0d0959f892f4a8e73b12b540ae877e39e6439d08b4d"
],
[
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"6fb53c3a6546151eead2bd6e72e9cf8334f3a2040ad0ee2f5b988ec96d6fc852"
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[
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]
]
}
],
"carried": [],
"claims": [
{
"ANSWERS": {
"BUOYANCY": "NO"
},
"BIND": {
"HEIGHT": [
"z"
],
"MASS": [
"m"
],
"UP_VELOCITY": [
"v_z"
]
},
"DIGEST": "24877ccb5c8ec300d29ed82ce6650592f35cf8899a3d878ccce9c08d4c72c025",
"ID": "GRAV-UNIFORM",
"VALUES": {
"h_max": {
"UNIT": "m",
"VALUE": "100"
}
},
"VERSION": "1.0.0"
},
{
"ANSWERS": {},
"BIND": {
"VELOCITY": [
"v_x",
"v_z"
]
},
"DIGEST": "6fb53c3a6546151eead2bd6e72e9cf8334f3a2040ad0ee2f5b988ec96d6fc852",
"ID": "AIR-QUADRATIC",
"VALUES": {
"A_ref": {},
"C_d": {},
"L_ref": {}
},
"VERSION": "1.0.0"
}
],
"lines": [
{
"ACT": "MODULE ADD",
"DATE": "2026-10-01",
"DIGEST": "5f3fe27b42378bce0830b0d0959f892f4a8e73b12b540ae877e39e6439d08b4d",
"ID": "AIR-LINEAR",
"VERSION": "1.0.0"
},
{
"ACT": "MODULE ADD",
"DATE": "2026-10-01",
"DIGEST": "6fb53c3a6546151eead2bd6e72e9cf8334f3a2040ad0ee2f5b988ec96d6fc852",
"ID": "AIR-QUADRATIC",
"VERSION": "1.0.0"
},
{
"ACT": "MODULE ADD",
"DATE": "2026-10-01",
"DIGEST": "24877ccb5c8ec300d29ed82ce6650592f35cf8899a3d878ccce9c08d4c72c025",
"ID": "GRAV-UNIFORM",
"VERSION": "1.0.0"
},
{
"ACT": "MODULE ADD",
"DATE": "2026-10-01",
"DIGEST": "8f39a356f35527b901fcee012764590f0819c8ffdeccad4bc05195ce3d2e0bcf",
"ID": "MATH",
"VERSION": "1.0.0"
}
],
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"modules": [
"{\"ID\": \"AIR-LINEAR\", \"VERSION\": \"1.0.0\", \"TITLE\": \"Air resistance at sea level, linear in the speed (Stokes drag on a sphere)\", \"SOURCE\": \"ISO 2533:1975, Standard Atmosphere, sea-level values: density 1.225 kg m-3, dynamic viscosity 1.7894e-5 Pa s\", \"PREREQUISITES\": [{\"SLOT\": \"VELOCITY\", \"KIND\": \"DOF\", \"DIMENSION\": \"L1 T-1\", \"MIN\": 1, \"MAX\": 3, \"LABEL\": \"the velocity components of the body, one per axis\"}], \"PARAMETERS\": [{\"NAME\": \"rho_air\", \"DIMENSION\": \"L-3 M1\", \"SUPPLY\": \"DECLARED\", \"VALUE\": \"1.225\", \"UNIT\": \"kg m-3\", \"OVERRIDABLE\": \"NO\", \"LABEL\": \"the density of air at sea level\"}, {\"NAME\": \"mu_air\", \"DIMENSION\": \"L-1 M1 T-1\", \"SUPPLY\": \"DECLARED\", \"VALUE\": \"1.7894e-5\", \"UNIT\": \"Pa s\", \"OVERRIDABLE\": \"NO\", \"LABEL\": \"the dynamic viscosity of air at sea level\"}, {\"NAME\": \"pi_c\", \"DIMENSION\": \"1\", \"SUPPLY\": \"DECLARED\", \"VALUE\": \"3.141592653589793\", \"UNIT\": \"1\", \"OVERRIDABLE\": \"NO\", \"LABEL\": \"pi, to 16 significant digits\"}, {\"NAME\": \"R_s\", \"DIMENSION\": \"L1\", \"SUPPLY\": \"AUTHOR\", \"LABEL\": \"the radius of the sphere\"}], \"SUMS\": [{\"NAME\": \"SPEED2\", \"OVER\": \"VELOCITY\", \"EACH\": \"VELOCITY^2\"}], \"TERMS\": [{\"TARGET\": \"VELOCITY\", \"SIGN\": \"-\", \"EXPR\": \"6*pi_c*mu_air*R_s*VELOCITY\", \"LABEL\": \"the linear (Stokes) drag\"}], \"ASSUMPTIONS\": [{\"NAME\": \"air_still\", \"PROPOSITION\": \"the air is at rest in the frame of the body's velocity\", \"REFS\": [\"VELOCITY\"]}, {\"NAME\": \"air_uniform\", \"PROPOSITION\": \"the air density is uniform over the region of motion\", \"REFS\": [\"rho_air\"]}, {\"NAME\": \"drag_sphere\", \"PROPOSITION\": \"the body is a rigid sphere of radius R_s\", \"REFS\": [\"R_s\"]}], \"BOUNDARIES\": [{\"NAME\": \"drag_linear_regime\", \"PREDICATE\": \"2 rho_air |v| R_s / mu_air < 1: the regime of the linear law\", \"CONDITION\": \"mu_air != 0 and SPEED2 >= 0 and 2*rho_air*sqrt(SPEED2)*R_s/mu_air < 1\"}], \"NOT_CHOSEN\": \"No linear (Stokes) air resistance.\", \"NOT_INCLUDED\": [\"No wind: the air is at rest.\", \"No change of air density or viscosity with altitude or temperature.\", \"No drag outside the regime of the linear law.\"], \"EXCLUDES\": [], \"INTERACTS_WITH\": [], \"TEST_BINDINGS\": [{\"NAME\": \"PROJECTILE_2D\", \"TPK\": {\"DOF\": [{\"NAME\": \"t\", \"DIMENSION\": \"T1\"}, {\"NAME\": \"x\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"z\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"v_x\", \"DIMENSION\": \"L1 T-1\"}, {\"NAME\": \"v_z\", \"DIMENSION\": \"L1 T-1\"}], \"CONSTANT\": [{\"NAME\": \"m\", \"DIMENSION\": \"M1\"}], \"LAW\": [{\"NAME\": \"KIN_X\", \"STATEMENT\": \"dx/dt = v_x\", \"REFS\": [\"t\", \"v_x\", \"x\"], \"ROLE\": \"EOM(x)\", \"EQUATION\": \"D(x,t)=v_x\"}, {\"NAME\": \"KIN_Z\", \"STATEMENT\": \"dz/dt = v_z\", \"REFS\": [\"t\", \"v_z\", \"z\"], \"ROLE\": \"EOM(z)\", \"EQUATION\": \"D(z,t)=v_z\"}, {\"NAME\": \"EOM_X\", \"STATEMENT\": \"m dv_x/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_x\"], \"ROLE\": \"EOM(v_x)\", \"EQUATION\": \"m*D(v_x,t)=0\"}, {\"NAME\": \"EOM_Z\", \"STATEMENT\": \"m dv_z/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_z\"], \"ROLE\": \"EOM(v_z)\", \"EQUATION\": \"m*D(v_z,t)=0\"}], \"ASSUMPTION\": [{\"NAME\": \"point_mass\", \"PROPOSITION\": \"the body is treated as a point mass\", \"REFS\": [\"m\"]}]}, \"BIND\": {\"VELOCITY\": [\"v_x\", \"v_z\"]}, \"VALUES\": {\"R_s\": {}}, \"ANSWERS\": {}}]}",
"{\"ID\": \"AIR-QUADRATIC\", \"VERSION\": \"1.0.0\", \"TITLE\": \"Air resistance at sea level, quadratic in the speed\", \"SOURCE\": \"ISO 2533:1975, Standard Atmosphere, sea-level values: density 1.225 kg m-3, dynamic viscosity 1.7894e-5 Pa s\", \"PREREQUISITES\": [{\"SLOT\": \"VELOCITY\", \"KIND\": \"DOF\", \"DIMENSION\": \"L1 T-1\", \"MIN\": 1, \"MAX\": 3, \"LABEL\": \"the velocity components of the body, one per axis\"}], \"PARAMETERS\": [{\"NAME\": \"rho_air\", \"DIMENSION\": \"L-3 M1\", \"SUPPLY\": \"DECLARED\", \"VALUE\": \"1.225\", \"UNIT\": \"kg m-3\", \"OVERRIDABLE\": \"NO\", \"LABEL\": \"the density of air at sea level\"}, {\"NAME\": \"mu_air\", \"DIMENSION\": \"L-1 M1 T-1\", \"SUPPLY\": \"DECLARED\", \"VALUE\": \"1.7894e-5\", \"UNIT\": \"Pa s\", \"OVERRIDABLE\": \"NO\", \"LABEL\": \"the dynamic viscosity of air at sea level\"}, {\"NAME\": \"C_d\", \"DIMENSION\": \"1\", \"SUPPLY\": \"AUTHOR\", \"LABEL\": \"the drag coefficient of the body\"}, {\"NAME\": \"A_ref\", \"DIMENSION\": \"L2\", \"SUPPLY\": \"AUTHOR\", \"LABEL\": \"the reference area of the drag coefficient\"}, {\"NAME\": \"L_ref\", \"DIMENSION\": \"L1\", \"SUPPLY\": \"AUTHOR\", \"LABEL\": \"the reference length of the Reynolds number\"}], \"SUMS\": [{\"NAME\": \"SPEED2\", \"OVER\": \"VELOCITY\", \"EACH\": \"VELOCITY^2\"}], \"TERMS\": [{\"TARGET\": \"VELOCITY\", \"SIGN\": \"-\", \"EXPR\": \"0.5*rho_air*C_d*A_ref*sqrt(SPEED2)*VELOCITY\", \"LABEL\": \"the quadratic drag\"}], \"ASSUMPTIONS\": [{\"NAME\": \"air_still\", \"PROPOSITION\": \"the air is at rest in the frame of the body's velocity\", \"REFS\": [\"VELOCITY\"]}, {\"NAME\": \"air_uniform\", \"PROPOSITION\": \"the air density is uniform over the region of motion\", \"REFS\": [\"rho_air\"]}, {\"NAME\": \"drag_cd_constant\", \"PROPOSITION\": \"the drag coefficient C_d is constant over the motion\", \"REFS\": [\"C_d\"]}, {\"NAME\": \"drag_no_lift\", \"PROPOSITION\": \"the body experiences no lift force\", \"REFS\": [\"VELOCITY\"]}, {\"NAME\": \"drag_no_magnus\", \"PROPOSITION\": \"the body experiences no Magnus force\", \"REFS\": [\"VELOCITY\"]}], \"BOUNDARIES\": [{\"NAME\": \"drag_quadratic_regime\", \"PREDICATE\": \"1e3 < rho_air |v| L_ref / mu_air < 2e5: the Reynolds window of the quadratic law\", \"CONDITION\": \"mu_air != 0 and SPEED2 >= 0 and rho_air*sqrt(SPEED2)*L_ref/mu_air > 1000 and rho_air*sqrt(SPEED2)*L_ref/mu_air < 200000\"}], \"NOT_CHOSEN\": \"No quadratic air resistance.\", \"NOT_INCLUDED\": [\"No wind: the air is at rest.\", \"No change of air density or viscosity with altitude or temperature.\", \"No lift, Magnus or added-mass force.\", \"No drag outside the Reynolds window of the quadratic law.\"], \"EXCLUDES\": [\"AIR-LINEAR\"], \"INTERACTS_WITH\": [], \"TEST_BINDINGS\": [{\"NAME\": \"PROJECTILE_2D\", \"TPK\": {\"DOF\": [{\"NAME\": \"t\", \"DIMENSION\": \"T1\"}, {\"NAME\": \"x\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"z\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"v_x\", \"DIMENSION\": \"L1 T-1\"}, {\"NAME\": \"v_z\", \"DIMENSION\": \"L1 T-1\"}], \"CONSTANT\": [{\"NAME\": \"m\", \"DIMENSION\": \"M1\"}], \"LAW\": [{\"NAME\": \"KIN_X\", \"STATEMENT\": \"dx/dt = v_x\", \"REFS\": [\"t\", \"v_x\", \"x\"], \"ROLE\": \"EOM(x)\", \"EQUATION\": \"D(x,t)=v_x\"}, {\"NAME\": \"KIN_Z\", \"STATEMENT\": \"dz/dt = v_z\", \"REFS\": [\"t\", \"v_z\", \"z\"], \"ROLE\": \"EOM(z)\", \"EQUATION\": \"D(z,t)=v_z\"}, {\"NAME\": \"EOM_X\", \"STATEMENT\": \"m dv_x/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_x\"], \"ROLE\": \"EOM(v_x)\", \"EQUATION\": \"m*D(v_x,t)=0\"}, {\"NAME\": \"EOM_Z\", \"STATEMENT\": \"m dv_z/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_z\"], \"ROLE\": \"EOM(v_z)\", \"EQUATION\": \"m*D(v_z,t)=0\"}], \"ASSUMPTION\": [{\"NAME\": \"point_mass\", \"PROPOSITION\": \"the body is treated as a point mass\", \"REFS\": [\"m\"]}]}, \"BIND\": {\"VELOCITY\": [\"v_x\", \"v_z\"]}, \"VALUES\": {\"A_ref\": {}, \"C_d\": {}, \"L_ref\": {}}, \"ANSWERS\": {}}]}",
"{\"ID\": \"GRAV-UNIFORM\", \"VERSION\": \"1.0.0\", \"TITLE\": \"Uniform gravity at the standard value g_n\", \"SOURCE\": \"g_n = 9.80665 m s-2, exact by definition: 3rd CGPM (1901), declaration on the unit of mass and on the definition of weight\", \"PREREQUISITES\": [{\"SLOT\": \"MASS\", \"KIND\": \"CONSTANT\", \"DIMENSION\": \"M1\", \"MIN\": 1, \"MAX\": 1, \"LABEL\": \"the mass of the body\"}, {\"SLOT\": \"UP_VELOCITY\", \"KIND\": \"DOF\", \"DIMENSION\": \"L1 T-1\", \"MIN\": 1, \"MAX\": 1, \"LABEL\": \"the velocity component pointing up; its equation of motion receives the weight\"}, {\"SLOT\": \"HEIGHT\", \"KIND\": \"DOF\", \"DIMENSION\": \"L1\", \"MIN\": 1, \"MAX\": 1, \"LABEL\": \"the position along the same upward axis\"}], \"PARAMETERS\": [{\"NAME\": \"g_n\", \"DIMENSION\": \"L1 T-2\", \"SUPPLY\": \"DECLARED\", \"VALUE\": \"9.80665\", \"UNIT\": \"m s-2\", \"OVERRIDABLE\": \"NO\", \"LABEL\": \"the standard acceleration of gravity\"}, {\"NAME\": \"h_max\", \"DIMENSION\": \"L1\", \"SUPPLY\": \"AUTHOR\", \"LABEL\": \"the largest height, above or below the origin, over which the field is taken as uniform\"}], \"SUMS\": [], \"TERMS\": [{\"TARGET\": \"UP_VELOCITY\", \"SIGN\": \"-\", \"EXPR\": \"MASS*g_n\", \"LABEL\": \"the weight\"}], \"ASSUMPTIONS\": [{\"NAME\": \"gravity_uniform\", \"PROPOSITION\": \"the gravitational field is uniform over the region abs({HEIGHT}) < h_max\", \"REFS\": [\"HEIGHT\", \"h_max\"]}, {\"NAME\": \"gravity_standard\", \"PROPOSITION\": \"the local gravitational acceleration equals the conventional standard value g_n\", \"REFS\": [\"g_n\"]}, {\"NAME\": \"frame_inertial\", \"PROPOSITION\": \"the frame in which {HEIGHT} is measured is treated as inertial\", \"REFS\": [\"HEIGHT\"]}], \"BOUNDARIES\": [{\"NAME\": \"gravity_region\", \"PREDICATE\": \"abs({HEIGHT}) < h_max\", \"CONDITION\": \"abs(HEIGHT) < h_max\"}], \"NOT_CHOSEN\": \"No gravity: no weight acts on any DOF.\", \"NOT_INCLUDED\": [\"No variation of gravity with height or latitude beyond what g_n contains.\", \"No Earth rotation (Coriolis or centrifugal force) beyond what g_n contains.\", \"No gravity of bodies other than the Earth.\"], \"EXCLUDES\": [], \"INTERACTS_WITH\": [{\"WITH\": \"AIR-*\", \"QUESTION_ID\": \"BUOYANCY\", \"QUESTION\": \"Does the air's buoyancy (upthrust) act on the body in the system you mean?\", \"YES_LINE\": \"Buoyancy acts (your answer): no module adds it; it acts in this kernel only where one of your own laws states it.\", \"NO_LINE\": \"No buoyancy: the air's upthrust on the body is not included.\"}], \"TEST_BINDINGS\": [{\"NAME\": \"PROJECTILE_2D\", \"TPK\": {\"DOF\": [{\"NAME\": \"t\", \"DIMENSION\": \"T1\"}, {\"NAME\": \"x\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"z\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"v_x\", \"DIMENSION\": \"L1 T-1\"}, {\"NAME\": \"v_z\", \"DIMENSION\": \"L1 T-1\"}], \"CONSTANT\": [{\"NAME\": \"m\", \"DIMENSION\": \"M1\"}], \"LAW\": [{\"NAME\": \"KIN_X\", \"STATEMENT\": \"dx/dt = v_x\", \"REFS\": [\"t\", \"v_x\", \"x\"], \"ROLE\": \"EOM(x)\", \"EQUATION\": \"D(x,t)=v_x\"}, {\"NAME\": \"KIN_Z\", \"STATEMENT\": \"dz/dt = v_z\", \"REFS\": [\"t\", \"v_z\", \"z\"], \"ROLE\": \"EOM(z)\", \"EQUATION\": \"D(z,t)=v_z\"}, {\"NAME\": \"EOM_X\", \"STATEMENT\": \"m dv_x/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_x\"], \"ROLE\": \"EOM(v_x)\", \"EQUATION\": \"m*D(v_x,t)=0\"}, {\"NAME\": \"EOM_Z\", \"STATEMENT\": \"m dv_z/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_z\"], \"ROLE\": \"EOM(v_z)\", \"EQUATION\": \"m*D(v_z,t)=0\"}], \"ASSUMPTION\": [{\"NAME\": \"point_mass\", \"PROPOSITION\": \"the body is treated as a point mass\", \"REFS\": [\"m\"]}]}, \"BIND\": {\"HEIGHT\": [\"z\"], \"MASS\": [\"m\"], \"UP_VELOCITY\": [\"v_z\"]}, \"VALUES\": {\"h_max\": {\"VALUE\": \"100\", \"UNIT\": \"m\"}}, \"ANSWERS\": {}}, {\"NAME\": \"TABLE\", \"TPK\": {\"DOF\": [{\"NAME\": \"t\", \"DIMENSION\": \"T1\"}, {\"NAME\": \"x\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"z\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"v_x\", \"DIMENSION\": \"L1 T-1\"}, {\"NAME\": \"v_z\", \"DIMENSION\": \"L1 T-1\"}], \"CONSTANT\": [{\"NAME\": \"m\", \"DIMENSION\": \"M1\"}], \"LAW\": [{\"NAME\": \"KIN_X\", \"STATEMENT\": \"dx/dt = v_x\", \"REFS\": [\"t\", \"v_x\", \"x\"], \"ROLE\": \"EOM(x)\", \"EQUATION\": \"D(x,t)=v_x\"}, {\"NAME\": \"KIN_Z\", \"STATEMENT\": \"dz/dt = v_z\", \"REFS\": [\"t\", \"v_z\", \"z\"], \"ROLE\": \"CONSTRAINT\", \"EQUATION\": \"D(z,t)=v_z\"}, {\"NAME\": \"EOM_X\", \"STATEMENT\": \"m dv_x/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_x\"], \"ROLE\": \"EOM(v_x)\", \"EQUATION\": \"m*D(v_x,t)=0\"}], \"CONSTRAINT\": [{\"NAME\": \"C_Z\", \"TARGET\": \"z\", \"ACTION\": \"FIX\", \"VALUE\": \"0\", \"UNIT\": \"m\", \"STATEMENT\": \"the puck stays on the table top, z = 0\"}, {\"NAME\": \"C_VZ\", \"TARGET\": \"v_z\", \"ACTION\": \"FIX\", \"VALUE\": \"0\", \"UNIT\": \"m s-1\", \"STATEMENT\": \"the puck has no vertical velocity\"}]}, \"BIND\": {\"HEIGHT\": [\"z\"], \"MASS\": [\"m\"], \"UP_VELOCITY\": [\"v_z\"]}, \"VALUES\": {\"h_max\": {\"VALUE\": \"1\", \"UNIT\": \"m\"}}, \"ANSWERS\": {\"FIXED:v_z\": \"YES\"}}]}",
"{\"ID\": \"MATH\", \"VERSION\": \"1.0.0\", \"TITLE\": \"The mathematical constant pi, as the CONSTANT pi_c\", \"SOURCE\": \"pi to 16 significant digits, 3.141592653589793, the nearest IEEE 754 binary64 value\", \"PREREQUISITES\": [], \"PARAMETERS\": [{\"NAME\": \"pi_c\", \"DIMENSION\": \"1\", \"SUPPLY\": \"DECLARED\", \"VALUE\": \"3.141592653589793\", \"UNIT\": \"1\", \"OVERRIDABLE\": \"NO\", \"LABEL\": \"pi, to 16 significant digits\"}], \"SUMS\": [], \"TERMS\": [], \"ASSUMPTIONS\": [], \"BOUNDARIES\": [], \"NOT_CHOSEN\": \"No mathematical constant: pi exists only if you declare it.\", \"NOT_INCLUDED\": [\"pi_c is pi rounded to 16 significant digits; no other mathematical constant is declared.\"], \"EXCLUDES\": [], \"INTERACTS_WITH\": [], \"TEST_BINDINGS\": [{\"NAME\": \"PROJECTILE_2D\", \"TPK\": {\"DOF\": [{\"NAME\": \"t\", \"DIMENSION\": \"T1\"}, {\"NAME\": \"x\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"z\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"v_x\", \"DIMENSION\": \"L1 T-1\"}, {\"NAME\": \"v_z\", \"DIMENSION\": \"L1 T-1\"}], \"CONSTANT\": [{\"NAME\": \"m\", \"DIMENSION\": \"M1\"}], \"LAW\": [{\"NAME\": \"KIN_X\", \"STATEMENT\": \"dx/dt = v_x\", \"REFS\": [\"t\", \"v_x\", \"x\"], \"ROLE\": \"EOM(x)\", \"EQUATION\": \"D(x,t)=v_x\"}, {\"NAME\": \"KIN_Z\", \"STATEMENT\": \"dz/dt = v_z\", \"REFS\": [\"t\", \"v_z\", \"z\"], \"ROLE\": \"EOM(z)\", \"EQUATION\": \"D(z,t)=v_z\"}, {\"NAME\": \"EOM_X\", \"STATEMENT\": \"m dv_x/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_x\"], \"ROLE\": \"EOM(v_x)\", \"EQUATION\": \"m*D(v_x,t)=0\"}, {\"NAME\": \"EOM_Z\", \"STATEMENT\": \"m dv_z/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_z\"], \"ROLE\": \"EOM(v_z)\", \"EQUATION\": \"m*D(v_z,t)=0\"}], \"ASSUMPTION\": [{\"NAME\": \"point_mass\", \"PROPOSITION\": \"the body is treated as a point mass\", \"REFS\": [\"m\"]}]}, \"BIND\": {}, \"VALUES\": {}, \"ANSWERS\": {}}]}"
]
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"fn": "interview_check",
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"name": "I03 two chosen, buoyancy answered"
},
{
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{
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{
"ACT": "MODULE ADD",
"DATE": "2026-10-01",
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{
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"modules": [
"{\"ID\": \"AIR-LINEAR\", \"VERSION\": \"1.0.0\", \"TITLE\": \"Air resistance at sea level, linear in the speed (Stokes drag on a sphere)\", \"SOURCE\": \"ISO 2533:1975, Standard Atmosphere, sea-level values: density 1.225 kg m-3, dynamic viscosity 1.7894e-5 Pa s\", \"PREREQUISITES\": [{\"SLOT\": \"VELOCITY\", \"KIND\": \"DOF\", \"DIMENSION\": \"L1 T-1\", \"MIN\": 1, \"MAX\": 3, \"LABEL\": \"the velocity components of the body, one per axis\"}], \"PARAMETERS\": [{\"NAME\": \"rho_air\", \"DIMENSION\": \"L-3 M1\", \"SUPPLY\": \"DECLARED\", \"VALUE\": \"1.225\", \"UNIT\": \"kg m-3\", \"OVERRIDABLE\": \"NO\", \"LABEL\": \"the density of air at sea level\"}, {\"NAME\": \"mu_air\", \"DIMENSION\": \"L-1 M1 T-1\", \"SUPPLY\": \"DECLARED\", \"VALUE\": \"1.7894e-5\", \"UNIT\": \"Pa s\", \"OVERRIDABLE\": \"NO\", \"LABEL\": \"the dynamic viscosity of air at sea level\"}, {\"NAME\": \"pi_c\", \"DIMENSION\": \"1\", \"SUPPLY\": \"DECLARED\", \"VALUE\": \"3.141592653589793\", \"UNIT\": \"1\", \"OVERRIDABLE\": \"NO\", \"LABEL\": \"pi, to 16 significant digits\"}, {\"NAME\": \"R_s\", \"DIMENSION\": \"L1\", \"SUPPLY\": \"AUTHOR\", \"LABEL\": \"the radius of the sphere\"}], \"SUMS\": [{\"NAME\": \"SPEED2\", \"OVER\": \"VELOCITY\", \"EACH\": \"VELOCITY^2\"}], \"TERMS\": [{\"TARGET\": \"VELOCITY\", \"SIGN\": \"-\", \"EXPR\": \"6*pi_c*mu_air*R_s*VELOCITY\", \"LABEL\": \"the linear (Stokes) drag\"}], \"ASSUMPTIONS\": [{\"NAME\": \"air_still\", \"PROPOSITION\": \"the air is at rest in the frame of the body's velocity\", \"REFS\": [\"VELOCITY\"]}, {\"NAME\": \"air_uniform\", \"PROPOSITION\": \"the air density is uniform over the region of motion\", \"REFS\": [\"rho_air\"]}, {\"NAME\": \"drag_sphere\", \"PROPOSITION\": \"the body is a rigid sphere of radius R_s\", \"REFS\": [\"R_s\"]}], \"BOUNDARIES\": [{\"NAME\": \"drag_linear_regime\", \"PREDICATE\": \"2 rho_air |v| R_s / mu_air < 1: the regime of the linear law\", \"CONDITION\": \"mu_air != 0 and SPEED2 >= 0 and 2*rho_air*sqrt(SPEED2)*R_s/mu_air < 1\"}], \"NOT_CHOSEN\": \"No linear (Stokes) air resistance.\", \"NOT_INCLUDED\": [\"No wind: the air is at rest.\", \"No change of air density or viscosity with altitude or temperature.\", \"No drag outside the regime of the linear law.\"], \"EXCLUDES\": [], \"INTERACTS_WITH\": [], \"TEST_BINDINGS\": [{\"NAME\": \"PROJECTILE_2D\", \"TPK\": {\"DOF\": [{\"NAME\": \"t\", \"DIMENSION\": \"T1\"}, {\"NAME\": \"x\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"z\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"v_x\", \"DIMENSION\": \"L1 T-1\"}, {\"NAME\": \"v_z\", \"DIMENSION\": \"L1 T-1\"}], \"CONSTANT\": [{\"NAME\": \"m\", \"DIMENSION\": \"M1\"}], \"LAW\": [{\"NAME\": \"KIN_X\", \"STATEMENT\": \"dx/dt = v_x\", \"REFS\": [\"t\", \"v_x\", \"x\"], \"ROLE\": \"EOM(x)\", \"EQUATION\": \"D(x,t)=v_x\"}, {\"NAME\": \"KIN_Z\", \"STATEMENT\": \"dz/dt = v_z\", \"REFS\": [\"t\", \"v_z\", \"z\"], \"ROLE\": \"EOM(z)\", \"EQUATION\": \"D(z,t)=v_z\"}, {\"NAME\": \"EOM_X\", \"STATEMENT\": \"m dv_x/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_x\"], \"ROLE\": \"EOM(v_x)\", \"EQUATION\": \"m*D(v_x,t)=0\"}, {\"NAME\": \"EOM_Z\", \"STATEMENT\": \"m dv_z/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_z\"], \"ROLE\": \"EOM(v_z)\", \"EQUATION\": \"m*D(v_z,t)=0\"}], \"ASSUMPTION\": [{\"NAME\": \"point_mass\", \"PROPOSITION\": \"the body is treated as a point mass\", \"REFS\": [\"m\"]}]}, \"BIND\": {\"VELOCITY\": [\"v_x\", \"v_z\"]}, \"VALUES\": {\"R_s\": {}}, \"ANSWERS\": {}}]}",
"{\"ID\": \"AIR-QUADRATIC\", \"VERSION\": \"1.0.0\", \"TITLE\": \"Air resistance at sea level, quadratic in the speed\", \"SOURCE\": \"ISO 2533:1975, Standard Atmosphere, sea-level values: density 1.225 kg m-3, dynamic viscosity 1.7894e-5 Pa s\", \"PREREQUISITES\": [{\"SLOT\": \"VELOCITY\", \"KIND\": \"DOF\", \"DIMENSION\": \"L1 T-1\", \"MIN\": 1, \"MAX\": 3, \"LABEL\": \"the velocity components of the body, one per axis\"}], \"PARAMETERS\": [{\"NAME\": \"rho_air\", \"DIMENSION\": \"L-3 M1\", \"SUPPLY\": \"DECLARED\", \"VALUE\": \"1.225\", \"UNIT\": \"kg m-3\", \"OVERRIDABLE\": \"NO\", \"LABEL\": \"the density of air at sea level\"}, {\"NAME\": \"mu_air\", \"DIMENSION\": \"L-1 M1 T-1\", \"SUPPLY\": \"DECLARED\", \"VALUE\": \"1.7894e-5\", \"UNIT\": \"Pa s\", \"OVERRIDABLE\": \"NO\", \"LABEL\": \"the dynamic viscosity of air at sea level\"}, {\"NAME\": \"C_d\", \"DIMENSION\": \"1\", \"SUPPLY\": \"AUTHOR\", \"LABEL\": \"the drag coefficient of the body\"}, {\"NAME\": \"A_ref\", \"DIMENSION\": \"L2\", \"SUPPLY\": \"AUTHOR\", \"LABEL\": \"the reference area of the drag coefficient\"}, {\"NAME\": \"L_ref\", \"DIMENSION\": \"L1\", \"SUPPLY\": \"AUTHOR\", \"LABEL\": \"the reference length of the Reynolds number\"}], \"SUMS\": [{\"NAME\": \"SPEED2\", \"OVER\": \"VELOCITY\", \"EACH\": \"VELOCITY^2\"}], \"TERMS\": [{\"TARGET\": \"VELOCITY\", \"SIGN\": \"-\", \"EXPR\": \"0.5*rho_air*C_d*A_ref*sqrt(SPEED2)*VELOCITY\", \"LABEL\": \"the quadratic drag\"}], \"ASSUMPTIONS\": [{\"NAME\": \"air_still\", \"PROPOSITION\": \"the air is at rest in the frame of the body's velocity\", \"REFS\": [\"VELOCITY\"]}, {\"NAME\": \"air_uniform\", \"PROPOSITION\": \"the air density is uniform over the region of motion\", \"REFS\": [\"rho_air\"]}, {\"NAME\": \"drag_cd_constant\", \"PROPOSITION\": \"the drag coefficient C_d is constant over the motion\", \"REFS\": [\"C_d\"]}, {\"NAME\": \"drag_no_lift\", \"PROPOSITION\": \"the body experiences no lift force\", \"REFS\": [\"VELOCITY\"]}, {\"NAME\": \"drag_no_magnus\", \"PROPOSITION\": \"the body experiences no Magnus force\", \"REFS\": [\"VELOCITY\"]}], \"BOUNDARIES\": [{\"NAME\": \"drag_quadratic_regime\", \"PREDICATE\": \"1e3 < rho_air |v| L_ref / mu_air < 2e5: the Reynolds window of the quadratic law\", \"CONDITION\": \"mu_air != 0 and SPEED2 >= 0 and rho_air*sqrt(SPEED2)*L_ref/mu_air > 1000 and rho_air*sqrt(SPEED2)*L_ref/mu_air < 200000\"}], \"NOT_CHOSEN\": \"No quadratic air resistance.\", \"NOT_INCLUDED\": [\"No wind: the air is at rest.\", \"No change of air density or viscosity with altitude or temperature.\", \"No lift, Magnus or added-mass force.\", \"No drag outside the Reynolds window of the quadratic law.\"], \"EXCLUDES\": [\"AIR-LINEAR\"], \"INTERACTS_WITH\": [], \"TEST_BINDINGS\": [{\"NAME\": \"PROJECTILE_2D\", \"TPK\": {\"DOF\": [{\"NAME\": \"t\", \"DIMENSION\": \"T1\"}, {\"NAME\": \"x\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"z\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"v_x\", \"DIMENSION\": \"L1 T-1\"}, {\"NAME\": \"v_z\", \"DIMENSION\": \"L1 T-1\"}], \"CONSTANT\": [{\"NAME\": \"m\", \"DIMENSION\": \"M1\"}], \"LAW\": [{\"NAME\": \"KIN_X\", \"STATEMENT\": \"dx/dt = v_x\", \"REFS\": [\"t\", \"v_x\", \"x\"], \"ROLE\": \"EOM(x)\", \"EQUATION\": \"D(x,t)=v_x\"}, {\"NAME\": \"KIN_Z\", \"STATEMENT\": \"dz/dt = v_z\", \"REFS\": [\"t\", \"v_z\", \"z\"], \"ROLE\": \"EOM(z)\", \"EQUATION\": \"D(z,t)=v_z\"}, {\"NAME\": \"EOM_X\", \"STATEMENT\": \"m dv_x/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_x\"], \"ROLE\": \"EOM(v_x)\", \"EQUATION\": \"m*D(v_x,t)=0\"}, {\"NAME\": \"EOM_Z\", \"STATEMENT\": \"m dv_z/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_z\"], \"ROLE\": \"EOM(v_z)\", \"EQUATION\": \"m*D(v_z,t)=0\"}], \"ASSUMPTION\": [{\"NAME\": \"point_mass\", \"PROPOSITION\": \"the body is treated as a point mass\", \"REFS\": [\"m\"]}]}, \"BIND\": {\"VELOCITY\": [\"v_x\", \"v_z\"]}, \"VALUES\": {\"A_ref\": {}, \"C_d\": {}, \"L_ref\": {}}, \"ANSWERS\": {}}]}",
"{\"ID\": \"GRAV-UNIFORM\", \"VERSION\": \"1.0.0\", \"TITLE\": \"Uniform gravity at the standard value g_n\", \"SOURCE\": \"g_n = 9.80665 m s-2, exact by definition: 3rd CGPM (1901), declaration on the unit of mass and on the definition of weight\", \"PREREQUISITES\": [{\"SLOT\": \"MASS\", \"KIND\": \"CONSTANT\", \"DIMENSION\": \"M1\", \"MIN\": 1, \"MAX\": 1, \"LABEL\": \"the mass of the body\"}, {\"SLOT\": \"UP_VELOCITY\", \"KIND\": \"DOF\", \"DIMENSION\": \"L1 T-1\", \"MIN\": 1, \"MAX\": 1, \"LABEL\": \"the velocity component pointing up; its equation of motion receives the weight\"}, {\"SLOT\": \"HEIGHT\", \"KIND\": \"DOF\", \"DIMENSION\": \"L1\", \"MIN\": 1, \"MAX\": 1, \"LABEL\": \"the position along the same upward axis\"}], \"PARAMETERS\": [{\"NAME\": \"g_n\", \"DIMENSION\": \"L1 T-2\", \"SUPPLY\": \"DECLARED\", \"VALUE\": \"9.80665\", \"UNIT\": \"m s-2\", \"OVERRIDABLE\": \"NO\", \"LABEL\": \"the standard acceleration of gravity\"}, {\"NAME\": \"h_max\", \"DIMENSION\": \"L1\", \"SUPPLY\": \"AUTHOR\", \"LABEL\": \"the largest height, above or below the origin, over which the field is taken as uniform\"}], \"SUMS\": [], \"TERMS\": [{\"TARGET\": \"UP_VELOCITY\", \"SIGN\": \"-\", \"EXPR\": \"MASS*g_n\", \"LABEL\": \"the weight\"}], \"ASSUMPTIONS\": [{\"NAME\": \"gravity_uniform\", \"PROPOSITION\": \"the gravitational field is uniform over the region abs({HEIGHT}) < h_max\", \"REFS\": [\"HEIGHT\", \"h_max\"]}, {\"NAME\": \"gravity_standard\", \"PROPOSITION\": \"the local gravitational acceleration equals the conventional standard value g_n\", \"REFS\": [\"g_n\"]}, {\"NAME\": \"frame_inertial\", \"PROPOSITION\": \"the frame in which {HEIGHT} is measured is treated as inertial\", \"REFS\": [\"HEIGHT\"]}], \"BOUNDARIES\": [{\"NAME\": \"gravity_region\", \"PREDICATE\": \"abs({HEIGHT}) < h_max\", \"CONDITION\": \"abs(HEIGHT) < h_max\"}], \"NOT_CHOSEN\": \"No gravity: no weight acts on any DOF.\", \"NOT_INCLUDED\": [\"No variation of gravity with height or latitude beyond what g_n contains.\", \"No Earth rotation (Coriolis or centrifugal force) beyond what g_n contains.\", \"No gravity of bodies other than the Earth.\"], \"EXCLUDES\": [], \"INTERACTS_WITH\": [{\"WITH\": \"AIR-*\", \"QUESTION_ID\": \"BUOYANCY\", \"QUESTION\": \"Does the air's buoyancy (upthrust) act on the body in the system you mean?\", \"YES_LINE\": \"Buoyancy acts (your answer): no module adds it; it acts in this kernel only where one of your own laws states it.\", \"NO_LINE\": \"No buoyancy: the air's upthrust on the body is not included.\"}], \"TEST_BINDINGS\": [{\"NAME\": \"PROJECTILE_2D\", \"TPK\": {\"DOF\": [{\"NAME\": \"t\", \"DIMENSION\": \"T1\"}, {\"NAME\": \"x\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"z\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"v_x\", \"DIMENSION\": \"L1 T-1\"}, {\"NAME\": \"v_z\", \"DIMENSION\": \"L1 T-1\"}], \"CONSTANT\": [{\"NAME\": \"m\", \"DIMENSION\": \"M1\"}], \"LAW\": [{\"NAME\": \"KIN_X\", \"STATEMENT\": \"dx/dt = v_x\", \"REFS\": [\"t\", \"v_x\", \"x\"], \"ROLE\": \"EOM(x)\", \"EQUATION\": \"D(x,t)=v_x\"}, {\"NAME\": \"KIN_Z\", \"STATEMENT\": \"dz/dt = v_z\", \"REFS\": [\"t\", \"v_z\", \"z\"], \"ROLE\": \"EOM(z)\", \"EQUATION\": \"D(z,t)=v_z\"}, {\"NAME\": \"EOM_X\", \"STATEMENT\": \"m dv_x/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_x\"], \"ROLE\": \"EOM(v_x)\", \"EQUATION\": \"m*D(v_x,t)=0\"}, {\"NAME\": \"EOM_Z\", \"STATEMENT\": \"m dv_z/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_z\"], \"ROLE\": \"EOM(v_z)\", \"EQUATION\": \"m*D(v_z,t)=0\"}], \"ASSUMPTION\": [{\"NAME\": \"point_mass\", \"PROPOSITION\": \"the body is treated as a point mass\", \"REFS\": [\"m\"]}]}, \"BIND\": {\"HEIGHT\": [\"z\"], \"MASS\": [\"m\"], \"UP_VELOCITY\": [\"v_z\"]}, \"VALUES\": {\"h_max\": {\"VALUE\": \"100\", \"UNIT\": \"m\"}}, \"ANSWERS\": {}}, {\"NAME\": \"TABLE\", \"TPK\": {\"DOF\": [{\"NAME\": \"t\", \"DIMENSION\": \"T1\"}, {\"NAME\": \"x\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"z\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"v_x\", \"DIMENSION\": \"L1 T-1\"}, {\"NAME\": \"v_z\", \"DIMENSION\": \"L1 T-1\"}], \"CONSTANT\": [{\"NAME\": \"m\", \"DIMENSION\": \"M1\"}], \"LAW\": [{\"NAME\": \"KIN_X\", \"STATEMENT\": \"dx/dt = v_x\", \"REFS\": [\"t\", \"v_x\", \"x\"], \"ROLE\": \"EOM(x)\", \"EQUATION\": \"D(x,t)=v_x\"}, {\"NAME\": \"KIN_Z\", \"STATEMENT\": \"dz/dt = v_z\", \"REFS\": [\"t\", \"v_z\", \"z\"], \"ROLE\": \"CONSTRAINT\", \"EQUATION\": \"D(z,t)=v_z\"}, {\"NAME\": \"EOM_X\", \"STATEMENT\": \"m dv_x/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_x\"], \"ROLE\": \"EOM(v_x)\", \"EQUATION\": \"m*D(v_x,t)=0\"}], \"CONSTRAINT\": [{\"NAME\": \"C_Z\", \"TARGET\": \"z\", \"ACTION\": \"FIX\", \"VALUE\": \"0\", \"UNIT\": \"m\", \"STATEMENT\": \"the puck stays on the table top, z = 0\"}, {\"NAME\": \"C_VZ\", \"TARGET\": \"v_z\", \"ACTION\": \"FIX\", \"VALUE\": \"0\", \"UNIT\": \"m s-1\", \"STATEMENT\": \"the puck has no vertical velocity\"}]}, \"BIND\": {\"HEIGHT\": [\"z\"], \"MASS\": [\"m\"], \"UP_VELOCITY\": [\"v_z\"]}, \"VALUES\": {\"h_max\": {\"VALUE\": \"1\", \"UNIT\": \"m\"}}, \"ANSWERS\": {\"FIXED:v_z\": \"YES\"}}]}",
"{\"ID\": \"MATH\", \"VERSION\": \"1.0.0\", \"TITLE\": \"The mathematical constant pi, as the CONSTANT pi_c\", \"SOURCE\": \"pi to 16 significant digits, 3.141592653589793, the nearest IEEE 754 binary64 value\", \"PREREQUISITES\": [], \"PARAMETERS\": [{\"NAME\": \"pi_c\", \"DIMENSION\": \"1\", \"SUPPLY\": \"DECLARED\", \"VALUE\": \"3.141592653589793\", \"UNIT\": \"1\", \"OVERRIDABLE\": \"NO\", \"LABEL\": \"pi, to 16 significant digits\"}], \"SUMS\": [], \"TERMS\": [], \"ASSUMPTIONS\": [], \"BOUNDARIES\": [], \"NOT_CHOSEN\": \"No mathematical constant: pi exists only if you declare it.\", \"NOT_INCLUDED\": [\"pi_c is pi rounded to 16 significant digits; no other mathematical constant is declared.\"], \"EXCLUDES\": [], \"INTERACTS_WITH\": [], \"TEST_BINDINGS\": [{\"NAME\": \"PROJECTILE_2D\", \"TPK\": {\"DOF\": [{\"NAME\": \"t\", \"DIMENSION\": \"T1\"}, {\"NAME\": \"x\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"z\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"v_x\", \"DIMENSION\": \"L1 T-1\"}, {\"NAME\": \"v_z\", \"DIMENSION\": \"L1 T-1\"}], \"CONSTANT\": [{\"NAME\": \"m\", \"DIMENSION\": \"M1\"}], \"LAW\": [{\"NAME\": \"KIN_X\", \"STATEMENT\": \"dx/dt = v_x\", \"REFS\": [\"t\", \"v_x\", \"x\"], \"ROLE\": \"EOM(x)\", \"EQUATION\": \"D(x,t)=v_x\"}, {\"NAME\": \"KIN_Z\", \"STATEMENT\": \"dz/dt = v_z\", \"REFS\": [\"t\", \"v_z\", \"z\"], \"ROLE\": \"EOM(z)\", \"EQUATION\": \"D(z,t)=v_z\"}, {\"NAME\": \"EOM_X\", \"STATEMENT\": \"m dv_x/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_x\"], \"ROLE\": \"EOM(v_x)\", \"EQUATION\": \"m*D(v_x,t)=0\"}, {\"NAME\": \"EOM_Z\", \"STATEMENT\": \"m dv_z/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_z\"], \"ROLE\": \"EOM(v_z)\", \"EQUATION\": \"m*D(v_z,t)=0\"}], \"ASSUMPTION\": [{\"NAME\": \"point_mass\", \"PROPOSITION\": \"the body is treated as a point mass\", \"REFS\": [\"m\"]}]}, \"BIND\": {}, \"VALUES\": {}, \"ANSWERS\": {}}]}",
"{\"ID\": \"TEST-X\", \"VERSION\": \"1.0.0\", \"TITLE\": \"Test interaction X\", \"SOURCE\": \"synthetic fixture\", \"PREREQUISITES\": [], \"PARAMETERS\": [{\"NAME\": \"x_test\", \"DIMENSION\": \"1\", \"SUPPLY\": \"DECLARED\", \"VALUE\": \"1\", \"UNIT\": \"1\", \"OVERRIDABLE\": \"NO\", \"LABEL\": \"a test constant\"}], \"SUMS\": [], \"TERMS\": [], \"ASSUMPTIONS\": [], \"BOUNDARIES\": [], \"NOT_CHOSEN\": \"No test interaction X.\", \"NOT_INCLUDED\": [\"Test X adds only a constant.\"], \"EXCLUDES\": [], \"INTERACTS_WITH\": [], \"TEST_BINDINGS\": [{\"NAME\": \"SOLO\", \"TPK\": {\"DOF\": [{\"NAME\": \"t\", \"DIMENSION\": \"T1\"}, {\"NAME\": \"q\", \"DIMENSION\": \"L1\"}], \"LAW\": [{\"NAME\": \"EQ_Q\", \"STATEMENT\": \"dq/dt = 0\", \"REFS\": [\"q\", \"t\"], \"ROLE\": \"EOM(q)\", \"EQUATION\": \"D(q,t)=0\"}]}, \"BIND\": {}, \"VALUES\": {}, \"ANSWERS\": {}}]}"
]
},
"computed": "digests by existing TPC-PY functions over literal data",
"expected": "[\"OK\",[\"ASK\",[[\"TEST-X\",\"1.0.0\",\"3ecd3a5b540cc15ae65165e5246c4814ef6cb2e7fd293e3578041cbe66efbcb3\"]]],[\"CLAIMS\",[]]]",
"fn": "interview_check",
"hand_checked": false,
"name": "I04 a module offered after the answer is asked about (the delta)"
},
{
"args": {
"answer": [
{
"AT": 4,
"CHOSEN": "NONE",
"COVERED": [
[
"AIR-LINEAR",
"1.0.0",
"5f3fe27b42378bce0830b0d0959f892f4a8e73b12b540ae877e39e6439d08b4d"
],
[
"AIR-QUADRATIC",
"1.0.0",
"6fb53c3a6546151eead2bd6e72e9cf8334f3a2040ad0ee2f5b988ec96d6fc852"
],
[
"GRAV-UNIFORM",
"1.0.0",
"24877ccb5c8ec300d29ed82ce6650592f35cf8899a3d878ccce9c08d4c72c025"
],
[
"MATH",
"1.0.0",
"8f39a356f35527b901fcee012764590f0819c8ffdeccad4bc05195ce3d2e0bcf"
]
]
},
{
"AT": 5,
"CHOSEN": "NONE",
"COVERED": [
[
"TEST-X",
"1.0.0",
"3ecd3a5b540cc15ae65165e5246c4814ef6cb2e7fd293e3578041cbe66efbcb3"
]
]
}
],
"carried": [],
"claims": [],
"lines": [
{
"ACT": "MODULE ADD",
"DATE": "2026-10-01",
"DIGEST": "5f3fe27b42378bce0830b0d0959f892f4a8e73b12b540ae877e39e6439d08b4d",
"ID": "AIR-LINEAR",
"VERSION": "1.0.0"
},
{
"ACT": "MODULE ADD",
"DATE": "2026-10-01",
"DIGEST": "6fb53c3a6546151eead2bd6e72e9cf8334f3a2040ad0ee2f5b988ec96d6fc852",
"ID": "AIR-QUADRATIC",
"VERSION": "1.0.0"
},
{
"ACT": "MODULE ADD",
"DATE": "2026-10-01",
"DIGEST": "24877ccb5c8ec300d29ed82ce6650592f35cf8899a3d878ccce9c08d4c72c025",
"ID": "GRAV-UNIFORM",
"VERSION": "1.0.0"
},
{
"ACT": "MODULE ADD",
"DATE": "2026-10-01",
"DIGEST": "8f39a356f35527b901fcee012764590f0819c8ffdeccad4bc05195ce3d2e0bcf",
"ID": "MATH",
"VERSION": "1.0.0"
},
{
"ACT": "MODULE ADD",
"DATE": "2026-10-02",
"DIGEST": "3ecd3a5b540cc15ae65165e5246c4814ef6cb2e7fd293e3578041cbe66efbcb3",
"ID": "TEST-X",
"VERSION": "1.0.0"
}
],
"modified": [],
"modules": [
"{\"ID\": \"AIR-LINEAR\", \"VERSION\": \"1.0.0\", \"TITLE\": \"Air resistance at sea level, linear in the speed (Stokes drag on a sphere)\", \"SOURCE\": \"ISO 2533:1975, Standard Atmosphere, sea-level values: density 1.225 kg m-3, dynamic viscosity 1.7894e-5 Pa s\", \"PREREQUISITES\": [{\"SLOT\": \"VELOCITY\", \"KIND\": \"DOF\", \"DIMENSION\": \"L1 T-1\", \"MIN\": 1, \"MAX\": 3, \"LABEL\": \"the velocity components of the body, one per axis\"}], \"PARAMETERS\": [{\"NAME\": \"rho_air\", \"DIMENSION\": \"L-3 M1\", \"SUPPLY\": \"DECLARED\", \"VALUE\": \"1.225\", \"UNIT\": \"kg m-3\", \"OVERRIDABLE\": \"NO\", \"LABEL\": \"the density of air at sea level\"}, {\"NAME\": \"mu_air\", \"DIMENSION\": \"L-1 M1 T-1\", \"SUPPLY\": \"DECLARED\", \"VALUE\": \"1.7894e-5\", \"UNIT\": \"Pa s\", \"OVERRIDABLE\": \"NO\", \"LABEL\": \"the dynamic viscosity of air at sea level\"}, {\"NAME\": \"pi_c\", \"DIMENSION\": \"1\", \"SUPPLY\": \"DECLARED\", \"VALUE\": \"3.141592653589793\", \"UNIT\": \"1\", \"OVERRIDABLE\": \"NO\", \"LABEL\": \"pi, to 16 significant digits\"}, {\"NAME\": \"R_s\", \"DIMENSION\": \"L1\", \"SUPPLY\": \"AUTHOR\", \"LABEL\": \"the radius of the sphere\"}], \"SUMS\": [{\"NAME\": \"SPEED2\", \"OVER\": \"VELOCITY\", \"EACH\": \"VELOCITY^2\"}], \"TERMS\": [{\"TARGET\": \"VELOCITY\", \"SIGN\": \"-\", \"EXPR\": \"6*pi_c*mu_air*R_s*VELOCITY\", \"LABEL\": \"the linear (Stokes) drag\"}], \"ASSUMPTIONS\": [{\"NAME\": \"air_still\", \"PROPOSITION\": \"the air is at rest in the frame of the body's velocity\", \"REFS\": [\"VELOCITY\"]}, {\"NAME\": \"air_uniform\", \"PROPOSITION\": \"the air density is uniform over the region of motion\", \"REFS\": [\"rho_air\"]}, {\"NAME\": \"drag_sphere\", \"PROPOSITION\": \"the body is a rigid sphere of radius R_s\", \"REFS\": [\"R_s\"]}], \"BOUNDARIES\": [{\"NAME\": \"drag_linear_regime\", \"PREDICATE\": \"2 rho_air |v| R_s / mu_air < 1: the regime of the linear law\", \"CONDITION\": \"mu_air != 0 and SPEED2 >= 0 and 2*rho_air*sqrt(SPEED2)*R_s/mu_air < 1\"}], \"NOT_CHOSEN\": \"No linear (Stokes) air resistance.\", \"NOT_INCLUDED\": [\"No wind: the air is at rest.\", \"No change of air density or viscosity with altitude or temperature.\", \"No drag outside the regime of the linear law.\"], \"EXCLUDES\": [], \"INTERACTS_WITH\": [], \"TEST_BINDINGS\": [{\"NAME\": \"PROJECTILE_2D\", \"TPK\": {\"DOF\": [{\"NAME\": \"t\", \"DIMENSION\": \"T1\"}, {\"NAME\": \"x\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"z\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"v_x\", \"DIMENSION\": \"L1 T-1\"}, {\"NAME\": \"v_z\", \"DIMENSION\": \"L1 T-1\"}], \"CONSTANT\": [{\"NAME\": \"m\", \"DIMENSION\": \"M1\"}], \"LAW\": [{\"NAME\": \"KIN_X\", \"STATEMENT\": \"dx/dt = v_x\", \"REFS\": [\"t\", \"v_x\", \"x\"], \"ROLE\": \"EOM(x)\", \"EQUATION\": \"D(x,t)=v_x\"}, {\"NAME\": \"KIN_Z\", \"STATEMENT\": \"dz/dt = v_z\", \"REFS\": [\"t\", \"v_z\", \"z\"], \"ROLE\": \"EOM(z)\", \"EQUATION\": \"D(z,t)=v_z\"}, {\"NAME\": \"EOM_X\", \"STATEMENT\": \"m dv_x/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_x\"], \"ROLE\": \"EOM(v_x)\", \"EQUATION\": \"m*D(v_x,t)=0\"}, {\"NAME\": \"EOM_Z\", \"STATEMENT\": \"m dv_z/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_z\"], \"ROLE\": \"EOM(v_z)\", \"EQUATION\": \"m*D(v_z,t)=0\"}], \"ASSUMPTION\": [{\"NAME\": \"point_mass\", \"PROPOSITION\": \"the body is treated as a point mass\", \"REFS\": [\"m\"]}]}, \"BIND\": {\"VELOCITY\": [\"v_x\", \"v_z\"]}, \"VALUES\": {\"R_s\": {}}, \"ANSWERS\": {}}]}",
"{\"ID\": \"AIR-QUADRATIC\", \"VERSION\": \"1.0.0\", \"TITLE\": \"Air resistance at sea level, quadratic in the speed\", \"SOURCE\": \"ISO 2533:1975, Standard Atmosphere, sea-level values: density 1.225 kg m-3, dynamic viscosity 1.7894e-5 Pa s\", \"PREREQUISITES\": [{\"SLOT\": \"VELOCITY\", \"KIND\": \"DOF\", \"DIMENSION\": \"L1 T-1\", \"MIN\": 1, \"MAX\": 3, \"LABEL\": \"the velocity components of the body, one per axis\"}], \"PARAMETERS\": [{\"NAME\": \"rho_air\", \"DIMENSION\": \"L-3 M1\", \"SUPPLY\": \"DECLARED\", \"VALUE\": \"1.225\", \"UNIT\": \"kg m-3\", \"OVERRIDABLE\": \"NO\", \"LABEL\": \"the density of air at sea level\"}, {\"NAME\": \"mu_air\", \"DIMENSION\": \"L-1 M1 T-1\", \"SUPPLY\": \"DECLARED\", \"VALUE\": \"1.7894e-5\", \"UNIT\": \"Pa s\", \"OVERRIDABLE\": \"NO\", \"LABEL\": \"the dynamic viscosity of air at sea level\"}, {\"NAME\": \"C_d\", \"DIMENSION\": \"1\", \"SUPPLY\": \"AUTHOR\", \"LABEL\": \"the drag coefficient of the body\"}, {\"NAME\": \"A_ref\", \"DIMENSION\": \"L2\", \"SUPPLY\": \"AUTHOR\", \"LABEL\": \"the reference area of the drag coefficient\"}, {\"NAME\": \"L_ref\", \"DIMENSION\": \"L1\", \"SUPPLY\": \"AUTHOR\", \"LABEL\": \"the reference length of the Reynolds number\"}], \"SUMS\": [{\"NAME\": \"SPEED2\", \"OVER\": \"VELOCITY\", \"EACH\": \"VELOCITY^2\"}], \"TERMS\": [{\"TARGET\": \"VELOCITY\", \"SIGN\": \"-\", \"EXPR\": \"0.5*rho_air*C_d*A_ref*sqrt(SPEED2)*VELOCITY\", \"LABEL\": \"the quadratic drag\"}], \"ASSUMPTIONS\": [{\"NAME\": \"air_still\", \"PROPOSITION\": \"the air is at rest in the frame of the body's velocity\", \"REFS\": [\"VELOCITY\"]}, {\"NAME\": \"air_uniform\", \"PROPOSITION\": \"the air density is uniform over the region of motion\", \"REFS\": [\"rho_air\"]}, {\"NAME\": \"drag_cd_constant\", \"PROPOSITION\": \"the drag coefficient C_d is constant over the motion\", \"REFS\": [\"C_d\"]}, {\"NAME\": \"drag_no_lift\", \"PROPOSITION\": \"the body experiences no lift force\", \"REFS\": [\"VELOCITY\"]}, {\"NAME\": \"drag_no_magnus\", \"PROPOSITION\": \"the body experiences no Magnus force\", \"REFS\": [\"VELOCITY\"]}], \"BOUNDARIES\": [{\"NAME\": \"drag_quadratic_regime\", \"PREDICATE\": \"1e3 < rho_air |v| L_ref / mu_air < 2e5: the Reynolds window of the quadratic law\", \"CONDITION\": \"mu_air != 0 and SPEED2 >= 0 and rho_air*sqrt(SPEED2)*L_ref/mu_air > 1000 and rho_air*sqrt(SPEED2)*L_ref/mu_air < 200000\"}], \"NOT_CHOSEN\": \"No quadratic air resistance.\", \"NOT_INCLUDED\": [\"No wind: the air is at rest.\", \"No change of air density or viscosity with altitude or temperature.\", \"No lift, Magnus or added-mass force.\", \"No drag outside the Reynolds window of the quadratic law.\"], \"EXCLUDES\": [\"AIR-LINEAR\"], \"INTERACTS_WITH\": [], \"TEST_BINDINGS\": [{\"NAME\": \"PROJECTILE_2D\", \"TPK\": {\"DOF\": [{\"NAME\": \"t\", \"DIMENSION\": \"T1\"}, {\"NAME\": \"x\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"z\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"v_x\", \"DIMENSION\": \"L1 T-1\"}, {\"NAME\": \"v_z\", \"DIMENSION\": \"L1 T-1\"}], \"CONSTANT\": [{\"NAME\": \"m\", \"DIMENSION\": \"M1\"}], \"LAW\": [{\"NAME\": \"KIN_X\", \"STATEMENT\": \"dx/dt = v_x\", \"REFS\": [\"t\", \"v_x\", \"x\"], \"ROLE\": \"EOM(x)\", \"EQUATION\": \"D(x,t)=v_x\"}, {\"NAME\": \"KIN_Z\", \"STATEMENT\": \"dz/dt = v_z\", \"REFS\": [\"t\", \"v_z\", \"z\"], \"ROLE\": \"EOM(z)\", \"EQUATION\": \"D(z,t)=v_z\"}, {\"NAME\": \"EOM_X\", \"STATEMENT\": \"m dv_x/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_x\"], \"ROLE\": \"EOM(v_x)\", \"EQUATION\": \"m*D(v_x,t)=0\"}, {\"NAME\": \"EOM_Z\", \"STATEMENT\": \"m dv_z/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_z\"], \"ROLE\": \"EOM(v_z)\", \"EQUATION\": \"m*D(v_z,t)=0\"}], \"ASSUMPTION\": [{\"NAME\": \"point_mass\", \"PROPOSITION\": \"the body is treated as a point mass\", \"REFS\": [\"m\"]}]}, \"BIND\": {\"VELOCITY\": [\"v_x\", \"v_z\"]}, \"VALUES\": {\"A_ref\": {}, \"C_d\": {}, \"L_ref\": {}}, \"ANSWERS\": {}}]}",
"{\"ID\": \"GRAV-UNIFORM\", \"VERSION\": \"1.0.0\", \"TITLE\": \"Uniform gravity at the standard value g_n\", \"SOURCE\": \"g_n = 9.80665 m s-2, exact by definition: 3rd CGPM (1901), declaration on the unit of mass and on the definition of weight\", \"PREREQUISITES\": [{\"SLOT\": \"MASS\", \"KIND\": \"CONSTANT\", \"DIMENSION\": \"M1\", \"MIN\": 1, \"MAX\": 1, \"LABEL\": \"the mass of the body\"}, {\"SLOT\": \"UP_VELOCITY\", \"KIND\": \"DOF\", \"DIMENSION\": \"L1 T-1\", \"MIN\": 1, \"MAX\": 1, \"LABEL\": \"the velocity component pointing up; its equation of motion receives the weight\"}, {\"SLOT\": \"HEIGHT\", \"KIND\": \"DOF\", \"DIMENSION\": \"L1\", \"MIN\": 1, \"MAX\": 1, \"LABEL\": \"the position along the same upward axis\"}], \"PARAMETERS\": [{\"NAME\": \"g_n\", \"DIMENSION\": \"L1 T-2\", \"SUPPLY\": \"DECLARED\", \"VALUE\": \"9.80665\", \"UNIT\": \"m s-2\", \"OVERRIDABLE\": \"NO\", \"LABEL\": \"the standard acceleration of gravity\"}, {\"NAME\": \"h_max\", \"DIMENSION\": \"L1\", \"SUPPLY\": \"AUTHOR\", \"LABEL\": \"the largest height, above or below the origin, over which the field is taken as uniform\"}], \"SUMS\": [], \"TERMS\": [{\"TARGET\": \"UP_VELOCITY\", \"SIGN\": \"-\", \"EXPR\": \"MASS*g_n\", \"LABEL\": \"the weight\"}], \"ASSUMPTIONS\": [{\"NAME\": \"gravity_uniform\", \"PROPOSITION\": \"the gravitational field is uniform over the region abs({HEIGHT}) < h_max\", \"REFS\": [\"HEIGHT\", \"h_max\"]}, {\"NAME\": \"gravity_standard\", \"PROPOSITION\": \"the local gravitational acceleration equals the conventional standard value g_n\", \"REFS\": [\"g_n\"]}, {\"NAME\": \"frame_inertial\", \"PROPOSITION\": \"the frame in which {HEIGHT} is measured is treated as inertial\", \"REFS\": [\"HEIGHT\"]}], \"BOUNDARIES\": [{\"NAME\": \"gravity_region\", \"PREDICATE\": \"abs({HEIGHT}) < h_max\", \"CONDITION\": \"abs(HEIGHT) < h_max\"}], \"NOT_CHOSEN\": \"No gravity: no weight acts on any DOF.\", \"NOT_INCLUDED\": [\"No variation of gravity with height or latitude beyond what g_n contains.\", \"No Earth rotation (Coriolis or centrifugal force) beyond what g_n contains.\", \"No gravity of bodies other than the Earth.\"], \"EXCLUDES\": [], \"INTERACTS_WITH\": [{\"WITH\": \"AIR-*\", \"QUESTION_ID\": \"BUOYANCY\", \"QUESTION\": \"Does the air's buoyancy (upthrust) act on the body in the system you mean?\", \"YES_LINE\": \"Buoyancy acts (your answer): no module adds it; it acts in this kernel only where one of your own laws states it.\", \"NO_LINE\": \"No buoyancy: the air's upthrust on the body is not included.\"}], \"TEST_BINDINGS\": [{\"NAME\": \"PROJECTILE_2D\", \"TPK\": {\"DOF\": [{\"NAME\": \"t\", \"DIMENSION\": \"T1\"}, {\"NAME\": \"x\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"z\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"v_x\", \"DIMENSION\": \"L1 T-1\"}, {\"NAME\": \"v_z\", \"DIMENSION\": \"L1 T-1\"}], \"CONSTANT\": [{\"NAME\": \"m\", \"DIMENSION\": \"M1\"}], \"LAW\": [{\"NAME\": \"KIN_X\", \"STATEMENT\": \"dx/dt = v_x\", \"REFS\": [\"t\", \"v_x\", \"x\"], \"ROLE\": \"EOM(x)\", \"EQUATION\": \"D(x,t)=v_x\"}, {\"NAME\": \"KIN_Z\", \"STATEMENT\": \"dz/dt = v_z\", \"REFS\": [\"t\", \"v_z\", \"z\"], \"ROLE\": \"EOM(z)\", \"EQUATION\": \"D(z,t)=v_z\"}, {\"NAME\": \"EOM_X\", \"STATEMENT\": \"m dv_x/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_x\"], \"ROLE\": \"EOM(v_x)\", \"EQUATION\": \"m*D(v_x,t)=0\"}, {\"NAME\": \"EOM_Z\", \"STATEMENT\": \"m dv_z/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_z\"], \"ROLE\": \"EOM(v_z)\", \"EQUATION\": \"m*D(v_z,t)=0\"}], \"ASSUMPTION\": [{\"NAME\": \"point_mass\", \"PROPOSITION\": \"the body is treated as a point mass\", \"REFS\": [\"m\"]}]}, \"BIND\": {\"HEIGHT\": [\"z\"], \"MASS\": [\"m\"], \"UP_VELOCITY\": [\"v_z\"]}, \"VALUES\": {\"h_max\": {\"VALUE\": \"100\", \"UNIT\": \"m\"}}, \"ANSWERS\": {}}, {\"NAME\": \"TABLE\", \"TPK\": {\"DOF\": [{\"NAME\": \"t\", \"DIMENSION\": \"T1\"}, {\"NAME\": \"x\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"z\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"v_x\", \"DIMENSION\": \"L1 T-1\"}, {\"NAME\": \"v_z\", \"DIMENSION\": \"L1 T-1\"}], \"CONSTANT\": [{\"NAME\": \"m\", \"DIMENSION\": \"M1\"}], \"LAW\": [{\"NAME\": \"KIN_X\", \"STATEMENT\": \"dx/dt = v_x\", \"REFS\": [\"t\", \"v_x\", \"x\"], \"ROLE\": \"EOM(x)\", \"EQUATION\": \"D(x,t)=v_x\"}, {\"NAME\": \"KIN_Z\", \"STATEMENT\": \"dz/dt = v_z\", \"REFS\": [\"t\", \"v_z\", \"z\"], \"ROLE\": \"CONSTRAINT\", \"EQUATION\": \"D(z,t)=v_z\"}, {\"NAME\": \"EOM_X\", \"STATEMENT\": \"m dv_x/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_x\"], \"ROLE\": \"EOM(v_x)\", \"EQUATION\": \"m*D(v_x,t)=0\"}], \"CONSTRAINT\": [{\"NAME\": \"C_Z\", \"TARGET\": \"z\", \"ACTION\": \"FIX\", \"VALUE\": \"0\", \"UNIT\": \"m\", \"STATEMENT\": \"the puck stays on the table top, z = 0\"}, {\"NAME\": \"C_VZ\", \"TARGET\": \"v_z\", \"ACTION\": \"FIX\", \"VALUE\": \"0\", \"UNIT\": \"m s-1\", \"STATEMENT\": \"the puck has no vertical velocity\"}]}, \"BIND\": {\"HEIGHT\": [\"z\"], \"MASS\": [\"m\"], \"UP_VELOCITY\": [\"v_z\"]}, \"VALUES\": {\"h_max\": {\"VALUE\": \"1\", \"UNIT\": \"m\"}}, \"ANSWERS\": {\"FIXED:v_z\": \"YES\"}}]}",
"{\"ID\": \"MATH\", \"VERSION\": \"1.0.0\", \"TITLE\": \"The mathematical constant pi, as the CONSTANT pi_c\", \"SOURCE\": \"pi to 16 significant digits, 3.141592653589793, the nearest IEEE 754 binary64 value\", \"PREREQUISITES\": [], \"PARAMETERS\": [{\"NAME\": \"pi_c\", \"DIMENSION\": \"1\", \"SUPPLY\": \"DECLARED\", \"VALUE\": \"3.141592653589793\", \"UNIT\": \"1\", \"OVERRIDABLE\": \"NO\", \"LABEL\": \"pi, to 16 significant digits\"}], \"SUMS\": [], \"TERMS\": [], \"ASSUMPTIONS\": [], \"BOUNDARIES\": [], \"NOT_CHOSEN\": \"No mathematical constant: pi exists only if you declare it.\", \"NOT_INCLUDED\": [\"pi_c is pi rounded to 16 significant digits; no other mathematical constant is declared.\"], \"EXCLUDES\": [], \"INTERACTS_WITH\": [], \"TEST_BINDINGS\": [{\"NAME\": \"PROJECTILE_2D\", \"TPK\": {\"DOF\": [{\"NAME\": \"t\", \"DIMENSION\": \"T1\"}, {\"NAME\": \"x\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"z\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"v_x\", \"DIMENSION\": \"L1 T-1\"}, {\"NAME\": \"v_z\", \"DIMENSION\": \"L1 T-1\"}], \"CONSTANT\": [{\"NAME\": \"m\", \"DIMENSION\": \"M1\"}], \"LAW\": [{\"NAME\": \"KIN_X\", \"STATEMENT\": \"dx/dt = v_x\", \"REFS\": [\"t\", \"v_x\", \"x\"], \"ROLE\": \"EOM(x)\", \"EQUATION\": \"D(x,t)=v_x\"}, {\"NAME\": \"KIN_Z\", \"STATEMENT\": \"dz/dt = v_z\", \"REFS\": [\"t\", \"v_z\", \"z\"], \"ROLE\": \"EOM(z)\", \"EQUATION\": \"D(z,t)=v_z\"}, {\"NAME\": \"EOM_X\", \"STATEMENT\": \"m dv_x/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_x\"], \"ROLE\": \"EOM(v_x)\", \"EQUATION\": \"m*D(v_x,t)=0\"}, {\"NAME\": \"EOM_Z\", \"STATEMENT\": \"m dv_z/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_z\"], \"ROLE\": \"EOM(v_z)\", \"EQUATION\": \"m*D(v_z,t)=0\"}], \"ASSUMPTION\": [{\"NAME\": \"point_mass\", \"PROPOSITION\": \"the body is treated as a point mass\", \"REFS\": [\"m\"]}]}, \"BIND\": {}, \"VALUES\": {}, \"ANSWERS\": {}}]}",
"{\"ID\": \"TEST-X\", \"VERSION\": \"1.0.0\", \"TITLE\": \"Test interaction X\", \"SOURCE\": \"synthetic fixture\", \"PREREQUISITES\": [], \"PARAMETERS\": [{\"NAME\": \"x_test\", \"DIMENSION\": \"1\", \"SUPPLY\": \"DECLARED\", \"VALUE\": \"1\", \"UNIT\": \"1\", \"OVERRIDABLE\": \"NO\", \"LABEL\": \"a test constant\"}], \"SUMS\": [], \"TERMS\": [], \"ASSUMPTIONS\": [], \"BOUNDARIES\": [], \"NOT_CHOSEN\": \"No test interaction X.\", \"NOT_INCLUDED\": [\"Test X adds only a constant.\"], \"EXCLUDES\": [], \"INTERACTS_WITH\": [], \"TEST_BINDINGS\": [{\"NAME\": \"SOLO\", \"TPK\": {\"DOF\": [{\"NAME\": \"t\", \"DIMENSION\": \"T1\"}, {\"NAME\": \"q\", \"DIMENSION\": \"L1\"}], \"LAW\": [{\"NAME\": \"EQ_Q\", \"STATEMENT\": \"dq/dt = 0\", \"REFS\": [\"q\", \"t\"], \"ROLE\": \"EOM(q)\", \"EQUATION\": \"D(q,t)=0\"}]}, \"BIND\": {}, \"VALUES\": {}, \"ANSWERS\": {}}]}"
]
},
"expected": "[\"OK\",[\"ASK\",[]],[\"CLAIMS\",[]]]",
"fn": "interview_check",
"hand_checked": true,
"name": "I05 the delta answered in a second round"
},
{
"args": {
"answer": [
{
"AT": 4,
"CHOSEN": "NONE",
"COVERED": [
[
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[
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]
},
{
"AT": 5,
"CHOSEN": "NONE",
"COVERED": [
[
"AIR-LINEAR",
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"5f3fe27b42378bce0830b0d0959f892f4a8e73b12b540ae877e39e6439d08b4d"
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[
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[
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[
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],
[
"TEST-X",
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"3ecd3a5b540cc15ae65165e5246c4814ef6cb2e7fd293e3578041cbe66efbcb3"
]
]
}
],
"carried": [],
"claims": [],
"lines": [
{
"ACT": "MODULE ADD",
"DATE": "2026-10-01",
"DIGEST": "5f3fe27b42378bce0830b0d0959f892f4a8e73b12b540ae877e39e6439d08b4d",
"ID": "AIR-LINEAR",
"VERSION": "1.0.0"
},
{
"ACT": "MODULE ADD",
"DATE": "2026-10-01",
"DIGEST": "6fb53c3a6546151eead2bd6e72e9cf8334f3a2040ad0ee2f5b988ec96d6fc852",
"ID": "AIR-QUADRATIC",
"VERSION": "1.0.0"
},
{
"ACT": "MODULE ADD",
"DATE": "2026-10-01",
"DIGEST": "24877ccb5c8ec300d29ed82ce6650592f35cf8899a3d878ccce9c08d4c72c025",
"ID": "GRAV-UNIFORM",
"VERSION": "1.0.0"
},
{
"ACT": "MODULE ADD",
"DATE": "2026-10-01",
"DIGEST": "8f39a356f35527b901fcee012764590f0819c8ffdeccad4bc05195ce3d2e0bcf",
"ID": "MATH",
"VERSION": "1.0.0"
},
{
"ACT": "MODULE ADD",
"DATE": "2026-10-02",
"DIGEST": "3ecd3a5b540cc15ae65165e5246c4814ef6cb2e7fd293e3578041cbe66efbcb3",
"ID": "TEST-X",
"VERSION": "1.0.0"
}
],
"modified": [],
"modules": [
"{\"ID\": \"AIR-LINEAR\", \"VERSION\": \"1.0.0\", \"TITLE\": \"Air resistance at sea level, linear in the speed (Stokes drag on a sphere)\", \"SOURCE\": \"ISO 2533:1975, Standard Atmosphere, sea-level values: density 1.225 kg m-3, dynamic viscosity 1.7894e-5 Pa s\", \"PREREQUISITES\": [{\"SLOT\": \"VELOCITY\", \"KIND\": \"DOF\", \"DIMENSION\": \"L1 T-1\", \"MIN\": 1, \"MAX\": 3, \"LABEL\": \"the velocity components of the body, one per axis\"}], \"PARAMETERS\": [{\"NAME\": \"rho_air\", \"DIMENSION\": \"L-3 M1\", \"SUPPLY\": \"DECLARED\", \"VALUE\": \"1.225\", \"UNIT\": \"kg m-3\", \"OVERRIDABLE\": \"NO\", \"LABEL\": \"the density of air at sea level\"}, {\"NAME\": \"mu_air\", \"DIMENSION\": \"L-1 M1 T-1\", \"SUPPLY\": \"DECLARED\", \"VALUE\": \"1.7894e-5\", \"UNIT\": \"Pa s\", \"OVERRIDABLE\": \"NO\", \"LABEL\": \"the dynamic viscosity of air at sea level\"}, {\"NAME\": \"pi_c\", \"DIMENSION\": \"1\", \"SUPPLY\": \"DECLARED\", \"VALUE\": \"3.141592653589793\", \"UNIT\": \"1\", \"OVERRIDABLE\": \"NO\", \"LABEL\": \"pi, to 16 significant digits\"}, {\"NAME\": \"R_s\", \"DIMENSION\": \"L1\", \"SUPPLY\": \"AUTHOR\", \"LABEL\": \"the radius of the sphere\"}], \"SUMS\": [{\"NAME\": \"SPEED2\", \"OVER\": \"VELOCITY\", \"EACH\": \"VELOCITY^2\"}], \"TERMS\": [{\"TARGET\": \"VELOCITY\", \"SIGN\": \"-\", \"EXPR\": \"6*pi_c*mu_air*R_s*VELOCITY\", \"LABEL\": \"the linear (Stokes) drag\"}], \"ASSUMPTIONS\": [{\"NAME\": \"air_still\", \"PROPOSITION\": \"the air is at rest in the frame of the body's velocity\", \"REFS\": [\"VELOCITY\"]}, {\"NAME\": \"air_uniform\", \"PROPOSITION\": \"the air density is uniform over the region of motion\", \"REFS\": [\"rho_air\"]}, {\"NAME\": \"drag_sphere\", \"PROPOSITION\": \"the body is a rigid sphere of radius R_s\", \"REFS\": [\"R_s\"]}], \"BOUNDARIES\": [{\"NAME\": \"drag_linear_regime\", \"PREDICATE\": \"2 rho_air |v| R_s / mu_air < 1: the regime of the linear law\", \"CONDITION\": \"mu_air != 0 and SPEED2 >= 0 and 2*rho_air*sqrt(SPEED2)*R_s/mu_air < 1\"}], \"NOT_CHOSEN\": \"No linear (Stokes) air resistance.\", \"NOT_INCLUDED\": [\"No wind: the air is at rest.\", \"No change of air density or viscosity with altitude or temperature.\", \"No drag outside the regime of the linear law.\"], \"EXCLUDES\": [], \"INTERACTS_WITH\": [], \"TEST_BINDINGS\": [{\"NAME\": \"PROJECTILE_2D\", \"TPK\": {\"DOF\": [{\"NAME\": \"t\", \"DIMENSION\": \"T1\"}, {\"NAME\": \"x\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"z\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"v_x\", \"DIMENSION\": \"L1 T-1\"}, {\"NAME\": \"v_z\", \"DIMENSION\": \"L1 T-1\"}], \"CONSTANT\": [{\"NAME\": \"m\", \"DIMENSION\": \"M1\"}], \"LAW\": [{\"NAME\": \"KIN_X\", \"STATEMENT\": \"dx/dt = v_x\", \"REFS\": [\"t\", \"v_x\", \"x\"], \"ROLE\": \"EOM(x)\", \"EQUATION\": \"D(x,t)=v_x\"}, {\"NAME\": \"KIN_Z\", \"STATEMENT\": \"dz/dt = v_z\", \"REFS\": [\"t\", \"v_z\", \"z\"], \"ROLE\": \"EOM(z)\", \"EQUATION\": \"D(z,t)=v_z\"}, {\"NAME\": \"EOM_X\", \"STATEMENT\": \"m dv_x/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_x\"], \"ROLE\": \"EOM(v_x)\", \"EQUATION\": \"m*D(v_x,t)=0\"}, {\"NAME\": \"EOM_Z\", \"STATEMENT\": \"m dv_z/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_z\"], \"ROLE\": \"EOM(v_z)\", \"EQUATION\": \"m*D(v_z,t)=0\"}], \"ASSUMPTION\": [{\"NAME\": \"point_mass\", \"PROPOSITION\": \"the body is treated as a point mass\", \"REFS\": [\"m\"]}]}, \"BIND\": {\"VELOCITY\": [\"v_x\", \"v_z\"]}, \"VALUES\": {\"R_s\": {}}, \"ANSWERS\": {}}]}",
"{\"ID\": \"AIR-QUADRATIC\", \"VERSION\": \"1.0.0\", \"TITLE\": \"Air resistance at sea level, quadratic in the speed\", \"SOURCE\": \"ISO 2533:1975, Standard Atmosphere, sea-level values: density 1.225 kg m-3, dynamic viscosity 1.7894e-5 Pa s\", \"PREREQUISITES\": [{\"SLOT\": \"VELOCITY\", \"KIND\": \"DOF\", \"DIMENSION\": \"L1 T-1\", \"MIN\": 1, \"MAX\": 3, \"LABEL\": \"the velocity components of the body, one per axis\"}], \"PARAMETERS\": [{\"NAME\": \"rho_air\", \"DIMENSION\": \"L-3 M1\", \"SUPPLY\": \"DECLARED\", \"VALUE\": \"1.225\", \"UNIT\": \"kg m-3\", \"OVERRIDABLE\": \"NO\", \"LABEL\": \"the density of air at sea level\"}, {\"NAME\": \"mu_air\", \"DIMENSION\": \"L-1 M1 T-1\", \"SUPPLY\": \"DECLARED\", \"VALUE\": \"1.7894e-5\", \"UNIT\": \"Pa s\", \"OVERRIDABLE\": \"NO\", \"LABEL\": \"the dynamic viscosity of air at sea level\"}, {\"NAME\": \"C_d\", \"DIMENSION\": \"1\", \"SUPPLY\": \"AUTHOR\", \"LABEL\": \"the drag coefficient of the body\"}, {\"NAME\": \"A_ref\", \"DIMENSION\": \"L2\", \"SUPPLY\": \"AUTHOR\", \"LABEL\": \"the reference area of the drag coefficient\"}, {\"NAME\": \"L_ref\", \"DIMENSION\": \"L1\", \"SUPPLY\": \"AUTHOR\", \"LABEL\": \"the reference length of the Reynolds number\"}], \"SUMS\": [{\"NAME\": \"SPEED2\", \"OVER\": \"VELOCITY\", \"EACH\": \"VELOCITY^2\"}], \"TERMS\": [{\"TARGET\": \"VELOCITY\", \"SIGN\": \"-\", \"EXPR\": \"0.5*rho_air*C_d*A_ref*sqrt(SPEED2)*VELOCITY\", \"LABEL\": \"the quadratic drag\"}], \"ASSUMPTIONS\": [{\"NAME\": \"air_still\", \"PROPOSITION\": \"the air is at rest in the frame of the body's velocity\", \"REFS\": [\"VELOCITY\"]}, {\"NAME\": \"air_uniform\", \"PROPOSITION\": \"the air density is uniform over the region of motion\", \"REFS\": [\"rho_air\"]}, {\"NAME\": \"drag_cd_constant\", \"PROPOSITION\": \"the drag coefficient C_d is constant over the motion\", \"REFS\": [\"C_d\"]}, {\"NAME\": \"drag_no_lift\", \"PROPOSITION\": \"the body experiences no lift force\", \"REFS\": [\"VELOCITY\"]}, {\"NAME\": \"drag_no_magnus\", \"PROPOSITION\": \"the body experiences no Magnus force\", \"REFS\": [\"VELOCITY\"]}], \"BOUNDARIES\": [{\"NAME\": \"drag_quadratic_regime\", \"PREDICATE\": \"1e3 < rho_air |v| L_ref / mu_air < 2e5: the Reynolds window of the quadratic law\", \"CONDITION\": \"mu_air != 0 and SPEED2 >= 0 and rho_air*sqrt(SPEED2)*L_ref/mu_air > 1000 and rho_air*sqrt(SPEED2)*L_ref/mu_air < 200000\"}], \"NOT_CHOSEN\": \"No quadratic air resistance.\", \"NOT_INCLUDED\": [\"No wind: the air is at rest.\", \"No change of air density or viscosity with altitude or temperature.\", \"No lift, Magnus or added-mass force.\", \"No drag outside the Reynolds window of the quadratic law.\"], \"EXCLUDES\": [\"AIR-LINEAR\"], \"INTERACTS_WITH\": [], \"TEST_BINDINGS\": [{\"NAME\": \"PROJECTILE_2D\", \"TPK\": {\"DOF\": [{\"NAME\": \"t\", \"DIMENSION\": \"T1\"}, {\"NAME\": \"x\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"z\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"v_x\", \"DIMENSION\": \"L1 T-1\"}, {\"NAME\": \"v_z\", \"DIMENSION\": \"L1 T-1\"}], \"CONSTANT\": [{\"NAME\": \"m\", \"DIMENSION\": \"M1\"}], \"LAW\": [{\"NAME\": \"KIN_X\", \"STATEMENT\": \"dx/dt = v_x\", \"REFS\": [\"t\", \"v_x\", \"x\"], \"ROLE\": \"EOM(x)\", \"EQUATION\": \"D(x,t)=v_x\"}, {\"NAME\": \"KIN_Z\", \"STATEMENT\": \"dz/dt = v_z\", \"REFS\": [\"t\", \"v_z\", \"z\"], \"ROLE\": \"EOM(z)\", \"EQUATION\": \"D(z,t)=v_z\"}, {\"NAME\": \"EOM_X\", \"STATEMENT\": \"m dv_x/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_x\"], \"ROLE\": \"EOM(v_x)\", \"EQUATION\": \"m*D(v_x,t)=0\"}, {\"NAME\": \"EOM_Z\", \"STATEMENT\": \"m dv_z/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_z\"], \"ROLE\": \"EOM(v_z)\", \"EQUATION\": \"m*D(v_z,t)=0\"}], \"ASSUMPTION\": [{\"NAME\": \"point_mass\", \"PROPOSITION\": \"the body is treated as a point mass\", \"REFS\": [\"m\"]}]}, \"BIND\": {\"VELOCITY\": [\"v_x\", \"v_z\"]}, \"VALUES\": {\"A_ref\": {}, \"C_d\": {}, \"L_ref\": {}}, \"ANSWERS\": {}}]}",
"{\"ID\": \"GRAV-UNIFORM\", \"VERSION\": \"1.0.0\", \"TITLE\": \"Uniform gravity at the standard value g_n\", \"SOURCE\": \"g_n = 9.80665 m s-2, exact by definition: 3rd CGPM (1901), declaration on the unit of mass and on the definition of weight\", \"PREREQUISITES\": [{\"SLOT\": \"MASS\", \"KIND\": \"CONSTANT\", \"DIMENSION\": \"M1\", \"MIN\": 1, \"MAX\": 1, \"LABEL\": \"the mass of the body\"}, {\"SLOT\": \"UP_VELOCITY\", \"KIND\": \"DOF\", \"DIMENSION\": \"L1 T-1\", \"MIN\": 1, \"MAX\": 1, \"LABEL\": \"the velocity component pointing up; its equation of motion receives the weight\"}, {\"SLOT\": \"HEIGHT\", \"KIND\": \"DOF\", \"DIMENSION\": \"L1\", \"MIN\": 1, \"MAX\": 1, \"LABEL\": \"the position along the same upward axis\"}], \"PARAMETERS\": [{\"NAME\": \"g_n\", \"DIMENSION\": \"L1 T-2\", \"SUPPLY\": \"DECLARED\", \"VALUE\": \"9.80665\", \"UNIT\": \"m s-2\", \"OVERRIDABLE\": \"NO\", \"LABEL\": \"the standard acceleration of gravity\"}, {\"NAME\": \"h_max\", \"DIMENSION\": \"L1\", \"SUPPLY\": \"AUTHOR\", \"LABEL\": \"the largest height, above or below the origin, over which the field is taken as uniform\"}], \"SUMS\": [], \"TERMS\": [{\"TARGET\": \"UP_VELOCITY\", \"SIGN\": \"-\", \"EXPR\": \"MASS*g_n\", \"LABEL\": \"the weight\"}], \"ASSUMPTIONS\": [{\"NAME\": \"gravity_uniform\", \"PROPOSITION\": \"the gravitational field is uniform over the region abs({HEIGHT}) < h_max\", \"REFS\": [\"HEIGHT\", \"h_max\"]}, {\"NAME\": \"gravity_standard\", \"PROPOSITION\": \"the local gravitational acceleration equals the conventional standard value g_n\", \"REFS\": [\"g_n\"]}, {\"NAME\": \"frame_inertial\", \"PROPOSITION\": \"the frame in which {HEIGHT} is measured is treated as inertial\", \"REFS\": [\"HEIGHT\"]}], \"BOUNDARIES\": [{\"NAME\": \"gravity_region\", \"PREDICATE\": \"abs({HEIGHT}) < h_max\", \"CONDITION\": \"abs(HEIGHT) < h_max\"}], \"NOT_CHOSEN\": \"No gravity: no weight acts on any DOF.\", \"NOT_INCLUDED\": [\"No variation of gravity with height or latitude beyond what g_n contains.\", \"No Earth rotation (Coriolis or centrifugal force) beyond what g_n contains.\", \"No gravity of bodies other than the Earth.\"], \"EXCLUDES\": [], \"INTERACTS_WITH\": [{\"WITH\": \"AIR-*\", \"QUESTION_ID\": \"BUOYANCY\", \"QUESTION\": \"Does the air's buoyancy (upthrust) act on the body in the system you mean?\", \"YES_LINE\": \"Buoyancy acts (your answer): no module adds it; it acts in this kernel only where one of your own laws states it.\", \"NO_LINE\": \"No buoyancy: the air's upthrust on the body is not included.\"}], \"TEST_BINDINGS\": [{\"NAME\": \"PROJECTILE_2D\", \"TPK\": {\"DOF\": [{\"NAME\": \"t\", \"DIMENSION\": \"T1\"}, {\"NAME\": \"x\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"z\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"v_x\", \"DIMENSION\": \"L1 T-1\"}, {\"NAME\": \"v_z\", \"DIMENSION\": \"L1 T-1\"}], \"CONSTANT\": [{\"NAME\": \"m\", \"DIMENSION\": \"M1\"}], \"LAW\": [{\"NAME\": \"KIN_X\", \"STATEMENT\": \"dx/dt = v_x\", \"REFS\": [\"t\", \"v_x\", \"x\"], \"ROLE\": \"EOM(x)\", \"EQUATION\": \"D(x,t)=v_x\"}, {\"NAME\": \"KIN_Z\", \"STATEMENT\": \"dz/dt = v_z\", \"REFS\": [\"t\", \"v_z\", \"z\"], \"ROLE\": \"EOM(z)\", \"EQUATION\": \"D(z,t)=v_z\"}, {\"NAME\": \"EOM_X\", \"STATEMENT\": \"m dv_x/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_x\"], \"ROLE\": \"EOM(v_x)\", \"EQUATION\": \"m*D(v_x,t)=0\"}, {\"NAME\": \"EOM_Z\", \"STATEMENT\": \"m dv_z/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_z\"], \"ROLE\": \"EOM(v_z)\", \"EQUATION\": \"m*D(v_z,t)=0\"}], \"ASSUMPTION\": [{\"NAME\": \"point_mass\", \"PROPOSITION\": \"the body is treated as a point mass\", \"REFS\": [\"m\"]}]}, \"BIND\": {\"HEIGHT\": [\"z\"], \"MASS\": [\"m\"], \"UP_VELOCITY\": [\"v_z\"]}, \"VALUES\": {\"h_max\": {\"VALUE\": \"100\", \"UNIT\": \"m\"}}, \"ANSWERS\": {}}, {\"NAME\": \"TABLE\", \"TPK\": {\"DOF\": [{\"NAME\": \"t\", \"DIMENSION\": \"T1\"}, {\"NAME\": \"x\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"z\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"v_x\", \"DIMENSION\": \"L1 T-1\"}, {\"NAME\": \"v_z\", \"DIMENSION\": \"L1 T-1\"}], \"CONSTANT\": [{\"NAME\": \"m\", \"DIMENSION\": \"M1\"}], \"LAW\": [{\"NAME\": \"KIN_X\", \"STATEMENT\": \"dx/dt = v_x\", \"REFS\": [\"t\", \"v_x\", \"x\"], \"ROLE\": \"EOM(x)\", \"EQUATION\": \"D(x,t)=v_x\"}, {\"NAME\": \"KIN_Z\", \"STATEMENT\": \"dz/dt = v_z\", \"REFS\": [\"t\", \"v_z\", \"z\"], \"ROLE\": \"CONSTRAINT\", \"EQUATION\": \"D(z,t)=v_z\"}, {\"NAME\": \"EOM_X\", \"STATEMENT\": \"m dv_x/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_x\"], \"ROLE\": \"EOM(v_x)\", \"EQUATION\": \"m*D(v_x,t)=0\"}], \"CONSTRAINT\": [{\"NAME\": \"C_Z\", \"TARGET\": \"z\", \"ACTION\": \"FIX\", \"VALUE\": \"0\", \"UNIT\": \"m\", \"STATEMENT\": \"the puck stays on the table top, z = 0\"}, {\"NAME\": \"C_VZ\", \"TARGET\": \"v_z\", \"ACTION\": \"FIX\", \"VALUE\": \"0\", \"UNIT\": \"m s-1\", \"STATEMENT\": \"the puck has no vertical velocity\"}]}, \"BIND\": {\"HEIGHT\": [\"z\"], \"MASS\": [\"m\"], \"UP_VELOCITY\": [\"v_z\"]}, \"VALUES\": {\"h_max\": {\"VALUE\": \"1\", \"UNIT\": \"m\"}}, \"ANSWERS\": {\"FIXED:v_z\": \"YES\"}}]}",
"{\"ID\": \"MATH\", \"VERSION\": \"1.0.0\", \"TITLE\": \"The mathematical constant pi, as the CONSTANT pi_c\", \"SOURCE\": \"pi to 16 significant digits, 3.141592653589793, the nearest IEEE 754 binary64 value\", \"PREREQUISITES\": [], \"PARAMETERS\": [{\"NAME\": \"pi_c\", \"DIMENSION\": \"1\", \"SUPPLY\": \"DECLARED\", \"VALUE\": \"3.141592653589793\", \"UNIT\": \"1\", \"OVERRIDABLE\": \"NO\", \"LABEL\": \"pi, to 16 significant digits\"}], \"SUMS\": [], \"TERMS\": [], \"ASSUMPTIONS\": [], \"BOUNDARIES\": [], \"NOT_CHOSEN\": \"No mathematical constant: pi exists only if you declare it.\", \"NOT_INCLUDED\": [\"pi_c is pi rounded to 16 significant digits; no other mathematical constant is declared.\"], \"EXCLUDES\": [], \"INTERACTS_WITH\": [], \"TEST_BINDINGS\": [{\"NAME\": \"PROJECTILE_2D\", \"TPK\": {\"DOF\": [{\"NAME\": \"t\", \"DIMENSION\": \"T1\"}, {\"NAME\": \"x\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"z\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"v_x\", \"DIMENSION\": \"L1 T-1\"}, {\"NAME\": \"v_z\", \"DIMENSION\": \"L1 T-1\"}], \"CONSTANT\": [{\"NAME\": \"m\", \"DIMENSION\": \"M1\"}], \"LAW\": [{\"NAME\": \"KIN_X\", \"STATEMENT\": \"dx/dt = v_x\", \"REFS\": [\"t\", \"v_x\", \"x\"], \"ROLE\": \"EOM(x)\", \"EQUATION\": \"D(x,t)=v_x\"}, {\"NAME\": \"KIN_Z\", \"STATEMENT\": \"dz/dt = v_z\", \"REFS\": [\"t\", \"v_z\", \"z\"], \"ROLE\": \"EOM(z)\", \"EQUATION\": \"D(z,t)=v_z\"}, {\"NAME\": \"EOM_X\", \"STATEMENT\": \"m dv_x/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_x\"], \"ROLE\": \"EOM(v_x)\", \"EQUATION\": \"m*D(v_x,t)=0\"}, {\"NAME\": \"EOM_Z\", \"STATEMENT\": \"m dv_z/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_z\"], \"ROLE\": \"EOM(v_z)\", \"EQUATION\": \"m*D(v_z,t)=0\"}], \"ASSUMPTION\": [{\"NAME\": \"point_mass\", \"PROPOSITION\": \"the body is treated as a point mass\", \"REFS\": [\"m\"]}]}, \"BIND\": {}, \"VALUES\": {}, \"ANSWERS\": {}}]}",
"{\"ID\": \"TEST-X\", \"VERSION\": \"1.0.0\", \"TITLE\": \"Test interaction X\", \"SOURCE\": \"synthetic fixture\", \"PREREQUISITES\": [], \"PARAMETERS\": [{\"NAME\": \"x_test\", \"DIMENSION\": \"1\", \"SUPPLY\": \"DECLARED\", \"VALUE\": \"1\", \"UNIT\": \"1\", \"OVERRIDABLE\": \"NO\", \"LABEL\": \"a test constant\"}], \"SUMS\": [], \"TERMS\": [], \"ASSUMPTIONS\": [], \"BOUNDARIES\": [], \"NOT_CHOSEN\": \"No test interaction X.\", \"NOT_INCLUDED\": [\"Test X adds only a constant.\"], \"EXCLUDES\": [], \"INTERACTS_WITH\": [], \"TEST_BINDINGS\": [{\"NAME\": \"SOLO\", \"TPK\": {\"DOF\": [{\"NAME\": \"t\", \"DIMENSION\": \"T1\"}, {\"NAME\": \"q\", \"DIMENSION\": \"L1\"}], \"LAW\": [{\"NAME\": \"EQ_Q\", \"STATEMENT\": \"dq/dt = 0\", \"REFS\": [\"q\", \"t\"], \"ROLE\": \"EOM(q)\", \"EQUATION\": \"D(q,t)=0\"}]}, \"BIND\": {}, \"VALUES\": {}, \"ANSWERS\": {}}]}"
]
},
"expected": "[\"REFUSED\",\"ANSWER ROUND 2: COVERED is not the offer the round was given over\"]",
"fn": "interview_check",
"hand_checked": true,
"name": "I06 a second round covering the whole offer"
},
{
"args": {
"answer": [
{
"AT": 4,
"CHOSEN": "NONE",
"COVERED": [
[
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[
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"6fb53c3a6546151eead2bd6e72e9cf8334f3a2040ad0ee2f5b988ec96d6fc852"
],
[
"GRAV-UNIFORM",
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"24877ccb5c8ec300d29ed82ce6650592f35cf8899a3d878ccce9c08d4c72c025"
],
[
"MATH",
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]
]
},
{
"AT": 4,
"CHOSEN": "NONE",
"COVERED": [
[
"TEST-X",
"1.0.0",
"3ecd3a5b540cc15ae65165e5246c4814ef6cb2e7fd293e3578041cbe66efbcb3"
]
]
}
],
"carried": [],
"claims": [],
"lines": [
{
"ACT": "MODULE ADD",
"DATE": "2026-10-01",
"DIGEST": "5f3fe27b42378bce0830b0d0959f892f4a8e73b12b540ae877e39e6439d08b4d",
"ID": "AIR-LINEAR",
"VERSION": "1.0.0"
},
{
"ACT": "MODULE ADD",
"DATE": "2026-10-01",
"DIGEST": "6fb53c3a6546151eead2bd6e72e9cf8334f3a2040ad0ee2f5b988ec96d6fc852",
"ID": "AIR-QUADRATIC",
"VERSION": "1.0.0"
},
{
"ACT": "MODULE ADD",
"DATE": "2026-10-01",
"DIGEST": "24877ccb5c8ec300d29ed82ce6650592f35cf8899a3d878ccce9c08d4c72c025",
"ID": "GRAV-UNIFORM",
"VERSION": "1.0.0"
},
{
"ACT": "MODULE ADD",
"DATE": "2026-10-01",
"DIGEST": "8f39a356f35527b901fcee012764590f0819c8ffdeccad4bc05195ce3d2e0bcf",
"ID": "MATH",
"VERSION": "1.0.0"
},
{
"ACT": "MODULE ADD",
"DATE": "2026-10-02",
"DIGEST": "3ecd3a5b540cc15ae65165e5246c4814ef6cb2e7fd293e3578041cbe66efbcb3",
"ID": "TEST-X",
"VERSION": "1.0.0"
}
],
"modified": [],
"modules": [
"{\"ID\": \"AIR-LINEAR\", \"VERSION\": \"1.0.0\", \"TITLE\": \"Air resistance at sea level, linear in the speed (Stokes drag on a sphere)\", \"SOURCE\": \"ISO 2533:1975, Standard Atmosphere, sea-level values: density 1.225 kg m-3, dynamic viscosity 1.7894e-5 Pa s\", \"PREREQUISITES\": [{\"SLOT\": \"VELOCITY\", \"KIND\": \"DOF\", \"DIMENSION\": \"L1 T-1\", \"MIN\": 1, \"MAX\": 3, \"LABEL\": \"the velocity components of the body, one per axis\"}], \"PARAMETERS\": [{\"NAME\": \"rho_air\", \"DIMENSION\": \"L-3 M1\", \"SUPPLY\": \"DECLARED\", \"VALUE\": \"1.225\", \"UNIT\": \"kg m-3\", \"OVERRIDABLE\": \"NO\", \"LABEL\": \"the density of air at sea level\"}, {\"NAME\": \"mu_air\", \"DIMENSION\": \"L-1 M1 T-1\", \"SUPPLY\": \"DECLARED\", \"VALUE\": \"1.7894e-5\", \"UNIT\": \"Pa s\", \"OVERRIDABLE\": \"NO\", \"LABEL\": \"the dynamic viscosity of air at sea level\"}, {\"NAME\": \"pi_c\", \"DIMENSION\": \"1\", \"SUPPLY\": \"DECLARED\", \"VALUE\": \"3.141592653589793\", \"UNIT\": \"1\", \"OVERRIDABLE\": \"NO\", \"LABEL\": \"pi, to 16 significant digits\"}, {\"NAME\": \"R_s\", \"DIMENSION\": \"L1\", \"SUPPLY\": \"AUTHOR\", \"LABEL\": \"the radius of the sphere\"}], \"SUMS\": [{\"NAME\": \"SPEED2\", \"OVER\": \"VELOCITY\", \"EACH\": \"VELOCITY^2\"}], \"TERMS\": [{\"TARGET\": \"VELOCITY\", \"SIGN\": \"-\", \"EXPR\": \"6*pi_c*mu_air*R_s*VELOCITY\", \"LABEL\": \"the linear (Stokes) drag\"}], \"ASSUMPTIONS\": [{\"NAME\": \"air_still\", \"PROPOSITION\": \"the air is at rest in the frame of the body's velocity\", \"REFS\": [\"VELOCITY\"]}, {\"NAME\": \"air_uniform\", \"PROPOSITION\": \"the air density is uniform over the region of motion\", \"REFS\": [\"rho_air\"]}, {\"NAME\": \"drag_sphere\", \"PROPOSITION\": \"the body is a rigid sphere of radius R_s\", \"REFS\": [\"R_s\"]}], \"BOUNDARIES\": [{\"NAME\": \"drag_linear_regime\", \"PREDICATE\": \"2 rho_air |v| R_s / mu_air < 1: the regime of the linear law\", \"CONDITION\": \"mu_air != 0 and SPEED2 >= 0 and 2*rho_air*sqrt(SPEED2)*R_s/mu_air < 1\"}], \"NOT_CHOSEN\": \"No linear (Stokes) air resistance.\", \"NOT_INCLUDED\": [\"No wind: the air is at rest.\", \"No change of air density or viscosity with altitude or temperature.\", \"No drag outside the regime of the linear law.\"], \"EXCLUDES\": [], \"INTERACTS_WITH\": [], \"TEST_BINDINGS\": [{\"NAME\": \"PROJECTILE_2D\", \"TPK\": {\"DOF\": [{\"NAME\": \"t\", \"DIMENSION\": \"T1\"}, {\"NAME\": \"x\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"z\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"v_x\", \"DIMENSION\": \"L1 T-1\"}, {\"NAME\": \"v_z\", \"DIMENSION\": \"L1 T-1\"}], \"CONSTANT\": [{\"NAME\": \"m\", \"DIMENSION\": \"M1\"}], \"LAW\": [{\"NAME\": \"KIN_X\", \"STATEMENT\": \"dx/dt = v_x\", \"REFS\": [\"t\", \"v_x\", \"x\"], \"ROLE\": \"EOM(x)\", \"EQUATION\": \"D(x,t)=v_x\"}, {\"NAME\": \"KIN_Z\", \"STATEMENT\": \"dz/dt = v_z\", \"REFS\": [\"t\", \"v_z\", \"z\"], \"ROLE\": \"EOM(z)\", \"EQUATION\": \"D(z,t)=v_z\"}, {\"NAME\": \"EOM_X\", \"STATEMENT\": \"m dv_x/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_x\"], \"ROLE\": \"EOM(v_x)\", \"EQUATION\": \"m*D(v_x,t)=0\"}, {\"NAME\": \"EOM_Z\", \"STATEMENT\": \"m dv_z/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_z\"], \"ROLE\": \"EOM(v_z)\", \"EQUATION\": \"m*D(v_z,t)=0\"}], \"ASSUMPTION\": [{\"NAME\": \"point_mass\", \"PROPOSITION\": \"the body is treated as a point mass\", \"REFS\": [\"m\"]}]}, \"BIND\": {\"VELOCITY\": [\"v_x\", \"v_z\"]}, \"VALUES\": {\"R_s\": {}}, \"ANSWERS\": {}}]}",
"{\"ID\": \"AIR-QUADRATIC\", \"VERSION\": \"1.0.0\", \"TITLE\": \"Air resistance at sea level, quadratic in the speed\", \"SOURCE\": \"ISO 2533:1975, Standard Atmosphere, sea-level values: density 1.225 kg m-3, dynamic viscosity 1.7894e-5 Pa s\", \"PREREQUISITES\": [{\"SLOT\": \"VELOCITY\", \"KIND\": \"DOF\", \"DIMENSION\": \"L1 T-1\", \"MIN\": 1, \"MAX\": 3, \"LABEL\": \"the velocity components of the body, one per axis\"}], \"PARAMETERS\": [{\"NAME\": \"rho_air\", \"DIMENSION\": \"L-3 M1\", \"SUPPLY\": \"DECLARED\", \"VALUE\": \"1.225\", \"UNIT\": \"kg m-3\", \"OVERRIDABLE\": \"NO\", \"LABEL\": \"the density of air at sea level\"}, {\"NAME\": \"mu_air\", \"DIMENSION\": \"L-1 M1 T-1\", \"SUPPLY\": \"DECLARED\", \"VALUE\": \"1.7894e-5\", \"UNIT\": \"Pa s\", \"OVERRIDABLE\": \"NO\", \"LABEL\": \"the dynamic viscosity of air at sea level\"}, {\"NAME\": \"C_d\", \"DIMENSION\": \"1\", \"SUPPLY\": \"AUTHOR\", \"LABEL\": \"the drag coefficient of the body\"}, {\"NAME\": \"A_ref\", \"DIMENSION\": \"L2\", \"SUPPLY\": \"AUTHOR\", \"LABEL\": \"the reference area of the drag coefficient\"}, {\"NAME\": \"L_ref\", \"DIMENSION\": \"L1\", \"SUPPLY\": \"AUTHOR\", \"LABEL\": \"the reference length of the Reynolds number\"}], \"SUMS\": [{\"NAME\": \"SPEED2\", \"OVER\": \"VELOCITY\", \"EACH\": \"VELOCITY^2\"}], \"TERMS\": [{\"TARGET\": \"VELOCITY\", \"SIGN\": \"-\", \"EXPR\": \"0.5*rho_air*C_d*A_ref*sqrt(SPEED2)*VELOCITY\", \"LABEL\": \"the quadratic drag\"}], \"ASSUMPTIONS\": [{\"NAME\": \"air_still\", \"PROPOSITION\": \"the air is at rest in the frame of the body's velocity\", \"REFS\": [\"VELOCITY\"]}, {\"NAME\": \"air_uniform\", \"PROPOSITION\": \"the air density is uniform over the region of motion\", \"REFS\": [\"rho_air\"]}, {\"NAME\": \"drag_cd_constant\", \"PROPOSITION\": \"the drag coefficient C_d is constant over the motion\", \"REFS\": [\"C_d\"]}, {\"NAME\": \"drag_no_lift\", \"PROPOSITION\": \"the body experiences no lift force\", \"REFS\": [\"VELOCITY\"]}, {\"NAME\": \"drag_no_magnus\", \"PROPOSITION\": \"the body experiences no Magnus force\", \"REFS\": [\"VELOCITY\"]}], \"BOUNDARIES\": [{\"NAME\": \"drag_quadratic_regime\", \"PREDICATE\": \"1e3 < rho_air |v| L_ref / mu_air < 2e5: the Reynolds window of the quadratic law\", \"CONDITION\": \"mu_air != 0 and SPEED2 >= 0 and rho_air*sqrt(SPEED2)*L_ref/mu_air > 1000 and rho_air*sqrt(SPEED2)*L_ref/mu_air < 200000\"}], \"NOT_CHOSEN\": \"No quadratic air resistance.\", \"NOT_INCLUDED\": [\"No wind: the air is at rest.\", \"No change of air density or viscosity with altitude or temperature.\", \"No lift, Magnus or added-mass force.\", \"No drag outside the Reynolds window of the quadratic law.\"], \"EXCLUDES\": [\"AIR-LINEAR\"], \"INTERACTS_WITH\": [], \"TEST_BINDINGS\": [{\"NAME\": \"PROJECTILE_2D\", \"TPK\": {\"DOF\": [{\"NAME\": \"t\", \"DIMENSION\": \"T1\"}, {\"NAME\": \"x\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"z\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"v_x\", \"DIMENSION\": \"L1 T-1\"}, {\"NAME\": \"v_z\", \"DIMENSION\": \"L1 T-1\"}], \"CONSTANT\": [{\"NAME\": \"m\", \"DIMENSION\": \"M1\"}], \"LAW\": [{\"NAME\": \"KIN_X\", \"STATEMENT\": \"dx/dt = v_x\", \"REFS\": [\"t\", \"v_x\", \"x\"], \"ROLE\": \"EOM(x)\", \"EQUATION\": \"D(x,t)=v_x\"}, {\"NAME\": \"KIN_Z\", \"STATEMENT\": \"dz/dt = v_z\", \"REFS\": [\"t\", \"v_z\", \"z\"], \"ROLE\": \"EOM(z)\", \"EQUATION\": \"D(z,t)=v_z\"}, {\"NAME\": \"EOM_X\", \"STATEMENT\": \"m dv_x/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_x\"], \"ROLE\": \"EOM(v_x)\", \"EQUATION\": \"m*D(v_x,t)=0\"}, {\"NAME\": \"EOM_Z\", \"STATEMENT\": \"m dv_z/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_z\"], \"ROLE\": \"EOM(v_z)\", \"EQUATION\": \"m*D(v_z,t)=0\"}], \"ASSUMPTION\": [{\"NAME\": \"point_mass\", \"PROPOSITION\": \"the body is treated as a point mass\", \"REFS\": [\"m\"]}]}, \"BIND\": {\"VELOCITY\": [\"v_x\", \"v_z\"]}, \"VALUES\": {\"A_ref\": {}, \"C_d\": {}, \"L_ref\": {}}, \"ANSWERS\": {}}]}",
"{\"ID\": \"GRAV-UNIFORM\", \"VERSION\": \"1.0.0\", \"TITLE\": \"Uniform gravity at the standard value g_n\", \"SOURCE\": \"g_n = 9.80665 m s-2, exact by definition: 3rd CGPM (1901), declaration on the unit of mass and on the definition of weight\", \"PREREQUISITES\": [{\"SLOT\": \"MASS\", \"KIND\": \"CONSTANT\", \"DIMENSION\": \"M1\", \"MIN\": 1, \"MAX\": 1, \"LABEL\": \"the mass of the body\"}, {\"SLOT\": \"UP_VELOCITY\", \"KIND\": \"DOF\", \"DIMENSION\": \"L1 T-1\", \"MIN\": 1, \"MAX\": 1, \"LABEL\": \"the velocity component pointing up; its equation of motion receives the weight\"}, {\"SLOT\": \"HEIGHT\", \"KIND\": \"DOF\", \"DIMENSION\": \"L1\", \"MIN\": 1, \"MAX\": 1, \"LABEL\": \"the position along the same upward axis\"}], \"PARAMETERS\": [{\"NAME\": \"g_n\", \"DIMENSION\": \"L1 T-2\", \"SUPPLY\": \"DECLARED\", \"VALUE\": \"9.80665\", \"UNIT\": \"m s-2\", \"OVERRIDABLE\": \"NO\", \"LABEL\": \"the standard acceleration of gravity\"}, {\"NAME\": \"h_max\", \"DIMENSION\": \"L1\", \"SUPPLY\": \"AUTHOR\", \"LABEL\": \"the largest height, above or below the origin, over which the field is taken as uniform\"}], \"SUMS\": [], \"TERMS\": [{\"TARGET\": \"UP_VELOCITY\", \"SIGN\": \"-\", \"EXPR\": \"MASS*g_n\", \"LABEL\": \"the weight\"}], \"ASSUMPTIONS\": [{\"NAME\": \"gravity_uniform\", \"PROPOSITION\": \"the gravitational field is uniform over the region abs({HEIGHT}) < h_max\", \"REFS\": [\"HEIGHT\", \"h_max\"]}, {\"NAME\": \"gravity_standard\", \"PROPOSITION\": \"the local gravitational acceleration equals the conventional standard value g_n\", \"REFS\": [\"g_n\"]}, {\"NAME\": \"frame_inertial\", \"PROPOSITION\": \"the frame in which {HEIGHT} is measured is treated as inertial\", \"REFS\": [\"HEIGHT\"]}], \"BOUNDARIES\": [{\"NAME\": \"gravity_region\", \"PREDICATE\": \"abs({HEIGHT}) < h_max\", \"CONDITION\": \"abs(HEIGHT) < h_max\"}], \"NOT_CHOSEN\": \"No gravity: no weight acts on any DOF.\", \"NOT_INCLUDED\": [\"No variation of gravity with height or latitude beyond what g_n contains.\", \"No Earth rotation (Coriolis or centrifugal force) beyond what g_n contains.\", \"No gravity of bodies other than the Earth.\"], \"EXCLUDES\": [], \"INTERACTS_WITH\": [{\"WITH\": \"AIR-*\", \"QUESTION_ID\": \"BUOYANCY\", \"QUESTION\": \"Does the air's buoyancy (upthrust) act on the body in the system you mean?\", \"YES_LINE\": \"Buoyancy acts (your answer): no module adds it; it acts in this kernel only where one of your own laws states it.\", \"NO_LINE\": \"No buoyancy: the air's upthrust on the body is not included.\"}], \"TEST_BINDINGS\": [{\"NAME\": \"PROJECTILE_2D\", \"TPK\": {\"DOF\": [{\"NAME\": \"t\", \"DIMENSION\": \"T1\"}, {\"NAME\": \"x\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"z\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"v_x\", \"DIMENSION\": \"L1 T-1\"}, {\"NAME\": \"v_z\", \"DIMENSION\": \"L1 T-1\"}], \"CONSTANT\": [{\"NAME\": \"m\", \"DIMENSION\": \"M1\"}], \"LAW\": [{\"NAME\": \"KIN_X\", \"STATEMENT\": \"dx/dt = v_x\", \"REFS\": [\"t\", \"v_x\", \"x\"], \"ROLE\": \"EOM(x)\", \"EQUATION\": \"D(x,t)=v_x\"}, {\"NAME\": \"KIN_Z\", \"STATEMENT\": \"dz/dt = v_z\", \"REFS\": [\"t\", \"v_z\", \"z\"], \"ROLE\": \"EOM(z)\", \"EQUATION\": \"D(z,t)=v_z\"}, {\"NAME\": \"EOM_X\", \"STATEMENT\": \"m dv_x/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_x\"], \"ROLE\": \"EOM(v_x)\", \"EQUATION\": \"m*D(v_x,t)=0\"}, {\"NAME\": \"EOM_Z\", \"STATEMENT\": \"m dv_z/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_z\"], \"ROLE\": \"EOM(v_z)\", \"EQUATION\": \"m*D(v_z,t)=0\"}], \"ASSUMPTION\": [{\"NAME\": \"point_mass\", \"PROPOSITION\": \"the body is treated as a point mass\", \"REFS\": [\"m\"]}]}, \"BIND\": {\"HEIGHT\": [\"z\"], \"MASS\": [\"m\"], \"UP_VELOCITY\": [\"v_z\"]}, \"VALUES\": {\"h_max\": {\"VALUE\": \"100\", \"UNIT\": \"m\"}}, \"ANSWERS\": {}}, {\"NAME\": \"TABLE\", \"TPK\": {\"DOF\": [{\"NAME\": \"t\", \"DIMENSION\": \"T1\"}, {\"NAME\": \"x\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"z\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"v_x\", \"DIMENSION\": \"L1 T-1\"}, {\"NAME\": \"v_z\", \"DIMENSION\": \"L1 T-1\"}], \"CONSTANT\": [{\"NAME\": \"m\", \"DIMENSION\": \"M1\"}], \"LAW\": [{\"NAME\": \"KIN_X\", \"STATEMENT\": \"dx/dt = v_x\", \"REFS\": [\"t\", \"v_x\", \"x\"], \"ROLE\": \"EOM(x)\", \"EQUATION\": \"D(x,t)=v_x\"}, {\"NAME\": \"KIN_Z\", \"STATEMENT\": \"dz/dt = v_z\", \"REFS\": [\"t\", \"v_z\", \"z\"], \"ROLE\": \"CONSTRAINT\", \"EQUATION\": \"D(z,t)=v_z\"}, {\"NAME\": \"EOM_X\", \"STATEMENT\": \"m dv_x/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_x\"], \"ROLE\": \"EOM(v_x)\", \"EQUATION\": \"m*D(v_x,t)=0\"}], \"CONSTRAINT\": [{\"NAME\": \"C_Z\", \"TARGET\": \"z\", \"ACTION\": \"FIX\", \"VALUE\": \"0\", \"UNIT\": \"m\", \"STATEMENT\": \"the puck stays on the table top, z = 0\"}, {\"NAME\": \"C_VZ\", \"TARGET\": \"v_z\", \"ACTION\": \"FIX\", \"VALUE\": \"0\", \"UNIT\": \"m s-1\", \"STATEMENT\": \"the puck has no vertical velocity\"}]}, \"BIND\": {\"HEIGHT\": [\"z\"], \"MASS\": [\"m\"], \"UP_VELOCITY\": [\"v_z\"]}, \"VALUES\": {\"h_max\": {\"VALUE\": \"1\", \"UNIT\": \"m\"}}, \"ANSWERS\": {\"FIXED:v_z\": \"YES\"}}]}",
"{\"ID\": \"MATH\", \"VERSION\": \"1.0.0\", \"TITLE\": \"The mathematical constant pi, as the CONSTANT pi_c\", \"SOURCE\": \"pi to 16 significant digits, 3.141592653589793, the nearest IEEE 754 binary64 value\", \"PREREQUISITES\": [], \"PARAMETERS\": [{\"NAME\": \"pi_c\", \"DIMENSION\": \"1\", \"SUPPLY\": \"DECLARED\", \"VALUE\": \"3.141592653589793\", \"UNIT\": \"1\", \"OVERRIDABLE\": \"NO\", \"LABEL\": \"pi, to 16 significant digits\"}], \"SUMS\": [], \"TERMS\": [], \"ASSUMPTIONS\": [], \"BOUNDARIES\": [], \"NOT_CHOSEN\": \"No mathematical constant: pi exists only if you declare it.\", \"NOT_INCLUDED\": [\"pi_c is pi rounded to 16 significant digits; no other mathematical constant is declared.\"], \"EXCLUDES\": [], \"INTERACTS_WITH\": [], \"TEST_BINDINGS\": [{\"NAME\": \"PROJECTILE_2D\", \"TPK\": {\"DOF\": [{\"NAME\": \"t\", \"DIMENSION\": \"T1\"}, {\"NAME\": \"x\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"z\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"v_x\", \"DIMENSION\": \"L1 T-1\"}, {\"NAME\": \"v_z\", \"DIMENSION\": \"L1 T-1\"}], \"CONSTANT\": [{\"NAME\": \"m\", \"DIMENSION\": \"M1\"}], \"LAW\": [{\"NAME\": \"KIN_X\", \"STATEMENT\": \"dx/dt = v_x\", \"REFS\": [\"t\", \"v_x\", \"x\"], \"ROLE\": \"EOM(x)\", \"EQUATION\": \"D(x,t)=v_x\"}, {\"NAME\": \"KIN_Z\", \"STATEMENT\": \"dz/dt = v_z\", \"REFS\": [\"t\", \"v_z\", \"z\"], \"ROLE\": \"EOM(z)\", \"EQUATION\": \"D(z,t)=v_z\"}, {\"NAME\": \"EOM_X\", \"STATEMENT\": \"m dv_x/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_x\"], \"ROLE\": \"EOM(v_x)\", \"EQUATION\": \"m*D(v_x,t)=0\"}, {\"NAME\": \"EOM_Z\", \"STATEMENT\": \"m dv_z/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_z\"], \"ROLE\": \"EOM(v_z)\", \"EQUATION\": \"m*D(v_z,t)=0\"}], \"ASSUMPTION\": [{\"NAME\": \"point_mass\", \"PROPOSITION\": \"the body is treated as a point mass\", \"REFS\": [\"m\"]}]}, \"BIND\": {}, \"VALUES\": {}, \"ANSWERS\": {}}]}",
"{\"ID\": \"TEST-X\", \"VERSION\": \"1.0.0\", \"TITLE\": \"Test interaction X\", \"SOURCE\": \"synthetic fixture\", \"PREREQUISITES\": [], \"PARAMETERS\": [{\"NAME\": \"x_test\", \"DIMENSION\": \"1\", \"SUPPLY\": \"DECLARED\", \"VALUE\": \"1\", \"UNIT\": \"1\", \"OVERRIDABLE\": \"NO\", \"LABEL\": \"a test constant\"}], \"SUMS\": [], \"TERMS\": [], \"ASSUMPTIONS\": [], \"BOUNDARIES\": [], \"NOT_CHOSEN\": \"No test interaction X.\", \"NOT_INCLUDED\": [\"Test X adds only a constant.\"], \"EXCLUDES\": [], \"INTERACTS_WITH\": [], \"TEST_BINDINGS\": [{\"NAME\": \"SOLO\", \"TPK\": {\"DOF\": [{\"NAME\": \"t\", \"DIMENSION\": \"T1\"}, {\"NAME\": \"q\", \"DIMENSION\": \"L1\"}], \"LAW\": [{\"NAME\": \"EQ_Q\", \"STATEMENT\": \"dq/dt = 0\", \"REFS\": [\"q\", \"t\"], \"ROLE\": \"EOM(q)\", \"EQUATION\": \"D(q,t)=0\"}]}, \"BIND\": {}, \"VALUES\": {}, \"ANSWERS\": {}}]}"
]
},
"expected": "[\"REFUSED\",\"ANSWER ROUND 2: AT is not after the previous round's\"]",
"fn": "interview_check",
"hand_checked": true,
"name": "I07 a second round not after the first"
},
{
"args": {
"answer": [
{
"AT": 4,
"CHOSEN": "NONE",
"COVERED": [
[
"AIR-LINEAR",
"1.0.0",
"5f3fe27b42378bce0830b0d0959f892f4a8e73b12b540ae877e39e6439d08b4d"
],
[
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"1.0.0",
"6fb53c3a6546151eead2bd6e72e9cf8334f3a2040ad0ee2f5b988ec96d6fc852"
],
[
"GRAV-UNIFORM",
"1.0.0",
"24877ccb5c8ec300d29ed82ce6650592f35cf8899a3d878ccce9c08d4c72c025"
],
[
"MATH",
"1.0.0",
"8f39a356f35527b901fcee012764590f0819c8ffdeccad4bc05195ce3d2e0bcf"
]
]
},
{
"AT": 5,
"CHOSEN": "NONE",
"COVERED": []
}
],
"carried": [],
"claims": [],
"lines": [
{
"ACT": "MODULE ADD",
"DATE": "2026-10-01",
"DIGEST": "5f3fe27b42378bce0830b0d0959f892f4a8e73b12b540ae877e39e6439d08b4d",
"ID": "AIR-LINEAR",
"VERSION": "1.0.0"
},
{
"ACT": "MODULE ADD",
"DATE": "2026-10-01",
"DIGEST": "6fb53c3a6546151eead2bd6e72e9cf8334f3a2040ad0ee2f5b988ec96d6fc852",
"ID": "AIR-QUADRATIC",
"VERSION": "1.0.0"
},
{
"ACT": "MODULE ADD",
"DATE": "2026-10-01",
"DIGEST": "24877ccb5c8ec300d29ed82ce6650592f35cf8899a3d878ccce9c08d4c72c025",
"ID": "GRAV-UNIFORM",
"VERSION": "1.0.0"
},
{
"ACT": "MODULE ADD",
"DATE": "2026-10-01",
"DIGEST": "8f39a356f35527b901fcee012764590f0819c8ffdeccad4bc05195ce3d2e0bcf",
"ID": "MATH",
"VERSION": "1.0.0"
},
{
"ACT": "MODULE VERSION",
"DATE": "2026-10-02",
"DIGEST": "5be3923c28dc8f8ff910b033c2d17154f267f2a20fdb32c74a07293a37dfe338",
"ID": "GRAV-UNIFORM",
"VERSION": "1.1.0"
}
],
"modified": [],
"modules": [
"{\"ID\": \"AIR-LINEAR\", \"VERSION\": \"1.0.0\", \"TITLE\": \"Air resistance at sea level, linear in the speed (Stokes drag on a sphere)\", \"SOURCE\": \"ISO 2533:1975, Standard Atmosphere, sea-level values: density 1.225 kg m-3, dynamic viscosity 1.7894e-5 Pa s\", \"PREREQUISITES\": [{\"SLOT\": \"VELOCITY\", \"KIND\": \"DOF\", \"DIMENSION\": \"L1 T-1\", \"MIN\": 1, \"MAX\": 3, \"LABEL\": \"the velocity components of the body, one per axis\"}], \"PARAMETERS\": [{\"NAME\": \"rho_air\", \"DIMENSION\": \"L-3 M1\", \"SUPPLY\": \"DECLARED\", \"VALUE\": \"1.225\", \"UNIT\": \"kg m-3\", \"OVERRIDABLE\": \"NO\", \"LABEL\": \"the density of air at sea level\"}, {\"NAME\": \"mu_air\", \"DIMENSION\": \"L-1 M1 T-1\", \"SUPPLY\": \"DECLARED\", \"VALUE\": \"1.7894e-5\", \"UNIT\": \"Pa s\", \"OVERRIDABLE\": \"NO\", \"LABEL\": \"the dynamic viscosity of air at sea level\"}, {\"NAME\": \"pi_c\", \"DIMENSION\": \"1\", \"SUPPLY\": \"DECLARED\", \"VALUE\": \"3.141592653589793\", \"UNIT\": \"1\", \"OVERRIDABLE\": \"NO\", \"LABEL\": \"pi, to 16 significant digits\"}, {\"NAME\": \"R_s\", \"DIMENSION\": \"L1\", \"SUPPLY\": \"AUTHOR\", \"LABEL\": \"the radius of the sphere\"}], \"SUMS\": [{\"NAME\": \"SPEED2\", \"OVER\": \"VELOCITY\", \"EACH\": \"VELOCITY^2\"}], \"TERMS\": [{\"TARGET\": \"VELOCITY\", \"SIGN\": \"-\", \"EXPR\": \"6*pi_c*mu_air*R_s*VELOCITY\", \"LABEL\": \"the linear (Stokes) drag\"}], \"ASSUMPTIONS\": [{\"NAME\": \"air_still\", \"PROPOSITION\": \"the air is at rest in the frame of the body's velocity\", \"REFS\": [\"VELOCITY\"]}, {\"NAME\": \"air_uniform\", \"PROPOSITION\": \"the air density is uniform over the region of motion\", \"REFS\": [\"rho_air\"]}, {\"NAME\": \"drag_sphere\", \"PROPOSITION\": \"the body is a rigid sphere of radius R_s\", \"REFS\": [\"R_s\"]}], \"BOUNDARIES\": [{\"NAME\": \"drag_linear_regime\", \"PREDICATE\": \"2 rho_air |v| R_s / mu_air < 1: the regime of the linear law\", \"CONDITION\": \"mu_air != 0 and SPEED2 >= 0 and 2*rho_air*sqrt(SPEED2)*R_s/mu_air < 1\"}], \"NOT_CHOSEN\": \"No linear (Stokes) air resistance.\", \"NOT_INCLUDED\": [\"No wind: the air is at rest.\", \"No change of air density or viscosity with altitude or temperature.\", \"No drag outside the regime of the linear law.\"], \"EXCLUDES\": [], \"INTERACTS_WITH\": [], \"TEST_BINDINGS\": [{\"NAME\": \"PROJECTILE_2D\", \"TPK\": {\"DOF\": [{\"NAME\": \"t\", \"DIMENSION\": \"T1\"}, {\"NAME\": \"x\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"z\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"v_x\", \"DIMENSION\": \"L1 T-1\"}, {\"NAME\": \"v_z\", \"DIMENSION\": \"L1 T-1\"}], \"CONSTANT\": [{\"NAME\": \"m\", \"DIMENSION\": \"M1\"}], \"LAW\": [{\"NAME\": \"KIN_X\", \"STATEMENT\": \"dx/dt = v_x\", \"REFS\": [\"t\", \"v_x\", \"x\"], \"ROLE\": \"EOM(x)\", \"EQUATION\": \"D(x,t)=v_x\"}, {\"NAME\": \"KIN_Z\", \"STATEMENT\": \"dz/dt = v_z\", \"REFS\": [\"t\", \"v_z\", \"z\"], \"ROLE\": \"EOM(z)\", \"EQUATION\": \"D(z,t)=v_z\"}, {\"NAME\": \"EOM_X\", \"STATEMENT\": \"m dv_x/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_x\"], \"ROLE\": \"EOM(v_x)\", \"EQUATION\": \"m*D(v_x,t)=0\"}, {\"NAME\": \"EOM_Z\", \"STATEMENT\": \"m dv_z/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_z\"], \"ROLE\": \"EOM(v_z)\", \"EQUATION\": \"m*D(v_z,t)=0\"}], \"ASSUMPTION\": [{\"NAME\": \"point_mass\", \"PROPOSITION\": \"the body is treated as a point mass\", \"REFS\": [\"m\"]}]}, \"BIND\": {\"VELOCITY\": [\"v_x\", \"v_z\"]}, \"VALUES\": {\"R_s\": {}}, \"ANSWERS\": {}}]}",
"{\"ID\": \"AIR-QUADRATIC\", \"VERSION\": \"1.0.0\", \"TITLE\": \"Air resistance at sea level, quadratic in the speed\", \"SOURCE\": \"ISO 2533:1975, Standard Atmosphere, sea-level values: density 1.225 kg m-3, dynamic viscosity 1.7894e-5 Pa s\", \"PREREQUISITES\": [{\"SLOT\": \"VELOCITY\", \"KIND\": \"DOF\", \"DIMENSION\": \"L1 T-1\", \"MIN\": 1, \"MAX\": 3, \"LABEL\": \"the velocity components of the body, one per axis\"}], \"PARAMETERS\": [{\"NAME\": \"rho_air\", \"DIMENSION\": \"L-3 M1\", \"SUPPLY\": \"DECLARED\", \"VALUE\": \"1.225\", \"UNIT\": \"kg m-3\", \"OVERRIDABLE\": \"NO\", \"LABEL\": \"the density of air at sea level\"}, {\"NAME\": \"mu_air\", \"DIMENSION\": \"L-1 M1 T-1\", \"SUPPLY\": \"DECLARED\", \"VALUE\": \"1.7894e-5\", \"UNIT\": \"Pa s\", \"OVERRIDABLE\": \"NO\", \"LABEL\": \"the dynamic viscosity of air at sea level\"}, {\"NAME\": \"C_d\", \"DIMENSION\": \"1\", \"SUPPLY\": \"AUTHOR\", \"LABEL\": \"the drag coefficient of the body\"}, {\"NAME\": \"A_ref\", \"DIMENSION\": \"L2\", \"SUPPLY\": \"AUTHOR\", \"LABEL\": \"the reference area of the drag coefficient\"}, {\"NAME\": \"L_ref\", \"DIMENSION\": \"L1\", \"SUPPLY\": \"AUTHOR\", \"LABEL\": \"the reference length of the Reynolds number\"}], \"SUMS\": [{\"NAME\": \"SPEED2\", \"OVER\": \"VELOCITY\", \"EACH\": \"VELOCITY^2\"}], \"TERMS\": [{\"TARGET\": \"VELOCITY\", \"SIGN\": \"-\", \"EXPR\": \"0.5*rho_air*C_d*A_ref*sqrt(SPEED2)*VELOCITY\", \"LABEL\": \"the quadratic drag\"}], \"ASSUMPTIONS\": [{\"NAME\": \"air_still\", \"PROPOSITION\": \"the air is at rest in the frame of the body's velocity\", \"REFS\": [\"VELOCITY\"]}, {\"NAME\": \"air_uniform\", \"PROPOSITION\": \"the air density is uniform over the region of motion\", \"REFS\": [\"rho_air\"]}, {\"NAME\": \"drag_cd_constant\", \"PROPOSITION\": \"the drag coefficient C_d is constant over the motion\", \"REFS\": [\"C_d\"]}, {\"NAME\": \"drag_no_lift\", \"PROPOSITION\": \"the body experiences no lift force\", \"REFS\": [\"VELOCITY\"]}, {\"NAME\": \"drag_no_magnus\", \"PROPOSITION\": \"the body experiences no Magnus force\", \"REFS\": [\"VELOCITY\"]}], \"BOUNDARIES\": [{\"NAME\": \"drag_quadratic_regime\", \"PREDICATE\": \"1e3 < rho_air |v| L_ref / mu_air < 2e5: the Reynolds window of the quadratic law\", \"CONDITION\": \"mu_air != 0 and SPEED2 >= 0 and rho_air*sqrt(SPEED2)*L_ref/mu_air > 1000 and rho_air*sqrt(SPEED2)*L_ref/mu_air < 200000\"}], \"NOT_CHOSEN\": \"No quadratic air resistance.\", \"NOT_INCLUDED\": [\"No wind: the air is at rest.\", \"No change of air density or viscosity with altitude or temperature.\", \"No lift, Magnus or added-mass force.\", \"No drag outside the Reynolds window of the quadratic law.\"], \"EXCLUDES\": [\"AIR-LINEAR\"], \"INTERACTS_WITH\": [], \"TEST_BINDINGS\": [{\"NAME\": \"PROJECTILE_2D\", \"TPK\": {\"DOF\": [{\"NAME\": \"t\", \"DIMENSION\": \"T1\"}, {\"NAME\": \"x\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"z\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"v_x\", \"DIMENSION\": \"L1 T-1\"}, {\"NAME\": \"v_z\", \"DIMENSION\": \"L1 T-1\"}], \"CONSTANT\": [{\"NAME\": \"m\", \"DIMENSION\": \"M1\"}], \"LAW\": [{\"NAME\": \"KIN_X\", \"STATEMENT\": \"dx/dt = v_x\", \"REFS\": [\"t\", \"v_x\", \"x\"], \"ROLE\": \"EOM(x)\", \"EQUATION\": \"D(x,t)=v_x\"}, {\"NAME\": \"KIN_Z\", \"STATEMENT\": \"dz/dt = v_z\", \"REFS\": [\"t\", \"v_z\", \"z\"], \"ROLE\": \"EOM(z)\", \"EQUATION\": \"D(z,t)=v_z\"}, {\"NAME\": \"EOM_X\", \"STATEMENT\": \"m dv_x/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_x\"], \"ROLE\": \"EOM(v_x)\", \"EQUATION\": \"m*D(v_x,t)=0\"}, {\"NAME\": \"EOM_Z\", \"STATEMENT\": \"m dv_z/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_z\"], \"ROLE\": \"EOM(v_z)\", \"EQUATION\": \"m*D(v_z,t)=0\"}], \"ASSUMPTION\": [{\"NAME\": \"point_mass\", \"PROPOSITION\": \"the body is treated as a point mass\", \"REFS\": [\"m\"]}]}, \"BIND\": {\"VELOCITY\": [\"v_x\", \"v_z\"]}, \"VALUES\": {\"A_ref\": {}, \"C_d\": {}, \"L_ref\": {}}, \"ANSWERS\": {}}]}",
"{\"ID\": \"GRAV-UNIFORM\", \"VERSION\": \"1.0.0\", \"TITLE\": \"Uniform gravity at the standard value g_n\", \"SOURCE\": \"g_n = 9.80665 m s-2, exact by definition: 3rd CGPM (1901), declaration on the unit of mass and on the definition of weight\", \"PREREQUISITES\": [{\"SLOT\": \"MASS\", \"KIND\": \"CONSTANT\", \"DIMENSION\": \"M1\", \"MIN\": 1, \"MAX\": 1, \"LABEL\": \"the mass of the body\"}, {\"SLOT\": \"UP_VELOCITY\", \"KIND\": \"DOF\", \"DIMENSION\": \"L1 T-1\", \"MIN\": 1, \"MAX\": 1, \"LABEL\": \"the velocity component pointing up; its equation of motion receives the weight\"}, {\"SLOT\": \"HEIGHT\", \"KIND\": \"DOF\", \"DIMENSION\": \"L1\", \"MIN\": 1, \"MAX\": 1, \"LABEL\": \"the position along the same upward axis\"}], \"PARAMETERS\": [{\"NAME\": \"g_n\", \"DIMENSION\": \"L1 T-2\", \"SUPPLY\": \"DECLARED\", \"VALUE\": \"9.80665\", \"UNIT\": \"m s-2\", \"OVERRIDABLE\": \"NO\", \"LABEL\": \"the standard acceleration of gravity\"}, {\"NAME\": \"h_max\", \"DIMENSION\": \"L1\", \"SUPPLY\": \"AUTHOR\", \"LABEL\": \"the largest height, above or below the origin, over which the field is taken as uniform\"}], \"SUMS\": [], \"TERMS\": [{\"TARGET\": \"UP_VELOCITY\", \"SIGN\": \"-\", \"EXPR\": \"MASS*g_n\", \"LABEL\": \"the weight\"}], \"ASSUMPTIONS\": [{\"NAME\": \"gravity_uniform\", \"PROPOSITION\": \"the gravitational field is uniform over the region abs({HEIGHT}) < h_max\", \"REFS\": [\"HEIGHT\", \"h_max\"]}, {\"NAME\": \"gravity_standard\", \"PROPOSITION\": \"the local gravitational acceleration equals the conventional standard value g_n\", \"REFS\": [\"g_n\"]}, {\"NAME\": \"frame_inertial\", \"PROPOSITION\": \"the frame in which {HEIGHT} is measured is treated as inertial\", \"REFS\": [\"HEIGHT\"]}], \"BOUNDARIES\": [{\"NAME\": \"gravity_region\", \"PREDICATE\": \"abs({HEIGHT}) < h_max\", \"CONDITION\": \"abs(HEIGHT) < h_max\"}], \"NOT_CHOSEN\": \"No gravity: no weight acts on any DOF.\", \"NOT_INCLUDED\": [\"No variation of gravity with height or latitude beyond what g_n contains.\", \"No Earth rotation (Coriolis or centrifugal force) beyond what g_n contains.\", \"No gravity of bodies other than the Earth.\"], \"EXCLUDES\": [], \"INTERACTS_WITH\": [{\"WITH\": \"AIR-*\", \"QUESTION_ID\": \"BUOYANCY\", \"QUESTION\": \"Does the air's buoyancy (upthrust) act on the body in the system you mean?\", \"YES_LINE\": \"Buoyancy acts (your answer): no module adds it; it acts in this kernel only where one of your own laws states it.\", \"NO_LINE\": \"No buoyancy: the air's upthrust on the body is not included.\"}], \"TEST_BINDINGS\": [{\"NAME\": \"PROJECTILE_2D\", \"TPK\": {\"DOF\": [{\"NAME\": \"t\", \"DIMENSION\": \"T1\"}, {\"NAME\": \"x\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"z\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"v_x\", \"DIMENSION\": \"L1 T-1\"}, {\"NAME\": \"v_z\", \"DIMENSION\": \"L1 T-1\"}], \"CONSTANT\": [{\"NAME\": \"m\", \"DIMENSION\": \"M1\"}], \"LAW\": [{\"NAME\": \"KIN_X\", \"STATEMENT\": \"dx/dt = v_x\", \"REFS\": [\"t\", \"v_x\", \"x\"], \"ROLE\": \"EOM(x)\", \"EQUATION\": \"D(x,t)=v_x\"}, {\"NAME\": \"KIN_Z\", \"STATEMENT\": \"dz/dt = v_z\", \"REFS\": [\"t\", \"v_z\", \"z\"], \"ROLE\": \"EOM(z)\", \"EQUATION\": \"D(z,t)=v_z\"}, {\"NAME\": \"EOM_X\", \"STATEMENT\": \"m dv_x/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_x\"], \"ROLE\": \"EOM(v_x)\", \"EQUATION\": \"m*D(v_x,t)=0\"}, {\"NAME\": \"EOM_Z\", \"STATEMENT\": \"m dv_z/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_z\"], \"ROLE\": \"EOM(v_z)\", \"EQUATION\": \"m*D(v_z,t)=0\"}], \"ASSUMPTION\": [{\"NAME\": \"point_mass\", \"PROPOSITION\": \"the body is treated as a point mass\", \"REFS\": [\"m\"]}]}, \"BIND\": {\"HEIGHT\": [\"z\"], \"MASS\": [\"m\"], \"UP_VELOCITY\": [\"v_z\"]}, \"VALUES\": {\"h_max\": {\"VALUE\": \"100\", \"UNIT\": \"m\"}}, \"ANSWERS\": {}}, {\"NAME\": \"TABLE\", \"TPK\": {\"DOF\": [{\"NAME\": \"t\", \"DIMENSION\": \"T1\"}, {\"NAME\": \"x\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"z\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"v_x\", \"DIMENSION\": \"L1 T-1\"}, {\"NAME\": \"v_z\", \"DIMENSION\": \"L1 T-1\"}], \"CONSTANT\": [{\"NAME\": \"m\", \"DIMENSION\": \"M1\"}], \"LAW\": [{\"NAME\": \"KIN_X\", \"STATEMENT\": \"dx/dt = v_x\", \"REFS\": [\"t\", \"v_x\", \"x\"], \"ROLE\": \"EOM(x)\", \"EQUATION\": \"D(x,t)=v_x\"}, {\"NAME\": \"KIN_Z\", \"STATEMENT\": \"dz/dt = v_z\", \"REFS\": [\"t\", \"v_z\", \"z\"], \"ROLE\": \"CONSTRAINT\", \"EQUATION\": \"D(z,t)=v_z\"}, {\"NAME\": \"EOM_X\", \"STATEMENT\": \"m dv_x/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_x\"], \"ROLE\": \"EOM(v_x)\", \"EQUATION\": \"m*D(v_x,t)=0\"}], \"CONSTRAINT\": [{\"NAME\": \"C_Z\", \"TARGET\": \"z\", \"ACTION\": \"FIX\", \"VALUE\": \"0\", \"UNIT\": \"m\", \"STATEMENT\": \"the puck stays on the table top, z = 0\"}, {\"NAME\": \"C_VZ\", \"TARGET\": \"v_z\", \"ACTION\": \"FIX\", \"VALUE\": \"0\", \"UNIT\": \"m s-1\", \"STATEMENT\": \"the puck has no vertical velocity\"}]}, \"BIND\": {\"HEIGHT\": [\"z\"], \"MASS\": [\"m\"], \"UP_VELOCITY\": [\"v_z\"]}, \"VALUES\": {\"h_max\": {\"VALUE\": \"1\", \"UNIT\": \"m\"}}, \"ANSWERS\": {\"FIXED:v_z\": \"YES\"}}]}",
"{\"ID\": \"MATH\", \"VERSION\": \"1.0.0\", \"TITLE\": \"The mathematical constant pi, as the CONSTANT pi_c\", \"SOURCE\": \"pi to 16 significant digits, 3.141592653589793, the nearest IEEE 754 binary64 value\", \"PREREQUISITES\": [], \"PARAMETERS\": [{\"NAME\": \"pi_c\", \"DIMENSION\": \"1\", \"SUPPLY\": \"DECLARED\", \"VALUE\": \"3.141592653589793\", \"UNIT\": \"1\", \"OVERRIDABLE\": \"NO\", \"LABEL\": \"pi, to 16 significant digits\"}], \"SUMS\": [], \"TERMS\": [], \"ASSUMPTIONS\": [], \"BOUNDARIES\": [], \"NOT_CHOSEN\": \"No mathematical constant: pi exists only if you declare it.\", \"NOT_INCLUDED\": [\"pi_c is pi rounded to 16 significant digits; no other mathematical constant is declared.\"], \"EXCLUDES\": [], \"INTERACTS_WITH\": [], \"TEST_BINDINGS\": [{\"NAME\": \"PROJECTILE_2D\", \"TPK\": {\"DOF\": [{\"NAME\": \"t\", \"DIMENSION\": \"T1\"}, {\"NAME\": \"x\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"z\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"v_x\", \"DIMENSION\": \"L1 T-1\"}, {\"NAME\": \"v_z\", \"DIMENSION\": \"L1 T-1\"}], \"CONSTANT\": [{\"NAME\": \"m\", \"DIMENSION\": \"M1\"}], \"LAW\": [{\"NAME\": \"KIN_X\", \"STATEMENT\": \"dx/dt = v_x\", \"REFS\": [\"t\", \"v_x\", \"x\"], \"ROLE\": \"EOM(x)\", \"EQUATION\": \"D(x,t)=v_x\"}, {\"NAME\": \"KIN_Z\", \"STATEMENT\": \"dz/dt = v_z\", \"REFS\": [\"t\", \"v_z\", \"z\"], \"ROLE\": \"EOM(z)\", \"EQUATION\": \"D(z,t)=v_z\"}, {\"NAME\": \"EOM_X\", \"STATEMENT\": \"m dv_x/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_x\"], \"ROLE\": \"EOM(v_x)\", \"EQUATION\": \"m*D(v_x,t)=0\"}, {\"NAME\": \"EOM_Z\", \"STATEMENT\": \"m dv_z/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_z\"], \"ROLE\": \"EOM(v_z)\", \"EQUATION\": \"m*D(v_z,t)=0\"}], \"ASSUMPTION\": [{\"NAME\": \"point_mass\", \"PROPOSITION\": \"the body is treated as a point mass\", \"REFS\": [\"m\"]}]}, \"BIND\": {}, \"VALUES\": {}, \"ANSWERS\": {}}]}",
"{\"ID\": \"GRAV-UNIFORM\", \"VERSION\": \"1.1.0\", \"TITLE\": \"Uniform gravity at the standard value g_n (text revised)\", \"SOURCE\": \"g_n = 9.80665 m s-2, exact by definition: 3rd CGPM (1901), declaration on the unit of mass and on the definition of weight\", \"PREREQUISITES\": [{\"SLOT\": \"MASS\", \"KIND\": \"CONSTANT\", \"DIMENSION\": \"M1\", \"MIN\": 1, \"MAX\": 1, \"LABEL\": \"the mass of the body\"}, {\"SLOT\": \"UP_VELOCITY\", \"KIND\": \"DOF\", \"DIMENSION\": \"L1 T-1\", \"MIN\": 1, \"MAX\": 1, \"LABEL\": \"the velocity component pointing up; its equation of motion receives the weight\"}, {\"SLOT\": \"HEIGHT\", \"KIND\": \"DOF\", \"DIMENSION\": \"L1\", \"MIN\": 1, \"MAX\": 1, \"LABEL\": \"the position along the same upward axis\"}], \"PARAMETERS\": [{\"NAME\": \"g_n\", \"DIMENSION\": \"L1 T-2\", \"SUPPLY\": \"DECLARED\", \"VALUE\": \"9.80665\", \"UNIT\": \"m s-2\", \"OVERRIDABLE\": \"NO\", \"LABEL\": \"the standard acceleration of gravity\"}, {\"NAME\": \"h_max\", \"DIMENSION\": \"L1\", \"SUPPLY\": \"AUTHOR\", \"LABEL\": \"the largest height, above or below the origin, over which the field is taken as uniform\"}], \"SUMS\": [], \"TERMS\": [{\"TARGET\": \"UP_VELOCITY\", \"SIGN\": \"-\", \"EXPR\": \"MASS*g_n\", \"LABEL\": \"the weight\"}], \"ASSUMPTIONS\": [{\"NAME\": \"gravity_uniform\", \"PROPOSITION\": \"the gravitational field is uniform over the region abs({HEIGHT}) < h_max\", \"REFS\": [\"HEIGHT\", \"h_max\"]}, {\"NAME\": \"gravity_standard\", \"PROPOSITION\": \"the local gravitational acceleration equals the conventional standard value g_n\", \"REFS\": [\"g_n\"]}, {\"NAME\": \"frame_inertial\", \"PROPOSITION\": \"the frame in which {HEIGHT} is measured is treated as inertial\", \"REFS\": [\"HEIGHT\"]}], \"BOUNDARIES\": [{\"NAME\": \"gravity_region\", \"PREDICATE\": \"abs({HEIGHT}) < h_max\", \"CONDITION\": \"abs(HEIGHT) < h_max\"}], \"NOT_CHOSEN\": \"No gravity: no weight acts on any DOF.\", \"NOT_INCLUDED\": [\"No variation of gravity with height or latitude beyond what g_n contains.\", \"No Earth rotation (Coriolis or centrifugal force) beyond what g_n contains.\", \"No gravity of bodies other than the Earth.\"], \"EXCLUDES\": [], \"INTERACTS_WITH\": [{\"WITH\": \"AIR-*\", \"QUESTION_ID\": \"BUOYANCY\", \"QUESTION\": \"Does the air's buoyancy (upthrust) act on the body in the system you mean?\", \"YES_LINE\": \"Buoyancy acts (your answer): no module adds it; it acts in this kernel only where one of your own laws states it.\", \"NO_LINE\": \"No buoyancy: the air's upthrust on the body is not included.\"}], \"TEST_BINDINGS\": [{\"NAME\": \"PROJECTILE_2D\", \"TPK\": {\"DOF\": [{\"NAME\": \"t\", \"DIMENSION\": \"T1\"}, {\"NAME\": \"x\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"z\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"v_x\", \"DIMENSION\": \"L1 T-1\"}, {\"NAME\": \"v_z\", \"DIMENSION\": \"L1 T-1\"}], \"CONSTANT\": [{\"NAME\": \"m\", \"DIMENSION\": \"M1\"}], \"LAW\": [{\"NAME\": \"KIN_X\", \"STATEMENT\": \"dx/dt = v_x\", \"REFS\": [\"t\", \"v_x\", \"x\"], \"ROLE\": \"EOM(x)\", \"EQUATION\": \"D(x,t)=v_x\"}, {\"NAME\": \"KIN_Z\", \"STATEMENT\": \"dz/dt = v_z\", \"REFS\": [\"t\", \"v_z\", \"z\"], \"ROLE\": \"EOM(z)\", \"EQUATION\": \"D(z,t)=v_z\"}, {\"NAME\": \"EOM_X\", \"STATEMENT\": \"m dv_x/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_x\"], \"ROLE\": \"EOM(v_x)\", \"EQUATION\": \"m*D(v_x,t)=0\"}, {\"NAME\": \"EOM_Z\", \"STATEMENT\": \"m dv_z/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_z\"], \"ROLE\": \"EOM(v_z)\", \"EQUATION\": \"m*D(v_z,t)=0\"}], \"ASSUMPTION\": [{\"NAME\": \"point_mass\", \"PROPOSITION\": \"the body is treated as a point mass\", \"REFS\": [\"m\"]}]}, \"BIND\": {\"HEIGHT\": [\"z\"], \"MASS\": [\"m\"], \"UP_VELOCITY\": [\"v_z\"]}, \"VALUES\": {\"h_max\": {\"VALUE\": \"100\", \"UNIT\": \"m\"}}, \"ANSWERS\": {}}, {\"NAME\": \"TABLE\", \"TPK\": {\"DOF\": [{\"NAME\": \"t\", \"DIMENSION\": \"T1\"}, {\"NAME\": \"x\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"z\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"v_x\", \"DIMENSION\": \"L1 T-1\"}, {\"NAME\": \"v_z\", \"DIMENSION\": \"L1 T-1\"}], \"CONSTANT\": [{\"NAME\": \"m\", \"DIMENSION\": \"M1\"}], \"LAW\": [{\"NAME\": \"KIN_X\", \"STATEMENT\": \"dx/dt = v_x\", \"REFS\": [\"t\", \"v_x\", \"x\"], \"ROLE\": \"EOM(x)\", \"EQUATION\": \"D(x,t)=v_x\"}, {\"NAME\": \"KIN_Z\", \"STATEMENT\": \"dz/dt = v_z\", \"REFS\": [\"t\", \"v_z\", \"z\"], \"ROLE\": \"CONSTRAINT\", \"EQUATION\": \"D(z,t)=v_z\"}, {\"NAME\": \"EOM_X\", \"STATEMENT\": \"m dv_x/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_x\"], \"ROLE\": \"EOM(v_x)\", \"EQUATION\": \"m*D(v_x,t)=0\"}], \"CONSTRAINT\": [{\"NAME\": \"C_Z\", \"TARGET\": \"z\", \"ACTION\": \"FIX\", \"VALUE\": \"0\", \"UNIT\": \"m\", \"STATEMENT\": \"the puck stays on the table top, z = 0\"}, {\"NAME\": \"C_VZ\", \"TARGET\": \"v_z\", \"ACTION\": \"FIX\", \"VALUE\": \"0\", \"UNIT\": \"m s-1\", \"STATEMENT\": \"the puck has no vertical velocity\"}]}, \"BIND\": {\"HEIGHT\": [\"z\"], \"MASS\": [\"m\"], \"UP_VELOCITY\": [\"v_z\"]}, \"VALUES\": {\"h_max\": {\"VALUE\": \"1\", \"UNIT\": \"m\"}}, \"ANSWERS\": {\"FIXED:v_z\": \"YES\"}}]}"
]
},
"expected": "[\"REFUSED\",\"ANSWER ROUND 2: no module was added since the previous round\"]",
"fn": "interview_check",
"hand_checked": true,
"name": "I08 a second round with nothing new (a new VERSION is no new module)"
},
{
"args": {
"answer": [
{
"AT": 7,
"CHOSEN": "NONE",
"COVERED": [
[
"AIR-LINEAR",
"1.0.0",
"5f3fe27b42378bce0830b0d0959f892f4a8e73b12b540ae877e39e6439d08b4d"
],
[
"AIR-QUADRATIC",
"1.0.0",
"6fb53c3a6546151eead2bd6e72e9cf8334f3a2040ad0ee2f5b988ec96d6fc852"
],
[
"GRAV-UNIFORM",
"1.0.0",
"24877ccb5c8ec300d29ed82ce6650592f35cf8899a3d878ccce9c08d4c72c025"
],
[
"MATH",
"1.0.0",
"8f39a356f35527b901fcee012764590f0819c8ffdeccad4bc05195ce3d2e0bcf"
]
]
}
],
"carried": [],
"claims": [],
"lines": [
{
"ACT": "MODULE ADD",
"DATE": "2026-10-01",
"DIGEST": "5f3fe27b42378bce0830b0d0959f892f4a8e73b12b540ae877e39e6439d08b4d",
"ID": "AIR-LINEAR",
"VERSION": "1.0.0"
},
{
"ACT": "MODULE ADD",
"DATE": "2026-10-01",
"DIGEST": "6fb53c3a6546151eead2bd6e72e9cf8334f3a2040ad0ee2f5b988ec96d6fc852",
"ID": "AIR-QUADRATIC",
"VERSION": "1.0.0"
},
{
"ACT": "MODULE ADD",
"DATE": "2026-10-01",
"DIGEST": "24877ccb5c8ec300d29ed82ce6650592f35cf8899a3d878ccce9c08d4c72c025",
"ID": "GRAV-UNIFORM",
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},
{
"ACT": "MODULE ADD",
"DATE": "2026-10-01",
"DIGEST": "8f39a356f35527b901fcee012764590f0819c8ffdeccad4bc05195ce3d2e0bcf",
"ID": "MATH",
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}
],
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"modules": [
"{\"ID\": \"AIR-LINEAR\", \"VERSION\": \"1.0.0\", \"TITLE\": \"Air resistance at sea level, linear in the speed (Stokes drag on a sphere)\", \"SOURCE\": \"ISO 2533:1975, Standard Atmosphere, sea-level values: density 1.225 kg m-3, dynamic viscosity 1.7894e-5 Pa s\", \"PREREQUISITES\": [{\"SLOT\": \"VELOCITY\", \"KIND\": \"DOF\", \"DIMENSION\": \"L1 T-1\", \"MIN\": 1, \"MAX\": 3, \"LABEL\": \"the velocity components of the body, one per axis\"}], \"PARAMETERS\": [{\"NAME\": \"rho_air\", \"DIMENSION\": \"L-3 M1\", \"SUPPLY\": \"DECLARED\", \"VALUE\": \"1.225\", \"UNIT\": \"kg m-3\", \"OVERRIDABLE\": \"NO\", \"LABEL\": \"the density of air at sea level\"}, {\"NAME\": \"mu_air\", \"DIMENSION\": \"L-1 M1 T-1\", \"SUPPLY\": \"DECLARED\", \"VALUE\": \"1.7894e-5\", \"UNIT\": \"Pa s\", \"OVERRIDABLE\": \"NO\", \"LABEL\": \"the dynamic viscosity of air at sea level\"}, {\"NAME\": \"pi_c\", \"DIMENSION\": \"1\", \"SUPPLY\": \"DECLARED\", \"VALUE\": \"3.141592653589793\", \"UNIT\": \"1\", \"OVERRIDABLE\": \"NO\", \"LABEL\": \"pi, to 16 significant digits\"}, {\"NAME\": \"R_s\", \"DIMENSION\": \"L1\", \"SUPPLY\": \"AUTHOR\", \"LABEL\": \"the radius of the sphere\"}], \"SUMS\": [{\"NAME\": \"SPEED2\", \"OVER\": \"VELOCITY\", \"EACH\": \"VELOCITY^2\"}], \"TERMS\": [{\"TARGET\": \"VELOCITY\", \"SIGN\": \"-\", \"EXPR\": \"6*pi_c*mu_air*R_s*VELOCITY\", \"LABEL\": \"the linear (Stokes) drag\"}], \"ASSUMPTIONS\": [{\"NAME\": \"air_still\", \"PROPOSITION\": \"the air is at rest in the frame of the body's velocity\", \"REFS\": [\"VELOCITY\"]}, {\"NAME\": \"air_uniform\", \"PROPOSITION\": \"the air density is uniform over the region of motion\", \"REFS\": [\"rho_air\"]}, {\"NAME\": \"drag_sphere\", \"PROPOSITION\": \"the body is a rigid sphere of radius R_s\", \"REFS\": [\"R_s\"]}], \"BOUNDARIES\": [{\"NAME\": \"drag_linear_regime\", \"PREDICATE\": \"2 rho_air |v| R_s / mu_air < 1: the regime of the linear law\", \"CONDITION\": \"mu_air != 0 and SPEED2 >= 0 and 2*rho_air*sqrt(SPEED2)*R_s/mu_air < 1\"}], \"NOT_CHOSEN\": \"No linear (Stokes) air resistance.\", \"NOT_INCLUDED\": [\"No wind: the air is at rest.\", \"No change of air density or viscosity with altitude or temperature.\", \"No drag outside the regime of the linear law.\"], \"EXCLUDES\": [], \"INTERACTS_WITH\": [], \"TEST_BINDINGS\": [{\"NAME\": \"PROJECTILE_2D\", \"TPK\": {\"DOF\": [{\"NAME\": \"t\", \"DIMENSION\": \"T1\"}, {\"NAME\": \"x\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"z\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"v_x\", \"DIMENSION\": \"L1 T-1\"}, {\"NAME\": \"v_z\", \"DIMENSION\": \"L1 T-1\"}], \"CONSTANT\": [{\"NAME\": \"m\", \"DIMENSION\": \"M1\"}], \"LAW\": [{\"NAME\": \"KIN_X\", \"STATEMENT\": \"dx/dt = v_x\", \"REFS\": [\"t\", \"v_x\", \"x\"], \"ROLE\": \"EOM(x)\", \"EQUATION\": \"D(x,t)=v_x\"}, {\"NAME\": \"KIN_Z\", \"STATEMENT\": \"dz/dt = v_z\", \"REFS\": [\"t\", \"v_z\", \"z\"], \"ROLE\": \"EOM(z)\", \"EQUATION\": \"D(z,t)=v_z\"}, {\"NAME\": \"EOM_X\", \"STATEMENT\": \"m dv_x/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_x\"], \"ROLE\": \"EOM(v_x)\", \"EQUATION\": \"m*D(v_x,t)=0\"}, {\"NAME\": \"EOM_Z\", \"STATEMENT\": \"m dv_z/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_z\"], \"ROLE\": \"EOM(v_z)\", \"EQUATION\": \"m*D(v_z,t)=0\"}], \"ASSUMPTION\": [{\"NAME\": \"point_mass\", \"PROPOSITION\": \"the body is treated as a point mass\", \"REFS\": [\"m\"]}]}, \"BIND\": {\"VELOCITY\": [\"v_x\", \"v_z\"]}, \"VALUES\": {\"R_s\": {}}, \"ANSWERS\": {}}]}",
"{\"ID\": \"AIR-QUADRATIC\", \"VERSION\": \"1.0.0\", \"TITLE\": \"Air resistance at sea level, quadratic in the speed\", \"SOURCE\": \"ISO 2533:1975, Standard Atmosphere, sea-level values: density 1.225 kg m-3, dynamic viscosity 1.7894e-5 Pa s\", \"PREREQUISITES\": [{\"SLOT\": \"VELOCITY\", \"KIND\": \"DOF\", \"DIMENSION\": \"L1 T-1\", \"MIN\": 1, \"MAX\": 3, \"LABEL\": \"the velocity components of the body, one per axis\"}], \"PARAMETERS\": [{\"NAME\": \"rho_air\", \"DIMENSION\": \"L-3 M1\", \"SUPPLY\": \"DECLARED\", \"VALUE\": \"1.225\", \"UNIT\": \"kg m-3\", \"OVERRIDABLE\": \"NO\", \"LABEL\": \"the density of air at sea level\"}, {\"NAME\": \"mu_air\", \"DIMENSION\": \"L-1 M1 T-1\", \"SUPPLY\": \"DECLARED\", \"VALUE\": \"1.7894e-5\", \"UNIT\": \"Pa s\", \"OVERRIDABLE\": \"NO\", \"LABEL\": \"the dynamic viscosity of air at sea level\"}, {\"NAME\": \"C_d\", \"DIMENSION\": \"1\", \"SUPPLY\": \"AUTHOR\", \"LABEL\": \"the drag coefficient of the body\"}, {\"NAME\": \"A_ref\", \"DIMENSION\": \"L2\", \"SUPPLY\": \"AUTHOR\", \"LABEL\": \"the reference area of the drag coefficient\"}, {\"NAME\": \"L_ref\", \"DIMENSION\": \"L1\", \"SUPPLY\": \"AUTHOR\", \"LABEL\": \"the reference length of the Reynolds number\"}], \"SUMS\": [{\"NAME\": \"SPEED2\", \"OVER\": \"VELOCITY\", \"EACH\": \"VELOCITY^2\"}], \"TERMS\": [{\"TARGET\": \"VELOCITY\", \"SIGN\": \"-\", \"EXPR\": \"0.5*rho_air*C_d*A_ref*sqrt(SPEED2)*VELOCITY\", \"LABEL\": \"the quadratic drag\"}], \"ASSUMPTIONS\": [{\"NAME\": \"air_still\", \"PROPOSITION\": \"the air is at rest in the frame of the body's velocity\", \"REFS\": [\"VELOCITY\"]}, {\"NAME\": \"air_uniform\", \"PROPOSITION\": \"the air density is uniform over the region of motion\", \"REFS\": [\"rho_air\"]}, {\"NAME\": \"drag_cd_constant\", \"PROPOSITION\": \"the drag coefficient C_d is constant over the motion\", \"REFS\": [\"C_d\"]}, {\"NAME\": \"drag_no_lift\", \"PROPOSITION\": \"the body experiences no lift force\", \"REFS\": [\"VELOCITY\"]}, {\"NAME\": \"drag_no_magnus\", \"PROPOSITION\": \"the body experiences no Magnus force\", \"REFS\": [\"VELOCITY\"]}], \"BOUNDARIES\": [{\"NAME\": \"drag_quadratic_regime\", \"PREDICATE\": \"1e3 < rho_air |v| L_ref / mu_air < 2e5: the Reynolds window of the quadratic law\", \"CONDITION\": \"mu_air != 0 and SPEED2 >= 0 and rho_air*sqrt(SPEED2)*L_ref/mu_air > 1000 and rho_air*sqrt(SPEED2)*L_ref/mu_air < 200000\"}], \"NOT_CHOSEN\": \"No quadratic air resistance.\", \"NOT_INCLUDED\": [\"No wind: the air is at rest.\", \"No change of air density or viscosity with altitude or temperature.\", \"No lift, Magnus or added-mass force.\", \"No drag outside the Reynolds window of the quadratic law.\"], \"EXCLUDES\": [\"AIR-LINEAR\"], \"INTERACTS_WITH\": [], \"TEST_BINDINGS\": [{\"NAME\": \"PROJECTILE_2D\", \"TPK\": {\"DOF\": [{\"NAME\": \"t\", \"DIMENSION\": \"T1\"}, {\"NAME\": \"x\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"z\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"v_x\", \"DIMENSION\": \"L1 T-1\"}, {\"NAME\": \"v_z\", \"DIMENSION\": \"L1 T-1\"}], \"CONSTANT\": [{\"NAME\": \"m\", \"DIMENSION\": \"M1\"}], \"LAW\": [{\"NAME\": \"KIN_X\", \"STATEMENT\": \"dx/dt = v_x\", \"REFS\": [\"t\", \"v_x\", \"x\"], \"ROLE\": \"EOM(x)\", \"EQUATION\": \"D(x,t)=v_x\"}, {\"NAME\": \"KIN_Z\", \"STATEMENT\": \"dz/dt = v_z\", \"REFS\": [\"t\", \"v_z\", \"z\"], \"ROLE\": \"EOM(z)\", \"EQUATION\": \"D(z,t)=v_z\"}, {\"NAME\": \"EOM_X\", \"STATEMENT\": \"m dv_x/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_x\"], \"ROLE\": \"EOM(v_x)\", \"EQUATION\": \"m*D(v_x,t)=0\"}, {\"NAME\": \"EOM_Z\", \"STATEMENT\": \"m dv_z/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_z\"], \"ROLE\": \"EOM(v_z)\", \"EQUATION\": \"m*D(v_z,t)=0\"}], \"ASSUMPTION\": [{\"NAME\": \"point_mass\", \"PROPOSITION\": \"the body is treated as a point mass\", \"REFS\": [\"m\"]}]}, \"BIND\": {\"VELOCITY\": [\"v_x\", \"v_z\"]}, \"VALUES\": {\"A_ref\": {}, \"C_d\": {}, \"L_ref\": {}}, \"ANSWERS\": {}}]}",
"{\"ID\": \"GRAV-UNIFORM\", \"VERSION\": \"1.0.0\", \"TITLE\": \"Uniform gravity at the standard value g_n\", \"SOURCE\": \"g_n = 9.80665 m s-2, exact by definition: 3rd CGPM (1901), declaration on the unit of mass and on the definition of weight\", \"PREREQUISITES\": [{\"SLOT\": \"MASS\", \"KIND\": \"CONSTANT\", \"DIMENSION\": \"M1\", \"MIN\": 1, \"MAX\": 1, \"LABEL\": \"the mass of the body\"}, {\"SLOT\": \"UP_VELOCITY\", \"KIND\": \"DOF\", \"DIMENSION\": \"L1 T-1\", \"MIN\": 1, \"MAX\": 1, \"LABEL\": \"the velocity component pointing up; its equation of motion receives the weight\"}, {\"SLOT\": \"HEIGHT\", \"KIND\": \"DOF\", \"DIMENSION\": \"L1\", \"MIN\": 1, \"MAX\": 1, \"LABEL\": \"the position along the same upward axis\"}], \"PARAMETERS\": [{\"NAME\": \"g_n\", \"DIMENSION\": \"L1 T-2\", \"SUPPLY\": \"DECLARED\", \"VALUE\": \"9.80665\", \"UNIT\": \"m s-2\", \"OVERRIDABLE\": \"NO\", \"LABEL\": \"the standard acceleration of gravity\"}, {\"NAME\": \"h_max\", \"DIMENSION\": \"L1\", \"SUPPLY\": \"AUTHOR\", \"LABEL\": \"the largest height, above or below the origin, over which the field is taken as uniform\"}], \"SUMS\": [], \"TERMS\": [{\"TARGET\": \"UP_VELOCITY\", \"SIGN\": \"-\", \"EXPR\": \"MASS*g_n\", \"LABEL\": \"the weight\"}], \"ASSUMPTIONS\": [{\"NAME\": \"gravity_uniform\", \"PROPOSITION\": \"the gravitational field is uniform over the region abs({HEIGHT}) < h_max\", \"REFS\": [\"HEIGHT\", \"h_max\"]}, {\"NAME\": \"gravity_standard\", \"PROPOSITION\": \"the local gravitational acceleration equals the conventional standard value g_n\", \"REFS\": [\"g_n\"]}, {\"NAME\": \"frame_inertial\", \"PROPOSITION\": \"the frame in which {HEIGHT} is measured is treated as inertial\", \"REFS\": [\"HEIGHT\"]}], \"BOUNDARIES\": [{\"NAME\": \"gravity_region\", \"PREDICATE\": \"abs({HEIGHT}) < h_max\", \"CONDITION\": \"abs(HEIGHT) < h_max\"}], \"NOT_CHOSEN\": \"No gravity: no weight acts on any DOF.\", \"NOT_INCLUDED\": [\"No variation of gravity with height or latitude beyond what g_n contains.\", \"No Earth rotation (Coriolis or centrifugal force) beyond what g_n contains.\", \"No gravity of bodies other than the Earth.\"], \"EXCLUDES\": [], \"INTERACTS_WITH\": [{\"WITH\": \"AIR-*\", \"QUESTION_ID\": \"BUOYANCY\", \"QUESTION\": \"Does the air's buoyancy (upthrust) act on the body in the system you mean?\", \"YES_LINE\": \"Buoyancy acts (your answer): no module adds it; it acts in this kernel only where one of your own laws states it.\", \"NO_LINE\": \"No buoyancy: the air's upthrust on the body is not included.\"}], \"TEST_BINDINGS\": [{\"NAME\": \"PROJECTILE_2D\", \"TPK\": {\"DOF\": [{\"NAME\": \"t\", \"DIMENSION\": \"T1\"}, {\"NAME\": \"x\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"z\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"v_x\", \"DIMENSION\": \"L1 T-1\"}, {\"NAME\": \"v_z\", \"DIMENSION\": \"L1 T-1\"}], \"CONSTANT\": [{\"NAME\": \"m\", \"DIMENSION\": \"M1\"}], \"LAW\": [{\"NAME\": \"KIN_X\", \"STATEMENT\": \"dx/dt = v_x\", \"REFS\": [\"t\", \"v_x\", \"x\"], \"ROLE\": \"EOM(x)\", \"EQUATION\": \"D(x,t)=v_x\"}, {\"NAME\": \"KIN_Z\", \"STATEMENT\": \"dz/dt = v_z\", \"REFS\": [\"t\", \"v_z\", \"z\"], \"ROLE\": \"EOM(z)\", \"EQUATION\": \"D(z,t)=v_z\"}, {\"NAME\": \"EOM_X\", \"STATEMENT\": \"m dv_x/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_x\"], \"ROLE\": \"EOM(v_x)\", \"EQUATION\": \"m*D(v_x,t)=0\"}, {\"NAME\": \"EOM_Z\", \"STATEMENT\": \"m dv_z/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_z\"], \"ROLE\": \"EOM(v_z)\", \"EQUATION\": \"m*D(v_z,t)=0\"}], \"ASSUMPTION\": [{\"NAME\": \"point_mass\", \"PROPOSITION\": \"the body is treated as a point mass\", \"REFS\": [\"m\"]}]}, \"BIND\": {\"HEIGHT\": [\"z\"], \"MASS\": [\"m\"], \"UP_VELOCITY\": [\"v_z\"]}, \"VALUES\": {\"h_max\": {\"VALUE\": \"100\", \"UNIT\": \"m\"}}, \"ANSWERS\": {}}, {\"NAME\": \"TABLE\", \"TPK\": {\"DOF\": [{\"NAME\": \"t\", \"DIMENSION\": \"T1\"}, {\"NAME\": \"x\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"z\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"v_x\", \"DIMENSION\": \"L1 T-1\"}, {\"NAME\": \"v_z\", \"DIMENSION\": \"L1 T-1\"}], \"CONSTANT\": [{\"NAME\": \"m\", \"DIMENSION\": \"M1\"}], \"LAW\": [{\"NAME\": \"KIN_X\", \"STATEMENT\": \"dx/dt = v_x\", \"REFS\": [\"t\", \"v_x\", \"x\"], \"ROLE\": \"EOM(x)\", \"EQUATION\": \"D(x,t)=v_x\"}, {\"NAME\": \"KIN_Z\", \"STATEMENT\": \"dz/dt = v_z\", \"REFS\": [\"t\", \"v_z\", \"z\"], \"ROLE\": \"CONSTRAINT\", \"EQUATION\": \"D(z,t)=v_z\"}, {\"NAME\": \"EOM_X\", \"STATEMENT\": \"m dv_x/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_x\"], \"ROLE\": \"EOM(v_x)\", \"EQUATION\": \"m*D(v_x,t)=0\"}], \"CONSTRAINT\": [{\"NAME\": \"C_Z\", \"TARGET\": \"z\", \"ACTION\": \"FIX\", \"VALUE\": \"0\", \"UNIT\": \"m\", \"STATEMENT\": \"the puck stays on the table top, z = 0\"}, {\"NAME\": \"C_VZ\", \"TARGET\": \"v_z\", \"ACTION\": \"FIX\", \"VALUE\": \"0\", \"UNIT\": \"m s-1\", \"STATEMENT\": \"the puck has no vertical velocity\"}]}, \"BIND\": {\"HEIGHT\": [\"z\"], \"MASS\": [\"m\"], \"UP_VELOCITY\": [\"v_z\"]}, \"VALUES\": {\"h_max\": {\"VALUE\": \"1\", \"UNIT\": \"m\"}}, \"ANSWERS\": {\"FIXED:v_z\": \"YES\"}}]}",
"{\"ID\": \"MATH\", \"VERSION\": \"1.0.0\", \"TITLE\": \"The mathematical constant pi, as the CONSTANT pi_c\", \"SOURCE\": \"pi to 16 significant digits, 3.141592653589793, the nearest IEEE 754 binary64 value\", \"PREREQUISITES\": [], \"PARAMETERS\": [{\"NAME\": \"pi_c\", \"DIMENSION\": \"1\", \"SUPPLY\": \"DECLARED\", \"VALUE\": \"3.141592653589793\", \"UNIT\": \"1\", \"OVERRIDABLE\": \"NO\", \"LABEL\": \"pi, to 16 significant digits\"}], \"SUMS\": [], \"TERMS\": [], \"ASSUMPTIONS\": [], \"BOUNDARIES\": [], \"NOT_CHOSEN\": \"No mathematical constant: pi exists only if you declare it.\", \"NOT_INCLUDED\": [\"pi_c is pi rounded to 16 significant digits; no other mathematical constant is declared.\"], \"EXCLUDES\": [], \"INTERACTS_WITH\": [], \"TEST_BINDINGS\": [{\"NAME\": \"PROJECTILE_2D\", \"TPK\": {\"DOF\": [{\"NAME\": \"t\", \"DIMENSION\": \"T1\"}, {\"NAME\": \"x\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"z\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"v_x\", \"DIMENSION\": \"L1 T-1\"}, {\"NAME\": \"v_z\", \"DIMENSION\": \"L1 T-1\"}], \"CONSTANT\": [{\"NAME\": \"m\", \"DIMENSION\": \"M1\"}], \"LAW\": [{\"NAME\": \"KIN_X\", \"STATEMENT\": \"dx/dt = v_x\", \"REFS\": [\"t\", \"v_x\", \"x\"], \"ROLE\": \"EOM(x)\", \"EQUATION\": \"D(x,t)=v_x\"}, {\"NAME\": \"KIN_Z\", \"STATEMENT\": \"dz/dt = v_z\", \"REFS\": [\"t\", \"v_z\", \"z\"], \"ROLE\": \"EOM(z)\", \"EQUATION\": \"D(z,t)=v_z\"}, {\"NAME\": \"EOM_X\", \"STATEMENT\": \"m dv_x/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_x\"], \"ROLE\": \"EOM(v_x)\", \"EQUATION\": \"m*D(v_x,t)=0\"}, {\"NAME\": \"EOM_Z\", \"STATEMENT\": \"m dv_z/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_z\"], \"ROLE\": \"EOM(v_z)\", \"EQUATION\": \"m*D(v_z,t)=0\"}], \"ASSUMPTION\": [{\"NAME\": \"point_mass\", \"PROPOSITION\": \"the body is treated as a point mass\", \"REFS\": [\"m\"]}]}, \"BIND\": {}, \"VALUES\": {}, \"ANSWERS\": {}}]}"
]
},
"expected": "[\"REFUSED\",\"ANSWER ROUND 1: AT is not a line count from 0 to 4\"]",
"fn": "interview_check",
"hand_checked": true,
"name": "I09 AT beyond the lines"
},
{
"args": {
"answer": [],
"carried": [],
"claims": [],
"lines": [
{
"ACT": "MODULE ADD",
"DATE": "2026-10-01",
"DIGEST": "5f3fe27b42378bce0830b0d0959f892f4a8e73b12b540ae877e39e6439d08b4d",
"ID": "AIR-LINEAR",
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},
{
"ACT": "MODULE ADD",
"DATE": "2026-10-01",
"DIGEST": "6fb53c3a6546151eead2bd6e72e9cf8334f3a2040ad0ee2f5b988ec96d6fc852",
"ID": "AIR-QUADRATIC",
"VERSION": "1.0.0"
},
{
"ACT": "MODULE ADD",
"DATE": "2026-10-01",
"DIGEST": "24877ccb5c8ec300d29ed82ce6650592f35cf8899a3d878ccce9c08d4c72c025",
"ID": "GRAV-UNIFORM",
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{
"ACT": "MODULE ADD",
"DATE": "2026-10-01",
"DIGEST": "8f39a356f35527b901fcee012764590f0819c8ffdeccad4bc05195ce3d2e0bcf",
"ID": "MATH",
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"modules": [
"{\"ID\": \"AIR-LINEAR\", \"VERSION\": \"1.0.0\", \"TITLE\": \"Air resistance at sea level, linear in the speed (Stokes drag on a sphere)\", \"SOURCE\": \"ISO 2533:1975, Standard Atmosphere, sea-level values: density 1.225 kg m-3, dynamic viscosity 1.7894e-5 Pa s\", \"PREREQUISITES\": [{\"SLOT\": \"VELOCITY\", \"KIND\": \"DOF\", \"DIMENSION\": \"L1 T-1\", \"MIN\": 1, \"MAX\": 3, \"LABEL\": \"the velocity components of the body, one per axis\"}], \"PARAMETERS\": [{\"NAME\": \"rho_air\", \"DIMENSION\": \"L-3 M1\", \"SUPPLY\": \"DECLARED\", \"VALUE\": \"1.225\", \"UNIT\": \"kg m-3\", \"OVERRIDABLE\": \"NO\", \"LABEL\": \"the density of air at sea level\"}, {\"NAME\": \"mu_air\", \"DIMENSION\": \"L-1 M1 T-1\", \"SUPPLY\": \"DECLARED\", \"VALUE\": \"1.7894e-5\", \"UNIT\": \"Pa s\", \"OVERRIDABLE\": \"NO\", \"LABEL\": \"the dynamic viscosity of air at sea level\"}, {\"NAME\": \"pi_c\", \"DIMENSION\": \"1\", \"SUPPLY\": \"DECLARED\", \"VALUE\": \"3.141592653589793\", \"UNIT\": \"1\", \"OVERRIDABLE\": \"NO\", \"LABEL\": \"pi, to 16 significant digits\"}, {\"NAME\": \"R_s\", \"DIMENSION\": \"L1\", \"SUPPLY\": \"AUTHOR\", \"LABEL\": \"the radius of the sphere\"}], \"SUMS\": [{\"NAME\": \"SPEED2\", \"OVER\": \"VELOCITY\", \"EACH\": \"VELOCITY^2\"}], \"TERMS\": [{\"TARGET\": \"VELOCITY\", \"SIGN\": \"-\", \"EXPR\": \"6*pi_c*mu_air*R_s*VELOCITY\", \"LABEL\": \"the linear (Stokes) drag\"}], \"ASSUMPTIONS\": [{\"NAME\": \"air_still\", \"PROPOSITION\": \"the air is at rest in the frame of the body's velocity\", \"REFS\": [\"VELOCITY\"]}, {\"NAME\": \"air_uniform\", \"PROPOSITION\": \"the air density is uniform over the region of motion\", \"REFS\": [\"rho_air\"]}, {\"NAME\": \"drag_sphere\", \"PROPOSITION\": \"the body is a rigid sphere of radius R_s\", \"REFS\": [\"R_s\"]}], \"BOUNDARIES\": [{\"NAME\": \"drag_linear_regime\", \"PREDICATE\": \"2 rho_air |v| R_s / mu_air < 1: the regime of the linear law\", \"CONDITION\": \"mu_air != 0 and SPEED2 >= 0 and 2*rho_air*sqrt(SPEED2)*R_s/mu_air < 1\"}], \"NOT_CHOSEN\": \"No linear (Stokes) air resistance.\", \"NOT_INCLUDED\": [\"No wind: the air is at rest.\", \"No change of air density or viscosity with altitude or temperature.\", \"No drag outside the regime of the linear law.\"], \"EXCLUDES\": [], \"INTERACTS_WITH\": [], \"TEST_BINDINGS\": [{\"NAME\": \"PROJECTILE_2D\", \"TPK\": {\"DOF\": [{\"NAME\": \"t\", \"DIMENSION\": \"T1\"}, {\"NAME\": \"x\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"z\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"v_x\", \"DIMENSION\": \"L1 T-1\"}, {\"NAME\": \"v_z\", \"DIMENSION\": \"L1 T-1\"}], \"CONSTANT\": [{\"NAME\": \"m\", \"DIMENSION\": \"M1\"}], \"LAW\": [{\"NAME\": \"KIN_X\", \"STATEMENT\": \"dx/dt = v_x\", \"REFS\": [\"t\", \"v_x\", \"x\"], \"ROLE\": \"EOM(x)\", \"EQUATION\": \"D(x,t)=v_x\"}, {\"NAME\": \"KIN_Z\", \"STATEMENT\": \"dz/dt = v_z\", \"REFS\": [\"t\", \"v_z\", \"z\"], \"ROLE\": \"EOM(z)\", \"EQUATION\": \"D(z,t)=v_z\"}, {\"NAME\": \"EOM_X\", \"STATEMENT\": \"m dv_x/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_x\"], \"ROLE\": \"EOM(v_x)\", \"EQUATION\": \"m*D(v_x,t)=0\"}, {\"NAME\": \"EOM_Z\", \"STATEMENT\": \"m dv_z/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_z\"], \"ROLE\": \"EOM(v_z)\", \"EQUATION\": \"m*D(v_z,t)=0\"}], \"ASSUMPTION\": [{\"NAME\": \"point_mass\", \"PROPOSITION\": \"the body is treated as a point mass\", \"REFS\": [\"m\"]}]}, \"BIND\": {\"VELOCITY\": [\"v_x\", \"v_z\"]}, \"VALUES\": {\"R_s\": {}}, \"ANSWERS\": {}}]}",
"{\"ID\": \"AIR-QUADRATIC\", \"VERSION\": \"1.0.0\", \"TITLE\": \"Air resistance at sea level, quadratic in the speed\", \"SOURCE\": \"ISO 2533:1975, Standard Atmosphere, sea-level values: density 1.225 kg m-3, dynamic viscosity 1.7894e-5 Pa s\", \"PREREQUISITES\": [{\"SLOT\": \"VELOCITY\", \"KIND\": \"DOF\", \"DIMENSION\": \"L1 T-1\", \"MIN\": 1, \"MAX\": 3, \"LABEL\": \"the velocity components of the body, one per axis\"}], \"PARAMETERS\": [{\"NAME\": \"rho_air\", \"DIMENSION\": \"L-3 M1\", \"SUPPLY\": \"DECLARED\", \"VALUE\": \"1.225\", \"UNIT\": \"kg m-3\", \"OVERRIDABLE\": \"NO\", \"LABEL\": \"the density of air at sea level\"}, {\"NAME\": \"mu_air\", \"DIMENSION\": \"L-1 M1 T-1\", \"SUPPLY\": \"DECLARED\", \"VALUE\": \"1.7894e-5\", \"UNIT\": \"Pa s\", \"OVERRIDABLE\": \"NO\", \"LABEL\": \"the dynamic viscosity of air at sea level\"}, {\"NAME\": \"C_d\", \"DIMENSION\": \"1\", \"SUPPLY\": \"AUTHOR\", \"LABEL\": \"the drag coefficient of the body\"}, {\"NAME\": \"A_ref\", \"DIMENSION\": \"L2\", \"SUPPLY\": \"AUTHOR\", \"LABEL\": \"the reference area of the drag coefficient\"}, {\"NAME\": \"L_ref\", \"DIMENSION\": \"L1\", \"SUPPLY\": \"AUTHOR\", \"LABEL\": \"the reference length of the Reynolds number\"}], \"SUMS\": [{\"NAME\": \"SPEED2\", \"OVER\": \"VELOCITY\", \"EACH\": \"VELOCITY^2\"}], \"TERMS\": [{\"TARGET\": \"VELOCITY\", \"SIGN\": \"-\", \"EXPR\": \"0.5*rho_air*C_d*A_ref*sqrt(SPEED2)*VELOCITY\", \"LABEL\": \"the quadratic drag\"}], \"ASSUMPTIONS\": [{\"NAME\": \"air_still\", \"PROPOSITION\": \"the air is at rest in the frame of the body's velocity\", \"REFS\": [\"VELOCITY\"]}, {\"NAME\": \"air_uniform\", \"PROPOSITION\": \"the air density is uniform over the region of motion\", \"REFS\": [\"rho_air\"]}, {\"NAME\": \"drag_cd_constant\", \"PROPOSITION\": \"the drag coefficient C_d is constant over the motion\", \"REFS\": [\"C_d\"]}, {\"NAME\": \"drag_no_lift\", \"PROPOSITION\": \"the body experiences no lift force\", \"REFS\": [\"VELOCITY\"]}, {\"NAME\": \"drag_no_magnus\", \"PROPOSITION\": \"the body experiences no Magnus force\", \"REFS\": [\"VELOCITY\"]}], \"BOUNDARIES\": [{\"NAME\": \"drag_quadratic_regime\", \"PREDICATE\": \"1e3 < rho_air |v| L_ref / mu_air < 2e5: the Reynolds window of the quadratic law\", \"CONDITION\": \"mu_air != 0 and SPEED2 >= 0 and rho_air*sqrt(SPEED2)*L_ref/mu_air > 1000 and rho_air*sqrt(SPEED2)*L_ref/mu_air < 200000\"}], \"NOT_CHOSEN\": \"No quadratic air resistance.\", \"NOT_INCLUDED\": [\"No wind: the air is at rest.\", \"No change of air density or viscosity with altitude or temperature.\", \"No lift, Magnus or added-mass force.\", \"No drag outside the Reynolds window of the quadratic law.\"], \"EXCLUDES\": [\"AIR-LINEAR\"], \"INTERACTS_WITH\": [], \"TEST_BINDINGS\": [{\"NAME\": \"PROJECTILE_2D\", \"TPK\": {\"DOF\": [{\"NAME\": \"t\", \"DIMENSION\": \"T1\"}, {\"NAME\": \"x\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"z\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"v_x\", \"DIMENSION\": \"L1 T-1\"}, {\"NAME\": \"v_z\", \"DIMENSION\": \"L1 T-1\"}], \"CONSTANT\": [{\"NAME\": \"m\", \"DIMENSION\": \"M1\"}], \"LAW\": [{\"NAME\": \"KIN_X\", \"STATEMENT\": \"dx/dt = v_x\", \"REFS\": [\"t\", \"v_x\", \"x\"], \"ROLE\": \"EOM(x)\", \"EQUATION\": \"D(x,t)=v_x\"}, {\"NAME\": \"KIN_Z\", \"STATEMENT\": \"dz/dt = v_z\", \"REFS\": [\"t\", \"v_z\", \"z\"], \"ROLE\": \"EOM(z)\", \"EQUATION\": \"D(z,t)=v_z\"}, {\"NAME\": \"EOM_X\", \"STATEMENT\": \"m dv_x/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_x\"], \"ROLE\": \"EOM(v_x)\", \"EQUATION\": \"m*D(v_x,t)=0\"}, {\"NAME\": \"EOM_Z\", \"STATEMENT\": \"m dv_z/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_z\"], \"ROLE\": \"EOM(v_z)\", \"EQUATION\": \"m*D(v_z,t)=0\"}], \"ASSUMPTION\": [{\"NAME\": \"point_mass\", \"PROPOSITION\": \"the body is treated as a point mass\", \"REFS\": [\"m\"]}]}, \"BIND\": {\"VELOCITY\": [\"v_x\", \"v_z\"]}, \"VALUES\": {\"A_ref\": {}, \"C_d\": {}, \"L_ref\": {}}, \"ANSWERS\": {}}]}",
"{\"ID\": \"GRAV-UNIFORM\", \"VERSION\": \"1.0.0\", \"TITLE\": \"Uniform gravity at the standard value g_n\", \"SOURCE\": \"g_n = 9.80665 m s-2, exact by definition: 3rd CGPM (1901), declaration on the unit of mass and on the definition of weight\", \"PREREQUISITES\": [{\"SLOT\": \"MASS\", \"KIND\": \"CONSTANT\", \"DIMENSION\": \"M1\", \"MIN\": 1, \"MAX\": 1, \"LABEL\": \"the mass of the body\"}, {\"SLOT\": \"UP_VELOCITY\", \"KIND\": \"DOF\", \"DIMENSION\": \"L1 T-1\", \"MIN\": 1, \"MAX\": 1, \"LABEL\": \"the velocity component pointing up; its equation of motion receives the weight\"}, {\"SLOT\": \"HEIGHT\", \"KIND\": \"DOF\", \"DIMENSION\": \"L1\", \"MIN\": 1, \"MAX\": 1, \"LABEL\": \"the position along the same upward axis\"}], \"PARAMETERS\": [{\"NAME\": \"g_n\", \"DIMENSION\": \"L1 T-2\", \"SUPPLY\": \"DECLARED\", \"VALUE\": \"9.80665\", \"UNIT\": \"m s-2\", \"OVERRIDABLE\": \"NO\", \"LABEL\": \"the standard acceleration of gravity\"}, {\"NAME\": \"h_max\", \"DIMENSION\": \"L1\", \"SUPPLY\": \"AUTHOR\", \"LABEL\": \"the largest height, above or below the origin, over which the field is taken as uniform\"}], \"SUMS\": [], \"TERMS\": [{\"TARGET\": \"UP_VELOCITY\", \"SIGN\": \"-\", \"EXPR\": \"MASS*g_n\", \"LABEL\": \"the weight\"}], \"ASSUMPTIONS\": [{\"NAME\": \"gravity_uniform\", \"PROPOSITION\": \"the gravitational field is uniform over the region abs({HEIGHT}) < h_max\", \"REFS\": [\"HEIGHT\", \"h_max\"]}, {\"NAME\": \"gravity_standard\", \"PROPOSITION\": \"the local gravitational acceleration equals the conventional standard value g_n\", \"REFS\": [\"g_n\"]}, {\"NAME\": \"frame_inertial\", \"PROPOSITION\": \"the frame in which {HEIGHT} is measured is treated as inertial\", \"REFS\": [\"HEIGHT\"]}], \"BOUNDARIES\": [{\"NAME\": \"gravity_region\", \"PREDICATE\": \"abs({HEIGHT}) < h_max\", \"CONDITION\": \"abs(HEIGHT) < h_max\"}], \"NOT_CHOSEN\": \"No gravity: no weight acts on any DOF.\", \"NOT_INCLUDED\": [\"No variation of gravity with height or latitude beyond what g_n contains.\", \"No Earth rotation (Coriolis or centrifugal force) beyond what g_n contains.\", \"No gravity of bodies other than the Earth.\"], \"EXCLUDES\": [], \"INTERACTS_WITH\": [{\"WITH\": \"AIR-*\", \"QUESTION_ID\": \"BUOYANCY\", \"QUESTION\": \"Does the air's buoyancy (upthrust) act on the body in the system you mean?\", \"YES_LINE\": \"Buoyancy acts (your answer): no module adds it; it acts in this kernel only where one of your own laws states it.\", \"NO_LINE\": \"No buoyancy: the air's upthrust on the body is not included.\"}], \"TEST_BINDINGS\": [{\"NAME\": \"PROJECTILE_2D\", \"TPK\": {\"DOF\": [{\"NAME\": \"t\", \"DIMENSION\": \"T1\"}, {\"NAME\": \"x\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"z\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"v_x\", \"DIMENSION\": \"L1 T-1\"}, {\"NAME\": \"v_z\", \"DIMENSION\": \"L1 T-1\"}], \"CONSTANT\": [{\"NAME\": \"m\", \"DIMENSION\": \"M1\"}], \"LAW\": [{\"NAME\": \"KIN_X\", \"STATEMENT\": \"dx/dt = v_x\", \"REFS\": [\"t\", \"v_x\", \"x\"], \"ROLE\": \"EOM(x)\", \"EQUATION\": \"D(x,t)=v_x\"}, {\"NAME\": \"KIN_Z\", \"STATEMENT\": \"dz/dt = v_z\", \"REFS\": [\"t\", \"v_z\", \"z\"], \"ROLE\": \"EOM(z)\", \"EQUATION\": \"D(z,t)=v_z\"}, {\"NAME\": \"EOM_X\", \"STATEMENT\": \"m dv_x/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_x\"], \"ROLE\": \"EOM(v_x)\", \"EQUATION\": \"m*D(v_x,t)=0\"}, {\"NAME\": \"EOM_Z\", \"STATEMENT\": \"m dv_z/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_z\"], \"ROLE\": \"EOM(v_z)\", \"EQUATION\": \"m*D(v_z,t)=0\"}], \"ASSUMPTION\": [{\"NAME\": \"point_mass\", \"PROPOSITION\": \"the body is treated as a point mass\", \"REFS\": [\"m\"]}]}, \"BIND\": {\"HEIGHT\": [\"z\"], \"MASS\": [\"m\"], \"UP_VELOCITY\": [\"v_z\"]}, \"VALUES\": {\"h_max\": {\"VALUE\": \"100\", \"UNIT\": \"m\"}}, \"ANSWERS\": {}}, {\"NAME\": \"TABLE\", \"TPK\": {\"DOF\": [{\"NAME\": \"t\", \"DIMENSION\": \"T1\"}, {\"NAME\": \"x\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"z\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"v_x\", \"DIMENSION\": \"L1 T-1\"}, {\"NAME\": \"v_z\", \"DIMENSION\": \"L1 T-1\"}], \"CONSTANT\": [{\"NAME\": \"m\", \"DIMENSION\": \"M1\"}], \"LAW\": [{\"NAME\": \"KIN_X\", \"STATEMENT\": \"dx/dt = v_x\", \"REFS\": [\"t\", \"v_x\", \"x\"], \"ROLE\": \"EOM(x)\", \"EQUATION\": \"D(x,t)=v_x\"}, {\"NAME\": \"KIN_Z\", \"STATEMENT\": \"dz/dt = v_z\", \"REFS\": [\"t\", \"v_z\", \"z\"], \"ROLE\": \"CONSTRAINT\", \"EQUATION\": \"D(z,t)=v_z\"}, {\"NAME\": \"EOM_X\", \"STATEMENT\": \"m dv_x/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_x\"], \"ROLE\": \"EOM(v_x)\", \"EQUATION\": \"m*D(v_x,t)=0\"}], \"CONSTRAINT\": [{\"NAME\": \"C_Z\", \"TARGET\": \"z\", \"ACTION\": \"FIX\", \"VALUE\": \"0\", \"UNIT\": \"m\", \"STATEMENT\": \"the puck stays on the table top, z = 0\"}, {\"NAME\": \"C_VZ\", \"TARGET\": \"v_z\", \"ACTION\": \"FIX\", \"VALUE\": \"0\", \"UNIT\": \"m s-1\", \"STATEMENT\": \"the puck has no vertical velocity\"}]}, \"BIND\": {\"HEIGHT\": [\"z\"], \"MASS\": [\"m\"], \"UP_VELOCITY\": [\"v_z\"]}, \"VALUES\": {\"h_max\": {\"VALUE\": \"1\", \"UNIT\": \"m\"}}, \"ANSWERS\": {\"FIXED:v_z\": \"YES\"}}]}",
"{\"ID\": \"MATH\", \"VERSION\": \"1.0.0\", \"TITLE\": \"The mathematical constant pi, as the CONSTANT pi_c\", \"SOURCE\": \"pi to 16 significant digits, 3.141592653589793, the nearest IEEE 754 binary64 value\", \"PREREQUISITES\": [], \"PARAMETERS\": [{\"NAME\": \"pi_c\", \"DIMENSION\": \"1\", \"SUPPLY\": \"DECLARED\", \"VALUE\": \"3.141592653589793\", \"UNIT\": \"1\", \"OVERRIDABLE\": \"NO\", \"LABEL\": \"pi, to 16 significant digits\"}], \"SUMS\": [], \"TERMS\": [], \"ASSUMPTIONS\": [], \"BOUNDARIES\": [], \"NOT_CHOSEN\": \"No mathematical constant: pi exists only if you declare it.\", \"NOT_INCLUDED\": [\"pi_c is pi rounded to 16 significant digits; no other mathematical constant is declared.\"], \"EXCLUDES\": [], \"INTERACTS_WITH\": [], \"TEST_BINDINGS\": [{\"NAME\": \"PROJECTILE_2D\", \"TPK\": {\"DOF\": [{\"NAME\": \"t\", \"DIMENSION\": \"T1\"}, {\"NAME\": \"x\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"z\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"v_x\", \"DIMENSION\": \"L1 T-1\"}, {\"NAME\": \"v_z\", \"DIMENSION\": \"L1 T-1\"}], \"CONSTANT\": [{\"NAME\": \"m\", \"DIMENSION\": \"M1\"}], \"LAW\": [{\"NAME\": \"KIN_X\", \"STATEMENT\": \"dx/dt = v_x\", \"REFS\": [\"t\", \"v_x\", \"x\"], \"ROLE\": \"EOM(x)\", \"EQUATION\": \"D(x,t)=v_x\"}, {\"NAME\": \"KIN_Z\", \"STATEMENT\": \"dz/dt = v_z\", \"REFS\": [\"t\", \"v_z\", \"z\"], \"ROLE\": \"EOM(z)\", \"EQUATION\": \"D(z,t)=v_z\"}, {\"NAME\": \"EOM_X\", \"STATEMENT\": \"m dv_x/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_x\"], \"ROLE\": \"EOM(v_x)\", \"EQUATION\": \"m*D(v_x,t)=0\"}, {\"NAME\": \"EOM_Z\", \"STATEMENT\": \"m dv_z/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_z\"], \"ROLE\": \"EOM(v_z)\", \"EQUATION\": \"m*D(v_z,t)=0\"}], \"ASSUMPTION\": [{\"NAME\": \"point_mass\", \"PROPOSITION\": \"the body is treated as a point mass\", \"REFS\": [\"m\"]}]}, \"BIND\": {}, \"VALUES\": {}, \"ANSWERS\": {}}]}"
]
},
"expected": "[\"REFUSED\",\"INTERACTIONS: not answered\"]",
"fn": "interview_check",
"hand_checked": true,
"name": "I10 no round: the interaction question not answered"
},
{
"args": {
"answer": {
"AT": 4,
"CHOSEN": "NONE",
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"lines": [
{
"ACT": "MODULE ADD",
"DATE": "2026-10-01",
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"{\"ID\": \"AIR-LINEAR\", \"VERSION\": \"1.0.0\", \"TITLE\": \"Air resistance at sea level, linear in the speed (Stokes drag on a sphere)\", \"SOURCE\": \"ISO 2533:1975, Standard Atmosphere, sea-level values: density 1.225 kg m-3, dynamic viscosity 1.7894e-5 Pa s\", \"PREREQUISITES\": [{\"SLOT\": \"VELOCITY\", \"KIND\": \"DOF\", \"DIMENSION\": \"L1 T-1\", \"MIN\": 1, \"MAX\": 3, \"LABEL\": \"the velocity components of the body, one per axis\"}], \"PARAMETERS\": [{\"NAME\": \"rho_air\", \"DIMENSION\": \"L-3 M1\", \"SUPPLY\": \"DECLARED\", \"VALUE\": \"1.225\", \"UNIT\": \"kg m-3\", \"OVERRIDABLE\": \"NO\", \"LABEL\": \"the density of air at sea level\"}, {\"NAME\": \"mu_air\", \"DIMENSION\": \"L-1 M1 T-1\", \"SUPPLY\": \"DECLARED\", \"VALUE\": \"1.7894e-5\", \"UNIT\": \"Pa s\", \"OVERRIDABLE\": \"NO\", \"LABEL\": \"the dynamic viscosity of air at sea level\"}, {\"NAME\": \"pi_c\", \"DIMENSION\": \"1\", \"SUPPLY\": \"DECLARED\", \"VALUE\": \"3.141592653589793\", \"UNIT\": \"1\", \"OVERRIDABLE\": \"NO\", \"LABEL\": \"pi, to 16 significant digits\"}, {\"NAME\": \"R_s\", \"DIMENSION\": \"L1\", \"SUPPLY\": \"AUTHOR\", \"LABEL\": \"the radius of the sphere\"}], \"SUMS\": [{\"NAME\": \"SPEED2\", \"OVER\": \"VELOCITY\", \"EACH\": \"VELOCITY^2\"}], \"TERMS\": [{\"TARGET\": \"VELOCITY\", \"SIGN\": \"-\", \"EXPR\": \"6*pi_c*mu_air*R_s*VELOCITY\", \"LABEL\": \"the linear (Stokes) drag\"}], \"ASSUMPTIONS\": [{\"NAME\": \"air_still\", \"PROPOSITION\": \"the air is at rest in the frame of the body's velocity\", \"REFS\": [\"VELOCITY\"]}, {\"NAME\": \"air_uniform\", \"PROPOSITION\": \"the air density is uniform over the region of motion\", \"REFS\": [\"rho_air\"]}, {\"NAME\": \"drag_sphere\", \"PROPOSITION\": \"the body is a rigid sphere of radius R_s\", \"REFS\": [\"R_s\"]}], \"BOUNDARIES\": [{\"NAME\": \"drag_linear_regime\", \"PREDICATE\": \"2 rho_air |v| R_s / mu_air < 1: the regime of the linear law\", \"CONDITION\": \"mu_air != 0 and SPEED2 >= 0 and 2*rho_air*sqrt(SPEED2)*R_s/mu_air < 1\"}], \"NOT_CHOSEN\": \"No linear (Stokes) air resistance.\", \"NOT_INCLUDED\": [\"No wind: the air is at rest.\", \"No change of air density or viscosity with altitude or temperature.\", \"No drag outside the regime of the linear law.\"], \"EXCLUDES\": [], \"INTERACTS_WITH\": [], \"TEST_BINDINGS\": [{\"NAME\": \"PROJECTILE_2D\", \"TPK\": {\"DOF\": [{\"NAME\": \"t\", \"DIMENSION\": \"T1\"}, {\"NAME\": \"x\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"z\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"v_x\", \"DIMENSION\": \"L1 T-1\"}, {\"NAME\": \"v_z\", \"DIMENSION\": \"L1 T-1\"}], \"CONSTANT\": [{\"NAME\": \"m\", \"DIMENSION\": \"M1\"}], \"LAW\": [{\"NAME\": \"KIN_X\", \"STATEMENT\": \"dx/dt = v_x\", \"REFS\": [\"t\", \"v_x\", \"x\"], \"ROLE\": \"EOM(x)\", \"EQUATION\": \"D(x,t)=v_x\"}, {\"NAME\": \"KIN_Z\", \"STATEMENT\": \"dz/dt = v_z\", \"REFS\": [\"t\", \"v_z\", \"z\"], \"ROLE\": \"EOM(z)\", \"EQUATION\": \"D(z,t)=v_z\"}, {\"NAME\": \"EOM_X\", \"STATEMENT\": \"m dv_x/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_x\"], \"ROLE\": \"EOM(v_x)\", \"EQUATION\": \"m*D(v_x,t)=0\"}, {\"NAME\": \"EOM_Z\", \"STATEMENT\": \"m dv_z/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_z\"], \"ROLE\": \"EOM(v_z)\", \"EQUATION\": \"m*D(v_z,t)=0\"}], \"ASSUMPTION\": [{\"NAME\": \"point_mass\", \"PROPOSITION\": \"the body is treated as a point mass\", \"REFS\": [\"m\"]}]}, \"BIND\": {\"VELOCITY\": [\"v_x\", \"v_z\"]}, \"VALUES\": {\"R_s\": {}}, \"ANSWERS\": {}}]}",
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it acts in this kernel only where one of your own laws states it.\", \"NO_LINE\": \"No buoyancy: the air's upthrust on the body is not included.\"}], \"TEST_BINDINGS\": [{\"NAME\": \"PROJECTILE_2D\", \"TPK\": {\"DOF\": [{\"NAME\": \"t\", \"DIMENSION\": \"T1\"}, {\"NAME\": \"x\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"z\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"v_x\", \"DIMENSION\": \"L1 T-1\"}, {\"NAME\": \"v_z\", \"DIMENSION\": \"L1 T-1\"}], \"CONSTANT\": [{\"NAME\": \"m\", \"DIMENSION\": \"M1\"}], \"LAW\": [{\"NAME\": \"KIN_X\", \"STATEMENT\": \"dx/dt = v_x\", \"REFS\": [\"t\", \"v_x\", \"x\"], \"ROLE\": \"EOM(x)\", \"EQUATION\": \"D(x,t)=v_x\"}, {\"NAME\": \"KIN_Z\", \"STATEMENT\": \"dz/dt = v_z\", \"REFS\": [\"t\", \"v_z\", \"z\"], \"ROLE\": \"EOM(z)\", \"EQUATION\": \"D(z,t)=v_z\"}, {\"NAME\": \"EOM_X\", \"STATEMENT\": \"m dv_x/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_x\"], \"ROLE\": \"EOM(v_x)\", \"EQUATION\": \"m*D(v_x,t)=0\"}, {\"NAME\": \"EOM_Z\", \"STATEMENT\": \"m dv_z/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_z\"], \"ROLE\": \"EOM(v_z)\", \"EQUATION\": \"m*D(v_z,t)=0\"}], \"ASSUMPTION\": [{\"NAME\": \"point_mass\", \"PROPOSITION\": \"the body is treated as a point mass\", \"REFS\": [\"m\"]}]}, \"BIND\": {\"HEIGHT\": [\"z\"], \"MASS\": [\"m\"], \"UP_VELOCITY\": [\"v_z\"]}, \"VALUES\": {\"h_max\": {\"VALUE\": \"100\", \"UNIT\": \"m\"}}, \"ANSWERS\": {}}, {\"NAME\": \"TABLE\", \"TPK\": {\"DOF\": [{\"NAME\": \"t\", \"DIMENSION\": \"T1\"}, {\"NAME\": \"x\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"z\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"v_x\", \"DIMENSION\": \"L1 T-1\"}, {\"NAME\": \"v_z\", \"DIMENSION\": \"L1 T-1\"}], \"CONSTANT\": [{\"NAME\": \"m\", \"DIMENSION\": \"M1\"}], \"LAW\": [{\"NAME\": \"KIN_X\", \"STATEMENT\": \"dx/dt = v_x\", \"REFS\": [\"t\", \"v_x\", \"x\"], \"ROLE\": \"EOM(x)\", \"EQUATION\": \"D(x,t)=v_x\"}, {\"NAME\": \"KIN_Z\", \"STATEMENT\": \"dz/dt = v_z\", \"REFS\": [\"t\", \"v_z\", \"z\"], \"ROLE\": \"CONSTRAINT\", \"EQUATION\": \"D(z,t)=v_z\"}, {\"NAME\": \"EOM_X\", \"STATEMENT\": \"m dv_x/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_x\"], \"ROLE\": \"EOM(v_x)\", \"EQUATION\": \"m*D(v_x,t)=0\"}], \"CONSTRAINT\": [{\"NAME\": \"C_Z\", \"TARGET\": \"z\", \"ACTION\": \"FIX\", \"VALUE\": \"0\", \"UNIT\": \"m\", \"STATEMENT\": \"the puck stays on the table top, z = 0\"}, {\"NAME\": \"C_VZ\", \"TARGET\": \"v_z\", \"ACTION\": \"FIX\", \"VALUE\": \"0\", \"UNIT\": \"m s-1\", \"STATEMENT\": \"the puck has no vertical velocity\"}]}, \"BIND\": {\"HEIGHT\": [\"z\"], \"MASS\": [\"m\"], \"UP_VELOCITY\": [\"v_z\"]}, \"VALUES\": {\"h_max\": {\"VALUE\": \"1\", \"UNIT\": \"m\"}}, \"ANSWERS\": {\"FIXED:v_z\": \"YES\"}}]}",
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"{\"ID\": \"AIR-LINEAR\", \"VERSION\": \"1.0.0\", \"TITLE\": \"Air resistance at sea level, linear in the speed (Stokes drag on a sphere)\", \"SOURCE\": \"ISO 2533:1975, Standard Atmosphere, sea-level values: density 1.225 kg m-3, dynamic viscosity 1.7894e-5 Pa s\", \"PREREQUISITES\": [{\"SLOT\": \"VELOCITY\", \"KIND\": \"DOF\", \"DIMENSION\": \"L1 T-1\", \"MIN\": 1, \"MAX\": 3, \"LABEL\": \"the velocity components of the body, one per axis\"}], \"PARAMETERS\": [{\"NAME\": \"rho_air\", \"DIMENSION\": \"L-3 M1\", \"SUPPLY\": \"DECLARED\", \"VALUE\": \"1.225\", \"UNIT\": \"kg m-3\", \"OVERRIDABLE\": \"NO\", \"LABEL\": \"the density of air at sea level\"}, {\"NAME\": \"mu_air\", \"DIMENSION\": \"L-1 M1 T-1\", \"SUPPLY\": \"DECLARED\", \"VALUE\": \"1.7894e-5\", \"UNIT\": \"Pa s\", \"OVERRIDABLE\": \"NO\", \"LABEL\": \"the dynamic viscosity of air at sea level\"}, {\"NAME\": \"pi_c\", \"DIMENSION\": \"1\", \"SUPPLY\": \"DECLARED\", \"VALUE\": \"3.141592653589793\", \"UNIT\": \"1\", \"OVERRIDABLE\": \"NO\", \"LABEL\": \"pi, to 16 significant digits\"}, {\"NAME\": \"R_s\", \"DIMENSION\": \"L1\", \"SUPPLY\": \"AUTHOR\", \"LABEL\": \"the radius of the sphere\"}], \"SUMS\": [{\"NAME\": \"SPEED2\", \"OVER\": \"VELOCITY\", \"EACH\": \"VELOCITY^2\"}], \"TERMS\": [{\"TARGET\": \"VELOCITY\", \"SIGN\": \"-\", \"EXPR\": \"6*pi_c*mu_air*R_s*VELOCITY\", \"LABEL\": \"the linear (Stokes) drag\"}], \"ASSUMPTIONS\": [{\"NAME\": \"air_still\", \"PROPOSITION\": \"the air is at rest in the frame of the body's velocity\", \"REFS\": [\"VELOCITY\"]}, {\"NAME\": \"air_uniform\", \"PROPOSITION\": \"the air density is uniform over the region of motion\", \"REFS\": [\"rho_air\"]}, {\"NAME\": \"drag_sphere\", \"PROPOSITION\": \"the body is a rigid sphere of radius R_s\", \"REFS\": [\"R_s\"]}], \"BOUNDARIES\": [{\"NAME\": \"drag_linear_regime\", \"PREDICATE\": \"2 rho_air |v| R_s / mu_air < 1: the regime of the linear law\", \"CONDITION\": \"mu_air != 0 and SPEED2 >= 0 and 2*rho_air*sqrt(SPEED2)*R_s/mu_air < 1\"}], \"NOT_CHOSEN\": \"No linear (Stokes) air resistance.\", \"NOT_INCLUDED\": [\"No wind: the air is at rest.\", \"No change of air density or viscosity with altitude or temperature.\", \"No drag outside the regime of the linear law.\"], \"EXCLUDES\": [], \"INTERACTS_WITH\": [], \"TEST_BINDINGS\": [{\"NAME\": \"PROJECTILE_2D\", \"TPK\": {\"DOF\": [{\"NAME\": \"t\", \"DIMENSION\": \"T1\"}, {\"NAME\": \"x\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"z\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"v_x\", \"DIMENSION\": \"L1 T-1\"}, {\"NAME\": \"v_z\", \"DIMENSION\": \"L1 T-1\"}], \"CONSTANT\": [{\"NAME\": \"m\", \"DIMENSION\": \"M1\"}], \"LAW\": [{\"NAME\": \"KIN_X\", \"STATEMENT\": \"dx/dt = v_x\", \"REFS\": [\"t\", \"v_x\", \"x\"], \"ROLE\": \"EOM(x)\", \"EQUATION\": \"D(x,t)=v_x\"}, {\"NAME\": \"KIN_Z\", \"STATEMENT\": \"dz/dt = v_z\", \"REFS\": [\"t\", \"v_z\", \"z\"], \"ROLE\": \"EOM(z)\", \"EQUATION\": \"D(z,t)=v_z\"}, {\"NAME\": \"EOM_X\", \"STATEMENT\": \"m dv_x/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_x\"], \"ROLE\": \"EOM(v_x)\", \"EQUATION\": \"m*D(v_x,t)=0\"}, {\"NAME\": \"EOM_Z\", \"STATEMENT\": \"m dv_z/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_z\"], \"ROLE\": \"EOM(v_z)\", \"EQUATION\": \"m*D(v_z,t)=0\"}], \"ASSUMPTION\": [{\"NAME\": \"point_mass\", \"PROPOSITION\": \"the body is treated as a point mass\", \"REFS\": [\"m\"]}]}, \"BIND\": {\"VELOCITY\": [\"v_x\", \"v_z\"]}, \"VALUES\": {\"R_s\": {}}, \"ANSWERS\": {}}]}",
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{
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{
"ACT": "MODULE ADD",
"DATE": "2026-10-01",
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"modules": [
"{\"ID\": \"AIR-LINEAR\", \"VERSION\": \"1.0.0\", \"TITLE\": \"Air resistance at sea level, linear in the speed (Stokes drag on a sphere)\", \"SOURCE\": \"ISO 2533:1975, Standard Atmosphere, sea-level values: density 1.225 kg m-3, dynamic viscosity 1.7894e-5 Pa s\", \"PREREQUISITES\": [{\"SLOT\": \"VELOCITY\", \"KIND\": \"DOF\", \"DIMENSION\": \"L1 T-1\", \"MIN\": 1, \"MAX\": 3, \"LABEL\": \"the velocity components of the body, one per axis\"}], \"PARAMETERS\": [{\"NAME\": \"rho_air\", \"DIMENSION\": \"L-3 M1\", \"SUPPLY\": \"DECLARED\", \"VALUE\": \"1.225\", \"UNIT\": \"kg m-3\", \"OVERRIDABLE\": \"NO\", \"LABEL\": \"the density of air at sea level\"}, {\"NAME\": \"mu_air\", \"DIMENSION\": \"L-1 M1 T-1\", \"SUPPLY\": \"DECLARED\", \"VALUE\": \"1.7894e-5\", \"UNIT\": \"Pa s\", \"OVERRIDABLE\": \"NO\", \"LABEL\": \"the dynamic viscosity of air at sea level\"}, {\"NAME\": \"pi_c\", \"DIMENSION\": \"1\", \"SUPPLY\": \"DECLARED\", \"VALUE\": \"3.141592653589793\", \"UNIT\": \"1\", \"OVERRIDABLE\": \"NO\", \"LABEL\": \"pi, to 16 significant digits\"}, {\"NAME\": \"R_s\", \"DIMENSION\": \"L1\", \"SUPPLY\": \"AUTHOR\", \"LABEL\": \"the radius of the sphere\"}], \"SUMS\": [{\"NAME\": \"SPEED2\", \"OVER\": \"VELOCITY\", \"EACH\": \"VELOCITY^2\"}], \"TERMS\": [{\"TARGET\": \"VELOCITY\", \"SIGN\": \"-\", \"EXPR\": \"6*pi_c*mu_air*R_s*VELOCITY\", \"LABEL\": \"the linear (Stokes) drag\"}], \"ASSUMPTIONS\": [{\"NAME\": \"air_still\", \"PROPOSITION\": \"the air is at rest in the frame of the body's velocity\", \"REFS\": [\"VELOCITY\"]}, {\"NAME\": \"air_uniform\", \"PROPOSITION\": \"the air density is uniform over the region of motion\", \"REFS\": [\"rho_air\"]}, {\"NAME\": \"drag_sphere\", \"PROPOSITION\": \"the body is a rigid sphere of radius R_s\", \"REFS\": [\"R_s\"]}], \"BOUNDARIES\": [{\"NAME\": \"drag_linear_regime\", \"PREDICATE\": \"2 rho_air |v| R_s / mu_air < 1: the regime of the linear law\", \"CONDITION\": \"mu_air != 0 and SPEED2 >= 0 and 2*rho_air*sqrt(SPEED2)*R_s/mu_air < 1\"}], \"NOT_CHOSEN\": \"No linear (Stokes) air resistance.\", \"NOT_INCLUDED\": [\"No wind: the air is at rest.\", \"No change of air density or viscosity with altitude or temperature.\", \"No drag outside the regime of the linear law.\"], \"EXCLUDES\": [], \"INTERACTS_WITH\": [], \"TEST_BINDINGS\": [{\"NAME\": \"PROJECTILE_2D\", \"TPK\": {\"DOF\": [{\"NAME\": \"t\", \"DIMENSION\": \"T1\"}, {\"NAME\": \"x\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"z\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"v_x\", \"DIMENSION\": \"L1 T-1\"}, {\"NAME\": \"v_z\", \"DIMENSION\": \"L1 T-1\"}], \"CONSTANT\": [{\"NAME\": \"m\", \"DIMENSION\": \"M1\"}], \"LAW\": [{\"NAME\": \"KIN_X\", \"STATEMENT\": \"dx/dt = v_x\", \"REFS\": [\"t\", \"v_x\", \"x\"], \"ROLE\": \"EOM(x)\", \"EQUATION\": \"D(x,t)=v_x\"}, {\"NAME\": \"KIN_Z\", \"STATEMENT\": \"dz/dt = v_z\", \"REFS\": [\"t\", \"v_z\", \"z\"], \"ROLE\": \"EOM(z)\", \"EQUATION\": \"D(z,t)=v_z\"}, {\"NAME\": \"EOM_X\", \"STATEMENT\": \"m dv_x/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_x\"], \"ROLE\": \"EOM(v_x)\", \"EQUATION\": \"m*D(v_x,t)=0\"}, {\"NAME\": \"EOM_Z\", \"STATEMENT\": \"m dv_z/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_z\"], \"ROLE\": \"EOM(v_z)\", \"EQUATION\": \"m*D(v_z,t)=0\"}], \"ASSUMPTION\": [{\"NAME\": \"point_mass\", \"PROPOSITION\": \"the body is treated as a point mass\", \"REFS\": [\"m\"]}]}, \"BIND\": {\"VELOCITY\": [\"v_x\", \"v_z\"]}, \"VALUES\": {\"R_s\": {}}, \"ANSWERS\": {}}]}",
"{\"ID\": \"AIR-QUADRATIC\", \"VERSION\": \"1.0.0\", \"TITLE\": \"Air resistance at sea level, quadratic in the speed\", \"SOURCE\": \"ISO 2533:1975, Standard Atmosphere, sea-level values: density 1.225 kg m-3, dynamic viscosity 1.7894e-5 Pa s\", \"PREREQUISITES\": [{\"SLOT\": \"VELOCITY\", \"KIND\": \"DOF\", \"DIMENSION\": \"L1 T-1\", \"MIN\": 1, \"MAX\": 3, \"LABEL\": \"the velocity components of the body, one per axis\"}], \"PARAMETERS\": [{\"NAME\": \"rho_air\", \"DIMENSION\": \"L-3 M1\", \"SUPPLY\": \"DECLARED\", \"VALUE\": \"1.225\", \"UNIT\": \"kg m-3\", \"OVERRIDABLE\": \"NO\", \"LABEL\": \"the density of air at sea level\"}, {\"NAME\": \"mu_air\", \"DIMENSION\": \"L-1 M1 T-1\", \"SUPPLY\": \"DECLARED\", \"VALUE\": \"1.7894e-5\", \"UNIT\": \"Pa s\", \"OVERRIDABLE\": \"NO\", \"LABEL\": \"the dynamic viscosity of air at sea level\"}, {\"NAME\": \"C_d\", \"DIMENSION\": \"1\", \"SUPPLY\": \"AUTHOR\", \"LABEL\": \"the drag coefficient of the body\"}, {\"NAME\": \"A_ref\", \"DIMENSION\": \"L2\", \"SUPPLY\": \"AUTHOR\", \"LABEL\": \"the reference area of the drag coefficient\"}, {\"NAME\": \"L_ref\", \"DIMENSION\": \"L1\", \"SUPPLY\": \"AUTHOR\", \"LABEL\": \"the reference length of the Reynolds number\"}], \"SUMS\": [{\"NAME\": \"SPEED2\", \"OVER\": \"VELOCITY\", \"EACH\": \"VELOCITY^2\"}], \"TERMS\": [{\"TARGET\": \"VELOCITY\", \"SIGN\": \"-\", \"EXPR\": \"0.5*rho_air*C_d*A_ref*sqrt(SPEED2)*VELOCITY\", \"LABEL\": \"the quadratic drag\"}], \"ASSUMPTIONS\": [{\"NAME\": \"air_still\", \"PROPOSITION\": \"the air is at rest in the frame of the body's velocity\", \"REFS\": [\"VELOCITY\"]}, {\"NAME\": \"air_uniform\", \"PROPOSITION\": \"the air density is uniform over the region of motion\", \"REFS\": [\"rho_air\"]}, {\"NAME\": \"drag_cd_constant\", \"PROPOSITION\": \"the drag coefficient C_d is constant over the motion\", \"REFS\": [\"C_d\"]}, {\"NAME\": \"drag_no_lift\", \"PROPOSITION\": \"the body experiences no lift force\", \"REFS\": [\"VELOCITY\"]}, {\"NAME\": \"drag_no_magnus\", \"PROPOSITION\": \"the body experiences no Magnus force\", \"REFS\": [\"VELOCITY\"]}], \"BOUNDARIES\": [{\"NAME\": \"drag_quadratic_regime\", \"PREDICATE\": \"1e3 < rho_air |v| L_ref / mu_air < 2e5: the Reynolds window of the quadratic law\", \"CONDITION\": \"mu_air != 0 and SPEED2 >= 0 and rho_air*sqrt(SPEED2)*L_ref/mu_air > 1000 and rho_air*sqrt(SPEED2)*L_ref/mu_air < 200000\"}], \"NOT_CHOSEN\": \"No quadratic air resistance.\", \"NOT_INCLUDED\": [\"No wind: the air is at rest.\", \"No change of air density or viscosity with altitude or temperature.\", \"No lift, Magnus or added-mass force.\", \"No drag outside the Reynolds window of the quadratic law.\"], \"EXCLUDES\": [\"AIR-LINEAR\"], \"INTERACTS_WITH\": [], \"TEST_BINDINGS\": [{\"NAME\": \"PROJECTILE_2D\", \"TPK\": {\"DOF\": [{\"NAME\": \"t\", \"DIMENSION\": \"T1\"}, {\"NAME\": \"x\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"z\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"v_x\", \"DIMENSION\": \"L1 T-1\"}, {\"NAME\": \"v_z\", \"DIMENSION\": \"L1 T-1\"}], \"CONSTANT\": [{\"NAME\": \"m\", \"DIMENSION\": \"M1\"}], \"LAW\": [{\"NAME\": \"KIN_X\", \"STATEMENT\": \"dx/dt = v_x\", \"REFS\": [\"t\", \"v_x\", \"x\"], \"ROLE\": \"EOM(x)\", \"EQUATION\": \"D(x,t)=v_x\"}, {\"NAME\": \"KIN_Z\", \"STATEMENT\": \"dz/dt = v_z\", \"REFS\": [\"t\", \"v_z\", \"z\"], \"ROLE\": \"EOM(z)\", \"EQUATION\": \"D(z,t)=v_z\"}, {\"NAME\": \"EOM_X\", \"STATEMENT\": \"m dv_x/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_x\"], \"ROLE\": \"EOM(v_x)\", \"EQUATION\": \"m*D(v_x,t)=0\"}, {\"NAME\": \"EOM_Z\", \"STATEMENT\": \"m dv_z/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_z\"], \"ROLE\": \"EOM(v_z)\", \"EQUATION\": \"m*D(v_z,t)=0\"}], \"ASSUMPTION\": [{\"NAME\": \"point_mass\", \"PROPOSITION\": \"the body is treated as a point mass\", \"REFS\": [\"m\"]}]}, \"BIND\": {\"VELOCITY\": [\"v_x\", \"v_z\"]}, \"VALUES\": {\"A_ref\": {}, \"C_d\": {}, \"L_ref\": {}}, \"ANSWERS\": {}}]}",
"{\"ID\": \"GRAV-UNIFORM\", \"VERSION\": \"1.0.0\", \"TITLE\": \"Uniform gravity at the standard value g_n\", \"SOURCE\": \"g_n = 9.80665 m s-2, exact by definition: 3rd CGPM (1901), declaration on the unit of mass and on the definition of weight\", \"PREREQUISITES\": [{\"SLOT\": \"MASS\", \"KIND\": \"CONSTANT\", \"DIMENSION\": \"M1\", \"MIN\": 1, \"MAX\": 1, \"LABEL\": \"the mass of the body\"}, {\"SLOT\": \"UP_VELOCITY\", \"KIND\": \"DOF\", \"DIMENSION\": \"L1 T-1\", \"MIN\": 1, \"MAX\": 1, \"LABEL\": \"the velocity component pointing up; its equation of motion receives the weight\"}, {\"SLOT\": \"HEIGHT\", \"KIND\": \"DOF\", \"DIMENSION\": \"L1\", \"MIN\": 1, \"MAX\": 1, \"LABEL\": \"the position along the same upward axis\"}], \"PARAMETERS\": [{\"NAME\": \"g_n\", \"DIMENSION\": \"L1 T-2\", \"SUPPLY\": \"DECLARED\", \"VALUE\": \"9.80665\", \"UNIT\": \"m s-2\", \"OVERRIDABLE\": \"NO\", \"LABEL\": \"the standard acceleration of gravity\"}, {\"NAME\": \"h_max\", \"DIMENSION\": \"L1\", \"SUPPLY\": \"AUTHOR\", \"LABEL\": \"the largest height, above or below the origin, over which the field is taken as uniform\"}], \"SUMS\": [], \"TERMS\": [{\"TARGET\": \"UP_VELOCITY\", \"SIGN\": \"-\", \"EXPR\": \"MASS*g_n\", \"LABEL\": \"the weight\"}], \"ASSUMPTIONS\": [{\"NAME\": \"gravity_uniform\", \"PROPOSITION\": \"the gravitational field is uniform over the region abs({HEIGHT}) < h_max\", \"REFS\": [\"HEIGHT\", \"h_max\"]}, {\"NAME\": \"gravity_standard\", \"PROPOSITION\": \"the local gravitational acceleration equals the conventional standard value g_n\", \"REFS\": [\"g_n\"]}, {\"NAME\": \"frame_inertial\", \"PROPOSITION\": \"the frame in which {HEIGHT} is measured is treated as inertial\", \"REFS\": [\"HEIGHT\"]}], \"BOUNDARIES\": [{\"NAME\": \"gravity_region\", \"PREDICATE\": \"abs({HEIGHT}) < h_max\", \"CONDITION\": \"abs(HEIGHT) < h_max\"}], \"NOT_CHOSEN\": \"No gravity: no weight acts on any DOF.\", \"NOT_INCLUDED\": [\"No variation of gravity with height or latitude beyond what g_n contains.\", \"No Earth rotation (Coriolis or centrifugal force) beyond what g_n contains.\", \"No gravity of bodies other than the Earth.\"], \"EXCLUDES\": [], \"INTERACTS_WITH\": [{\"WITH\": \"AIR-*\", \"QUESTION_ID\": \"BUOYANCY\", \"QUESTION\": \"Does the air's buoyancy (upthrust) act on the body in the system you mean?\", \"YES_LINE\": \"Buoyancy acts (your answer): no module adds it; it acts in this kernel only where one of your own laws states it.\", \"NO_LINE\": \"No buoyancy: the air's upthrust on the body is not included.\"}], \"TEST_BINDINGS\": [{\"NAME\": \"PROJECTILE_2D\", \"TPK\": {\"DOF\": [{\"NAME\": \"t\", \"DIMENSION\": \"T1\"}, {\"NAME\": \"x\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"z\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"v_x\", \"DIMENSION\": \"L1 T-1\"}, {\"NAME\": \"v_z\", \"DIMENSION\": \"L1 T-1\"}], \"CONSTANT\": [{\"NAME\": \"m\", \"DIMENSION\": \"M1\"}], \"LAW\": [{\"NAME\": \"KIN_X\", \"STATEMENT\": \"dx/dt = v_x\", \"REFS\": [\"t\", \"v_x\", \"x\"], \"ROLE\": \"EOM(x)\", \"EQUATION\": \"D(x,t)=v_x\"}, {\"NAME\": \"KIN_Z\", \"STATEMENT\": \"dz/dt = v_z\", \"REFS\": [\"t\", \"v_z\", \"z\"], \"ROLE\": \"EOM(z)\", \"EQUATION\": \"D(z,t)=v_z\"}, {\"NAME\": \"EOM_X\", \"STATEMENT\": \"m dv_x/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_x\"], \"ROLE\": \"EOM(v_x)\", \"EQUATION\": \"m*D(v_x,t)=0\"}, {\"NAME\": \"EOM_Z\", \"STATEMENT\": \"m dv_z/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_z\"], \"ROLE\": \"EOM(v_z)\", \"EQUATION\": \"m*D(v_z,t)=0\"}], \"ASSUMPTION\": [{\"NAME\": \"point_mass\", \"PROPOSITION\": \"the body is treated as a point mass\", \"REFS\": [\"m\"]}]}, \"BIND\": {\"HEIGHT\": [\"z\"], \"MASS\": [\"m\"], \"UP_VELOCITY\": [\"v_z\"]}, \"VALUES\": {\"h_max\": {\"VALUE\": \"100\", \"UNIT\": \"m\"}}, \"ANSWERS\": {}}, {\"NAME\": \"TABLE\", \"TPK\": {\"DOF\": [{\"NAME\": \"t\", \"DIMENSION\": \"T1\"}, {\"NAME\": \"x\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"z\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"v_x\", \"DIMENSION\": \"L1 T-1\"}, {\"NAME\": \"v_z\", \"DIMENSION\": \"L1 T-1\"}], \"CONSTANT\": [{\"NAME\": \"m\", \"DIMENSION\": \"M1\"}], \"LAW\": [{\"NAME\": \"KIN_X\", \"STATEMENT\": \"dx/dt = v_x\", \"REFS\": [\"t\", \"v_x\", \"x\"], \"ROLE\": \"EOM(x)\", \"EQUATION\": \"D(x,t)=v_x\"}, {\"NAME\": \"KIN_Z\", \"STATEMENT\": \"dz/dt = v_z\", \"REFS\": [\"t\", \"v_z\", \"z\"], \"ROLE\": \"CONSTRAINT\", \"EQUATION\": \"D(z,t)=v_z\"}, {\"NAME\": \"EOM_X\", \"STATEMENT\": \"m dv_x/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_x\"], \"ROLE\": \"EOM(v_x)\", \"EQUATION\": \"m*D(v_x,t)=0\"}], \"CONSTRAINT\": [{\"NAME\": \"C_Z\", \"TARGET\": \"z\", \"ACTION\": \"FIX\", \"VALUE\": \"0\", \"UNIT\": \"m\", \"STATEMENT\": \"the puck stays on the table top, z = 0\"}, {\"NAME\": \"C_VZ\", \"TARGET\": \"v_z\", \"ACTION\": \"FIX\", \"VALUE\": \"0\", \"UNIT\": \"m s-1\", \"STATEMENT\": \"the puck has no vertical velocity\"}]}, \"BIND\": {\"HEIGHT\": [\"z\"], \"MASS\": [\"m\"], \"UP_VELOCITY\": [\"v_z\"]}, \"VALUES\": {\"h_max\": {\"VALUE\": \"1\", \"UNIT\": \"m\"}}, \"ANSWERS\": {\"FIXED:v_z\": \"YES\"}}]}",
"{\"ID\": \"MATH\", \"VERSION\": \"1.0.0\", \"TITLE\": \"The mathematical constant pi, as the CONSTANT pi_c\", \"SOURCE\": \"pi to 16 significant digits, 3.141592653589793, the nearest IEEE 754 binary64 value\", \"PREREQUISITES\": [], \"PARAMETERS\": [{\"NAME\": \"pi_c\", \"DIMENSION\": \"1\", \"SUPPLY\": \"DECLARED\", \"VALUE\": \"3.141592653589793\", \"UNIT\": \"1\", \"OVERRIDABLE\": \"NO\", \"LABEL\": \"pi, to 16 significant digits\"}], \"SUMS\": [], \"TERMS\": [], \"ASSUMPTIONS\": [], \"BOUNDARIES\": [], \"NOT_CHOSEN\": \"No mathematical constant: pi exists only if you declare it.\", \"NOT_INCLUDED\": [\"pi_c is pi rounded to 16 significant digits; no other mathematical constant is declared.\"], \"EXCLUDES\": [], \"INTERACTS_WITH\": [], \"TEST_BINDINGS\": [{\"NAME\": \"PROJECTILE_2D\", \"TPK\": {\"DOF\": [{\"NAME\": \"t\", \"DIMENSION\": \"T1\"}, {\"NAME\": \"x\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"z\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"v_x\", \"DIMENSION\": \"L1 T-1\"}, {\"NAME\": \"v_z\", \"DIMENSION\": \"L1 T-1\"}], \"CONSTANT\": [{\"NAME\": \"m\", \"DIMENSION\": \"M1\"}], \"LAW\": [{\"NAME\": \"KIN_X\", \"STATEMENT\": \"dx/dt = v_x\", \"REFS\": [\"t\", \"v_x\", \"x\"], \"ROLE\": \"EOM(x)\", \"EQUATION\": \"D(x,t)=v_x\"}, {\"NAME\": \"KIN_Z\", \"STATEMENT\": \"dz/dt = v_z\", \"REFS\": [\"t\", \"v_z\", \"z\"], \"ROLE\": \"EOM(z)\", \"EQUATION\": \"D(z,t)=v_z\"}, {\"NAME\": \"EOM_X\", \"STATEMENT\": \"m dv_x/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_x\"], \"ROLE\": \"EOM(v_x)\", \"EQUATION\": \"m*D(v_x,t)=0\"}, {\"NAME\": \"EOM_Z\", \"STATEMENT\": \"m dv_z/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_z\"], \"ROLE\": \"EOM(v_z)\", \"EQUATION\": \"m*D(v_z,t)=0\"}], \"ASSUMPTION\": [{\"NAME\": \"point_mass\", \"PROPOSITION\": \"the body is treated as a point mass\", \"REFS\": [\"m\"]}]}, \"BIND\": {}, \"VALUES\": {}, \"ANSWERS\": {}}]}"
]
},
"expected": "[\"REFUSED\",\"ANSWER ROUND 1: CHOSEN is not in code point order without repeats\"]",
"fn": "interview_check",
"hand_checked": true,
"name": "I13 CHOSEN out of order"
},
{
"args": {
"answer": [
{
"AT": 4,
"CHOSEN": [
"TEST-X"
],
"COVERED": [
[
"AIR-LINEAR",
"1.0.0",
"5f3fe27b42378bce0830b0d0959f892f4a8e73b12b540ae877e39e6439d08b4d"
],
[
"AIR-QUADRATIC",
"1.0.0",
"6fb53c3a6546151eead2bd6e72e9cf8334f3a2040ad0ee2f5b988ec96d6fc852"
],
[
"GRAV-UNIFORM",
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"24877ccb5c8ec300d29ed82ce6650592f35cf8899a3d878ccce9c08d4c72c025"
],
[
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"8f39a356f35527b901fcee012764590f0819c8ffdeccad4bc05195ce3d2e0bcf"
]
]
}
],
"carried": [],
"claims": [],
"lines": [
{
"ACT": "MODULE ADD",
"DATE": "2026-10-01",
"DIGEST": "5f3fe27b42378bce0830b0d0959f892f4a8e73b12b540ae877e39e6439d08b4d",
"ID": "AIR-LINEAR",
"VERSION": "1.0.0"
},
{
"ACT": "MODULE ADD",
"DATE": "2026-10-01",
"DIGEST": "6fb53c3a6546151eead2bd6e72e9cf8334f3a2040ad0ee2f5b988ec96d6fc852",
"ID": "AIR-QUADRATIC",
"VERSION": "1.0.0"
},
{
"ACT": "MODULE ADD",
"DATE": "2026-10-01",
"DIGEST": "24877ccb5c8ec300d29ed82ce6650592f35cf8899a3d878ccce9c08d4c72c025",
"ID": "GRAV-UNIFORM",
"VERSION": "1.0.0"
},
{
"ACT": "MODULE ADD",
"DATE": "2026-10-01",
"DIGEST": "8f39a356f35527b901fcee012764590f0819c8ffdeccad4bc05195ce3d2e0bcf",
"ID": "MATH",
"VERSION": "1.0.0"
}
],
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"modules": [
"{\"ID\": \"AIR-LINEAR\", \"VERSION\": \"1.0.0\", \"TITLE\": \"Air resistance at sea level, linear in the speed (Stokes drag on a sphere)\", \"SOURCE\": \"ISO 2533:1975, Standard Atmosphere, sea-level values: density 1.225 kg m-3, dynamic viscosity 1.7894e-5 Pa s\", \"PREREQUISITES\": [{\"SLOT\": \"VELOCITY\", \"KIND\": \"DOF\", \"DIMENSION\": \"L1 T-1\", \"MIN\": 1, \"MAX\": 3, \"LABEL\": \"the velocity components of the body, one per axis\"}], \"PARAMETERS\": [{\"NAME\": \"rho_air\", \"DIMENSION\": \"L-3 M1\", \"SUPPLY\": \"DECLARED\", \"VALUE\": \"1.225\", \"UNIT\": \"kg m-3\", \"OVERRIDABLE\": \"NO\", \"LABEL\": \"the density of air at sea level\"}, {\"NAME\": \"mu_air\", \"DIMENSION\": \"L-1 M1 T-1\", \"SUPPLY\": \"DECLARED\", \"VALUE\": \"1.7894e-5\", \"UNIT\": \"Pa s\", \"OVERRIDABLE\": \"NO\", \"LABEL\": \"the dynamic viscosity of air at sea level\"}, {\"NAME\": \"pi_c\", \"DIMENSION\": \"1\", \"SUPPLY\": \"DECLARED\", \"VALUE\": \"3.141592653589793\", \"UNIT\": \"1\", \"OVERRIDABLE\": \"NO\", \"LABEL\": \"pi, to 16 significant digits\"}, {\"NAME\": \"R_s\", \"DIMENSION\": \"L1\", \"SUPPLY\": \"AUTHOR\", \"LABEL\": \"the radius of the sphere\"}], \"SUMS\": [{\"NAME\": \"SPEED2\", \"OVER\": \"VELOCITY\", \"EACH\": \"VELOCITY^2\"}], \"TERMS\": [{\"TARGET\": \"VELOCITY\", \"SIGN\": \"-\", \"EXPR\": \"6*pi_c*mu_air*R_s*VELOCITY\", \"LABEL\": \"the linear (Stokes) drag\"}], \"ASSUMPTIONS\": [{\"NAME\": \"air_still\", \"PROPOSITION\": \"the air is at rest in the frame of the body's velocity\", \"REFS\": [\"VELOCITY\"]}, {\"NAME\": \"air_uniform\", \"PROPOSITION\": \"the air density is uniform over the region of motion\", \"REFS\": [\"rho_air\"]}, {\"NAME\": \"drag_sphere\", \"PROPOSITION\": \"the body is a rigid sphere of radius R_s\", \"REFS\": [\"R_s\"]}], \"BOUNDARIES\": [{\"NAME\": \"drag_linear_regime\", \"PREDICATE\": \"2 rho_air |v| R_s / mu_air < 1: the regime of the linear law\", \"CONDITION\": \"mu_air != 0 and SPEED2 >= 0 and 2*rho_air*sqrt(SPEED2)*R_s/mu_air < 1\"}], \"NOT_CHOSEN\": \"No linear (Stokes) air resistance.\", \"NOT_INCLUDED\": [\"No wind: the air is at rest.\", \"No change of air density or viscosity with altitude or temperature.\", \"No drag outside the regime of the linear law.\"], \"EXCLUDES\": [], \"INTERACTS_WITH\": [], \"TEST_BINDINGS\": [{\"NAME\": \"PROJECTILE_2D\", \"TPK\": {\"DOF\": [{\"NAME\": \"t\", \"DIMENSION\": \"T1\"}, {\"NAME\": \"x\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"z\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"v_x\", \"DIMENSION\": \"L1 T-1\"}, {\"NAME\": \"v_z\", \"DIMENSION\": \"L1 T-1\"}], \"CONSTANT\": [{\"NAME\": \"m\", \"DIMENSION\": \"M1\"}], \"LAW\": [{\"NAME\": \"KIN_X\", \"STATEMENT\": \"dx/dt = v_x\", \"REFS\": [\"t\", \"v_x\", \"x\"], \"ROLE\": \"EOM(x)\", \"EQUATION\": \"D(x,t)=v_x\"}, {\"NAME\": \"KIN_Z\", \"STATEMENT\": \"dz/dt = v_z\", \"REFS\": [\"t\", \"v_z\", \"z\"], \"ROLE\": \"EOM(z)\", \"EQUATION\": \"D(z,t)=v_z\"}, {\"NAME\": \"EOM_X\", \"STATEMENT\": \"m dv_x/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_x\"], \"ROLE\": \"EOM(v_x)\", \"EQUATION\": \"m*D(v_x,t)=0\"}, {\"NAME\": \"EOM_Z\", \"STATEMENT\": \"m dv_z/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_z\"], \"ROLE\": \"EOM(v_z)\", \"EQUATION\": \"m*D(v_z,t)=0\"}], \"ASSUMPTION\": [{\"NAME\": \"point_mass\", \"PROPOSITION\": \"the body is treated as a point mass\", \"REFS\": [\"m\"]}]}, \"BIND\": {\"VELOCITY\": [\"v_x\", \"v_z\"]}, \"VALUES\": {\"R_s\": {}}, \"ANSWERS\": {}}]}",
"{\"ID\": \"AIR-QUADRATIC\", \"VERSION\": \"1.0.0\", \"TITLE\": \"Air resistance at sea level, quadratic in the speed\", \"SOURCE\": \"ISO 2533:1975, Standard Atmosphere, sea-level values: density 1.225 kg m-3, dynamic viscosity 1.7894e-5 Pa s\", \"PREREQUISITES\": [{\"SLOT\": \"VELOCITY\", \"KIND\": \"DOF\", \"DIMENSION\": \"L1 T-1\", \"MIN\": 1, \"MAX\": 3, \"LABEL\": \"the velocity components of the body, one per axis\"}], \"PARAMETERS\": [{\"NAME\": \"rho_air\", \"DIMENSION\": \"L-3 M1\", \"SUPPLY\": \"DECLARED\", \"VALUE\": \"1.225\", \"UNIT\": \"kg m-3\", \"OVERRIDABLE\": \"NO\", \"LABEL\": \"the density of air at sea level\"}, {\"NAME\": \"mu_air\", \"DIMENSION\": \"L-1 M1 T-1\", \"SUPPLY\": \"DECLARED\", \"VALUE\": \"1.7894e-5\", \"UNIT\": \"Pa s\", \"OVERRIDABLE\": \"NO\", \"LABEL\": \"the dynamic viscosity of air at sea level\"}, {\"NAME\": \"C_d\", \"DIMENSION\": \"1\", \"SUPPLY\": \"AUTHOR\", \"LABEL\": \"the drag coefficient of the body\"}, {\"NAME\": \"A_ref\", \"DIMENSION\": \"L2\", \"SUPPLY\": \"AUTHOR\", \"LABEL\": \"the reference area of the drag coefficient\"}, {\"NAME\": \"L_ref\", \"DIMENSION\": \"L1\", \"SUPPLY\": \"AUTHOR\", \"LABEL\": \"the reference length of the Reynolds number\"}], \"SUMS\": [{\"NAME\": \"SPEED2\", \"OVER\": \"VELOCITY\", \"EACH\": \"VELOCITY^2\"}], \"TERMS\": [{\"TARGET\": \"VELOCITY\", \"SIGN\": \"-\", \"EXPR\": \"0.5*rho_air*C_d*A_ref*sqrt(SPEED2)*VELOCITY\", \"LABEL\": \"the quadratic drag\"}], \"ASSUMPTIONS\": [{\"NAME\": \"air_still\", \"PROPOSITION\": \"the air is at rest in the frame of the body's velocity\", \"REFS\": [\"VELOCITY\"]}, {\"NAME\": \"air_uniform\", \"PROPOSITION\": \"the air density is uniform over the region of motion\", \"REFS\": [\"rho_air\"]}, {\"NAME\": \"drag_cd_constant\", \"PROPOSITION\": \"the drag coefficient C_d is constant over the motion\", \"REFS\": [\"C_d\"]}, {\"NAME\": \"drag_no_lift\", \"PROPOSITION\": \"the body experiences no lift force\", \"REFS\": [\"VELOCITY\"]}, {\"NAME\": \"drag_no_magnus\", \"PROPOSITION\": \"the body experiences no Magnus force\", \"REFS\": [\"VELOCITY\"]}], \"BOUNDARIES\": [{\"NAME\": \"drag_quadratic_regime\", \"PREDICATE\": \"1e3 < rho_air |v| L_ref / mu_air < 2e5: the Reynolds window of the quadratic law\", \"CONDITION\": \"mu_air != 0 and SPEED2 >= 0 and rho_air*sqrt(SPEED2)*L_ref/mu_air > 1000 and rho_air*sqrt(SPEED2)*L_ref/mu_air < 200000\"}], \"NOT_CHOSEN\": \"No quadratic air resistance.\", \"NOT_INCLUDED\": [\"No wind: the air is at rest.\", \"No change of air density or viscosity with altitude or temperature.\", \"No lift, Magnus or added-mass force.\", \"No drag outside the Reynolds window of the quadratic law.\"], \"EXCLUDES\": [\"AIR-LINEAR\"], \"INTERACTS_WITH\": [], \"TEST_BINDINGS\": [{\"NAME\": \"PROJECTILE_2D\", \"TPK\": {\"DOF\": [{\"NAME\": \"t\", \"DIMENSION\": \"T1\"}, {\"NAME\": \"x\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"z\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"v_x\", \"DIMENSION\": \"L1 T-1\"}, {\"NAME\": \"v_z\", \"DIMENSION\": \"L1 T-1\"}], \"CONSTANT\": [{\"NAME\": \"m\", \"DIMENSION\": \"M1\"}], \"LAW\": [{\"NAME\": \"KIN_X\", \"STATEMENT\": \"dx/dt = v_x\", \"REFS\": [\"t\", \"v_x\", \"x\"], \"ROLE\": \"EOM(x)\", \"EQUATION\": \"D(x,t)=v_x\"}, {\"NAME\": \"KIN_Z\", \"STATEMENT\": \"dz/dt = v_z\", \"REFS\": [\"t\", \"v_z\", \"z\"], \"ROLE\": \"EOM(z)\", \"EQUATION\": \"D(z,t)=v_z\"}, {\"NAME\": \"EOM_X\", \"STATEMENT\": \"m dv_x/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_x\"], \"ROLE\": \"EOM(v_x)\", \"EQUATION\": \"m*D(v_x,t)=0\"}, {\"NAME\": \"EOM_Z\", \"STATEMENT\": \"m dv_z/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_z\"], \"ROLE\": \"EOM(v_z)\", \"EQUATION\": \"m*D(v_z,t)=0\"}], \"ASSUMPTION\": [{\"NAME\": \"point_mass\", \"PROPOSITION\": \"the body is treated as a point mass\", \"REFS\": [\"m\"]}]}, \"BIND\": {\"VELOCITY\": [\"v_x\", \"v_z\"]}, \"VALUES\": {\"A_ref\": {}, \"C_d\": {}, \"L_ref\": {}}, \"ANSWERS\": {}}]}",
"{\"ID\": \"GRAV-UNIFORM\", \"VERSION\": \"1.0.0\", \"TITLE\": \"Uniform gravity at the standard value g_n\", \"SOURCE\": \"g_n = 9.80665 m s-2, exact by definition: 3rd CGPM (1901), declaration on the unit of mass and on the definition of weight\", \"PREREQUISITES\": [{\"SLOT\": \"MASS\", \"KIND\": \"CONSTANT\", \"DIMENSION\": \"M1\", \"MIN\": 1, \"MAX\": 1, \"LABEL\": \"the mass of the body\"}, {\"SLOT\": \"UP_VELOCITY\", \"KIND\": \"DOF\", \"DIMENSION\": \"L1 T-1\", \"MIN\": 1, \"MAX\": 1, \"LABEL\": \"the velocity component pointing up; its equation of motion receives the weight\"}, {\"SLOT\": \"HEIGHT\", \"KIND\": \"DOF\", \"DIMENSION\": \"L1\", \"MIN\": 1, \"MAX\": 1, \"LABEL\": \"the position along the same upward axis\"}], \"PARAMETERS\": [{\"NAME\": \"g_n\", \"DIMENSION\": \"L1 T-2\", \"SUPPLY\": \"DECLARED\", \"VALUE\": \"9.80665\", \"UNIT\": \"m s-2\", \"OVERRIDABLE\": \"NO\", \"LABEL\": \"the standard acceleration of gravity\"}, {\"NAME\": \"h_max\", \"DIMENSION\": \"L1\", \"SUPPLY\": \"AUTHOR\", \"LABEL\": \"the largest height, above or below the origin, over which the field is taken as uniform\"}], \"SUMS\": [], \"TERMS\": [{\"TARGET\": \"UP_VELOCITY\", \"SIGN\": \"-\", \"EXPR\": \"MASS*g_n\", \"LABEL\": \"the weight\"}], \"ASSUMPTIONS\": [{\"NAME\": \"gravity_uniform\", \"PROPOSITION\": \"the gravitational field is uniform over the region abs({HEIGHT}) < h_max\", \"REFS\": [\"HEIGHT\", \"h_max\"]}, {\"NAME\": \"gravity_standard\", \"PROPOSITION\": \"the local gravitational acceleration equals the conventional standard value g_n\", \"REFS\": [\"g_n\"]}, {\"NAME\": \"frame_inertial\", \"PROPOSITION\": \"the frame in which {HEIGHT} is measured is treated as inertial\", \"REFS\": [\"HEIGHT\"]}], \"BOUNDARIES\": [{\"NAME\": \"gravity_region\", \"PREDICATE\": \"abs({HEIGHT}) < h_max\", \"CONDITION\": \"abs(HEIGHT) < h_max\"}], \"NOT_CHOSEN\": \"No gravity: no weight acts on any DOF.\", \"NOT_INCLUDED\": [\"No variation of gravity with height or latitude beyond what g_n contains.\", \"No Earth rotation (Coriolis or centrifugal force) beyond what g_n contains.\", \"No gravity of bodies other than the Earth.\"], \"EXCLUDES\": [], \"INTERACTS_WITH\": [{\"WITH\": \"AIR-*\", \"QUESTION_ID\": \"BUOYANCY\", \"QUESTION\": \"Does the air's buoyancy (upthrust) act on the body in the system you mean?\", \"YES_LINE\": \"Buoyancy acts (your answer): no module adds it; it acts in this kernel only where one of your own laws states it.\", \"NO_LINE\": \"No buoyancy: the air's upthrust on the body is not included.\"}], \"TEST_BINDINGS\": [{\"NAME\": \"PROJECTILE_2D\", \"TPK\": {\"DOF\": [{\"NAME\": \"t\", \"DIMENSION\": \"T1\"}, {\"NAME\": \"x\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"z\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"v_x\", \"DIMENSION\": \"L1 T-1\"}, {\"NAME\": \"v_z\", \"DIMENSION\": \"L1 T-1\"}], \"CONSTANT\": [{\"NAME\": \"m\", \"DIMENSION\": \"M1\"}], \"LAW\": [{\"NAME\": \"KIN_X\", \"STATEMENT\": \"dx/dt = v_x\", \"REFS\": [\"t\", \"v_x\", \"x\"], \"ROLE\": \"EOM(x)\", \"EQUATION\": \"D(x,t)=v_x\"}, {\"NAME\": \"KIN_Z\", \"STATEMENT\": \"dz/dt = v_z\", \"REFS\": [\"t\", \"v_z\", \"z\"], \"ROLE\": \"EOM(z)\", \"EQUATION\": \"D(z,t)=v_z\"}, {\"NAME\": \"EOM_X\", \"STATEMENT\": \"m dv_x/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_x\"], \"ROLE\": \"EOM(v_x)\", \"EQUATION\": \"m*D(v_x,t)=0\"}, {\"NAME\": \"EOM_Z\", \"STATEMENT\": \"m dv_z/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_z\"], \"ROLE\": \"EOM(v_z)\", \"EQUATION\": \"m*D(v_z,t)=0\"}], \"ASSUMPTION\": [{\"NAME\": \"point_mass\", \"PROPOSITION\": \"the body is treated as a point mass\", \"REFS\": [\"m\"]}]}, \"BIND\": {\"HEIGHT\": [\"z\"], \"MASS\": [\"m\"], \"UP_VELOCITY\": [\"v_z\"]}, \"VALUES\": {\"h_max\": {\"VALUE\": \"100\", \"UNIT\": \"m\"}}, \"ANSWERS\": {}}, {\"NAME\": \"TABLE\", \"TPK\": {\"DOF\": [{\"NAME\": \"t\", \"DIMENSION\": \"T1\"}, {\"NAME\": \"x\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"z\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"v_x\", \"DIMENSION\": \"L1 T-1\"}, {\"NAME\": \"v_z\", \"DIMENSION\": \"L1 T-1\"}], \"CONSTANT\": [{\"NAME\": \"m\", \"DIMENSION\": \"M1\"}], \"LAW\": [{\"NAME\": \"KIN_X\", \"STATEMENT\": \"dx/dt = v_x\", \"REFS\": [\"t\", \"v_x\", \"x\"], \"ROLE\": \"EOM(x)\", \"EQUATION\": \"D(x,t)=v_x\"}, {\"NAME\": \"KIN_Z\", \"STATEMENT\": \"dz/dt = v_z\", \"REFS\": [\"t\", \"v_z\", \"z\"], \"ROLE\": \"CONSTRAINT\", \"EQUATION\": \"D(z,t)=v_z\"}, {\"NAME\": \"EOM_X\", \"STATEMENT\": \"m dv_x/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_x\"], \"ROLE\": \"EOM(v_x)\", \"EQUATION\": \"m*D(v_x,t)=0\"}], \"CONSTRAINT\": [{\"NAME\": \"C_Z\", \"TARGET\": \"z\", \"ACTION\": \"FIX\", \"VALUE\": \"0\", \"UNIT\": \"m\", \"STATEMENT\": \"the puck stays on the table top, z = 0\"}, {\"NAME\": \"C_VZ\", \"TARGET\": \"v_z\", \"ACTION\": \"FIX\", \"VALUE\": \"0\", \"UNIT\": \"m s-1\", \"STATEMENT\": \"the puck has no vertical velocity\"}]}, \"BIND\": {\"HEIGHT\": [\"z\"], \"MASS\": [\"m\"], \"UP_VELOCITY\": [\"v_z\"]}, \"VALUES\": {\"h_max\": {\"VALUE\": \"1\", \"UNIT\": \"m\"}}, \"ANSWERS\": {\"FIXED:v_z\": \"YES\"}}]}",
"{\"ID\": \"MATH\", \"VERSION\": \"1.0.0\", \"TITLE\": \"The mathematical constant pi, as the CONSTANT pi_c\", \"SOURCE\": \"pi to 16 significant digits, 3.141592653589793, the nearest IEEE 754 binary64 value\", \"PREREQUISITES\": [], \"PARAMETERS\": [{\"NAME\": \"pi_c\", \"DIMENSION\": \"1\", \"SUPPLY\": \"DECLARED\", \"VALUE\": \"3.141592653589793\", \"UNIT\": \"1\", \"OVERRIDABLE\": \"NO\", \"LABEL\": \"pi, to 16 significant digits\"}], \"SUMS\": [], \"TERMS\": [], \"ASSUMPTIONS\": [], \"BOUNDARIES\": [], \"NOT_CHOSEN\": \"No mathematical constant: pi exists only if you declare it.\", \"NOT_INCLUDED\": [\"pi_c is pi rounded to 16 significant digits; no other mathematical constant is declared.\"], \"EXCLUDES\": [], \"INTERACTS_WITH\": [], \"TEST_BINDINGS\": [{\"NAME\": \"PROJECTILE_2D\", \"TPK\": {\"DOF\": [{\"NAME\": \"t\", \"DIMENSION\": \"T1\"}, {\"NAME\": \"x\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"z\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"v_x\", \"DIMENSION\": \"L1 T-1\"}, {\"NAME\": \"v_z\", \"DIMENSION\": \"L1 T-1\"}], \"CONSTANT\": [{\"NAME\": \"m\", \"DIMENSION\": \"M1\"}], \"LAW\": [{\"NAME\": \"KIN_X\", \"STATEMENT\": \"dx/dt = v_x\", \"REFS\": [\"t\", \"v_x\", \"x\"], \"ROLE\": \"EOM(x)\", \"EQUATION\": \"D(x,t)=v_x\"}, {\"NAME\": \"KIN_Z\", \"STATEMENT\": \"dz/dt = v_z\", \"REFS\": [\"t\", \"v_z\", \"z\"], \"ROLE\": \"EOM(z)\", \"EQUATION\": \"D(z,t)=v_z\"}, {\"NAME\": \"EOM_X\", \"STATEMENT\": \"m dv_x/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_x\"], \"ROLE\": \"EOM(v_x)\", \"EQUATION\": \"m*D(v_x,t)=0\"}, {\"NAME\": \"EOM_Z\", \"STATEMENT\": \"m dv_z/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_z\"], \"ROLE\": \"EOM(v_z)\", \"EQUATION\": \"m*D(v_z,t)=0\"}], \"ASSUMPTION\": [{\"NAME\": \"point_mass\", \"PROPOSITION\": \"the body is treated as a point mass\", \"REFS\": [\"m\"]}]}, \"BIND\": {}, \"VALUES\": {}, \"ANSWERS\": {}}]}"
]
},
"expected": "[\"REFUSED\",\"ANSWER ROUND 1: CHOSEN TEST-X is not in COVERED\"]",
"fn": "interview_check",
"hand_checked": true,
"name": "I14 CHOSEN an ID the round did not cover"
},
{
"args": {
"answer": [
{
"AT": 4,
"CHOSEN": "ALL",
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"carried": [],
"claims": [],
"lines": [
{
"ACT": "MODULE ADD",
"DATE": "2026-10-01",
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{
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"modules": [
"{\"ID\": \"AIR-LINEAR\", \"VERSION\": \"1.0.0\", \"TITLE\": \"Air resistance at sea level, linear in the speed (Stokes drag on a sphere)\", \"SOURCE\": \"ISO 2533:1975, Standard Atmosphere, sea-level values: density 1.225 kg m-3, dynamic viscosity 1.7894e-5 Pa s\", \"PREREQUISITES\": [{\"SLOT\": \"VELOCITY\", \"KIND\": \"DOF\", \"DIMENSION\": \"L1 T-1\", \"MIN\": 1, \"MAX\": 3, \"LABEL\": \"the velocity components of the body, one per axis\"}], \"PARAMETERS\": [{\"NAME\": \"rho_air\", \"DIMENSION\": \"L-3 M1\", \"SUPPLY\": \"DECLARED\", \"VALUE\": \"1.225\", \"UNIT\": \"kg m-3\", \"OVERRIDABLE\": \"NO\", \"LABEL\": \"the density of air at sea level\"}, {\"NAME\": \"mu_air\", \"DIMENSION\": \"L-1 M1 T-1\", \"SUPPLY\": \"DECLARED\", \"VALUE\": \"1.7894e-5\", \"UNIT\": \"Pa s\", \"OVERRIDABLE\": \"NO\", \"LABEL\": \"the dynamic viscosity of air at sea level\"}, {\"NAME\": \"pi_c\", \"DIMENSION\": \"1\", \"SUPPLY\": \"DECLARED\", \"VALUE\": \"3.141592653589793\", \"UNIT\": \"1\", \"OVERRIDABLE\": \"NO\", \"LABEL\": \"pi, to 16 significant digits\"}, {\"NAME\": \"R_s\", \"DIMENSION\": \"L1\", \"SUPPLY\": \"AUTHOR\", \"LABEL\": \"the radius of the sphere\"}], \"SUMS\": [{\"NAME\": \"SPEED2\", \"OVER\": \"VELOCITY\", \"EACH\": \"VELOCITY^2\"}], \"TERMS\": [{\"TARGET\": \"VELOCITY\", \"SIGN\": \"-\", \"EXPR\": \"6*pi_c*mu_air*R_s*VELOCITY\", \"LABEL\": \"the linear (Stokes) drag\"}], \"ASSUMPTIONS\": [{\"NAME\": \"air_still\", \"PROPOSITION\": \"the air is at rest in the frame of the body's velocity\", \"REFS\": [\"VELOCITY\"]}, {\"NAME\": \"air_uniform\", \"PROPOSITION\": \"the air density is uniform over the region of motion\", \"REFS\": [\"rho_air\"]}, {\"NAME\": \"drag_sphere\", \"PROPOSITION\": \"the body is a rigid sphere of radius R_s\", \"REFS\": [\"R_s\"]}], \"BOUNDARIES\": [{\"NAME\": \"drag_linear_regime\", \"PREDICATE\": \"2 rho_air |v| R_s / mu_air < 1: the regime of the linear law\", \"CONDITION\": \"mu_air != 0 and SPEED2 >= 0 and 2*rho_air*sqrt(SPEED2)*R_s/mu_air < 1\"}], \"NOT_CHOSEN\": \"No linear (Stokes) air resistance.\", \"NOT_INCLUDED\": [\"No wind: the air is at rest.\", \"No change of air density or viscosity with altitude or temperature.\", \"No drag outside the regime of the linear law.\"], \"EXCLUDES\": [], \"INTERACTS_WITH\": [], \"TEST_BINDINGS\": [{\"NAME\": \"PROJECTILE_2D\", \"TPK\": {\"DOF\": [{\"NAME\": \"t\", \"DIMENSION\": \"T1\"}, {\"NAME\": \"x\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"z\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"v_x\", \"DIMENSION\": \"L1 T-1\"}, {\"NAME\": \"v_z\", \"DIMENSION\": \"L1 T-1\"}], \"CONSTANT\": [{\"NAME\": \"m\", \"DIMENSION\": \"M1\"}], \"LAW\": [{\"NAME\": \"KIN_X\", \"STATEMENT\": \"dx/dt = v_x\", \"REFS\": [\"t\", \"v_x\", \"x\"], \"ROLE\": \"EOM(x)\", \"EQUATION\": \"D(x,t)=v_x\"}, {\"NAME\": \"KIN_Z\", \"STATEMENT\": \"dz/dt = v_z\", \"REFS\": [\"t\", \"v_z\", \"z\"], \"ROLE\": \"EOM(z)\", \"EQUATION\": \"D(z,t)=v_z\"}, {\"NAME\": \"EOM_X\", \"STATEMENT\": \"m dv_x/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_x\"], \"ROLE\": \"EOM(v_x)\", \"EQUATION\": \"m*D(v_x,t)=0\"}, {\"NAME\": \"EOM_Z\", \"STATEMENT\": \"m dv_z/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_z\"], \"ROLE\": \"EOM(v_z)\", \"EQUATION\": \"m*D(v_z,t)=0\"}], \"ASSUMPTION\": [{\"NAME\": \"point_mass\", \"PROPOSITION\": \"the body is treated as a point mass\", \"REFS\": [\"m\"]}]}, \"BIND\": {\"VELOCITY\": [\"v_x\", \"v_z\"]}, \"VALUES\": {\"R_s\": {}}, \"ANSWERS\": {}}]}",
"{\"ID\": \"AIR-QUADRATIC\", \"VERSION\": \"1.0.0\", \"TITLE\": \"Air resistance at sea level, quadratic in the speed\", \"SOURCE\": \"ISO 2533:1975, Standard Atmosphere, sea-level values: density 1.225 kg m-3, dynamic viscosity 1.7894e-5 Pa s\", \"PREREQUISITES\": [{\"SLOT\": \"VELOCITY\", \"KIND\": \"DOF\", \"DIMENSION\": \"L1 T-1\", \"MIN\": 1, \"MAX\": 3, \"LABEL\": \"the velocity components of the body, one per axis\"}], \"PARAMETERS\": [{\"NAME\": \"rho_air\", \"DIMENSION\": \"L-3 M1\", \"SUPPLY\": \"DECLARED\", \"VALUE\": \"1.225\", \"UNIT\": \"kg m-3\", \"OVERRIDABLE\": \"NO\", \"LABEL\": \"the density of air at sea level\"}, {\"NAME\": \"mu_air\", \"DIMENSION\": \"L-1 M1 T-1\", \"SUPPLY\": \"DECLARED\", \"VALUE\": \"1.7894e-5\", \"UNIT\": \"Pa s\", \"OVERRIDABLE\": \"NO\", \"LABEL\": \"the dynamic viscosity of air at sea level\"}, {\"NAME\": \"C_d\", \"DIMENSION\": \"1\", \"SUPPLY\": \"AUTHOR\", \"LABEL\": \"the drag coefficient of the body\"}, {\"NAME\": \"A_ref\", \"DIMENSION\": \"L2\", \"SUPPLY\": \"AUTHOR\", \"LABEL\": \"the reference area of the drag coefficient\"}, {\"NAME\": \"L_ref\", \"DIMENSION\": \"L1\", \"SUPPLY\": \"AUTHOR\", \"LABEL\": \"the reference length of the Reynolds number\"}], \"SUMS\": [{\"NAME\": \"SPEED2\", \"OVER\": \"VELOCITY\", \"EACH\": \"VELOCITY^2\"}], \"TERMS\": [{\"TARGET\": \"VELOCITY\", \"SIGN\": \"-\", \"EXPR\": \"0.5*rho_air*C_d*A_ref*sqrt(SPEED2)*VELOCITY\", \"LABEL\": \"the quadratic drag\"}], \"ASSUMPTIONS\": [{\"NAME\": \"air_still\", \"PROPOSITION\": \"the air is at rest in the frame of the body's velocity\", \"REFS\": [\"VELOCITY\"]}, {\"NAME\": \"air_uniform\", \"PROPOSITION\": \"the air density is uniform over the region of motion\", \"REFS\": [\"rho_air\"]}, {\"NAME\": \"drag_cd_constant\", \"PROPOSITION\": \"the drag coefficient C_d is constant over the motion\", \"REFS\": [\"C_d\"]}, {\"NAME\": \"drag_no_lift\", \"PROPOSITION\": \"the body experiences no lift force\", \"REFS\": [\"VELOCITY\"]}, {\"NAME\": \"drag_no_magnus\", \"PROPOSITION\": \"the body experiences no Magnus force\", \"REFS\": [\"VELOCITY\"]}], \"BOUNDARIES\": [{\"NAME\": \"drag_quadratic_regime\", \"PREDICATE\": \"1e3 < rho_air |v| L_ref / mu_air < 2e5: the Reynolds window of the quadratic law\", \"CONDITION\": \"mu_air != 0 and SPEED2 >= 0 and rho_air*sqrt(SPEED2)*L_ref/mu_air > 1000 and rho_air*sqrt(SPEED2)*L_ref/mu_air < 200000\"}], \"NOT_CHOSEN\": \"No quadratic air resistance.\", \"NOT_INCLUDED\": [\"No wind: the air is at rest.\", \"No change of air density or viscosity with altitude or temperature.\", \"No lift, Magnus or added-mass force.\", \"No drag outside the Reynolds window of the quadratic law.\"], \"EXCLUDES\": [\"AIR-LINEAR\"], \"INTERACTS_WITH\": [], \"TEST_BINDINGS\": [{\"NAME\": \"PROJECTILE_2D\", \"TPK\": {\"DOF\": [{\"NAME\": \"t\", \"DIMENSION\": \"T1\"}, {\"NAME\": \"x\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"z\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"v_x\", \"DIMENSION\": \"L1 T-1\"}, {\"NAME\": \"v_z\", \"DIMENSION\": \"L1 T-1\"}], \"CONSTANT\": [{\"NAME\": \"m\", \"DIMENSION\": \"M1\"}], \"LAW\": [{\"NAME\": \"KIN_X\", \"STATEMENT\": \"dx/dt = v_x\", \"REFS\": [\"t\", \"v_x\", \"x\"], \"ROLE\": \"EOM(x)\", \"EQUATION\": \"D(x,t)=v_x\"}, {\"NAME\": \"KIN_Z\", \"STATEMENT\": \"dz/dt = v_z\", \"REFS\": [\"t\", \"v_z\", \"z\"], \"ROLE\": \"EOM(z)\", \"EQUATION\": \"D(z,t)=v_z\"}, {\"NAME\": \"EOM_X\", \"STATEMENT\": \"m dv_x/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_x\"], \"ROLE\": \"EOM(v_x)\", \"EQUATION\": \"m*D(v_x,t)=0\"}, {\"NAME\": \"EOM_Z\", \"STATEMENT\": \"m dv_z/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_z\"], \"ROLE\": \"EOM(v_z)\", \"EQUATION\": \"m*D(v_z,t)=0\"}], \"ASSUMPTION\": [{\"NAME\": \"point_mass\", \"PROPOSITION\": \"the body is treated as a point mass\", \"REFS\": [\"m\"]}]}, \"BIND\": {\"VELOCITY\": [\"v_x\", \"v_z\"]}, \"VALUES\": {\"A_ref\": {}, \"C_d\": {}, \"L_ref\": {}}, \"ANSWERS\": {}}]}",
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it acts in this kernel only where one of your own laws states it.\", \"NO_LINE\": \"No buoyancy: the air's upthrust on the body is not included.\"}], \"TEST_BINDINGS\": [{\"NAME\": \"PROJECTILE_2D\", \"TPK\": {\"DOF\": [{\"NAME\": \"t\", \"DIMENSION\": \"T1\"}, {\"NAME\": \"x\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"z\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"v_x\", \"DIMENSION\": \"L1 T-1\"}, {\"NAME\": \"v_z\", \"DIMENSION\": \"L1 T-1\"}], \"CONSTANT\": [{\"NAME\": \"m\", \"DIMENSION\": \"M1\"}], \"LAW\": [{\"NAME\": \"KIN_X\", \"STATEMENT\": \"dx/dt = v_x\", \"REFS\": [\"t\", \"v_x\", \"x\"], \"ROLE\": \"EOM(x)\", \"EQUATION\": \"D(x,t)=v_x\"}, {\"NAME\": \"KIN_Z\", \"STATEMENT\": \"dz/dt = v_z\", \"REFS\": [\"t\", \"v_z\", \"z\"], \"ROLE\": \"EOM(z)\", \"EQUATION\": \"D(z,t)=v_z\"}, {\"NAME\": \"EOM_X\", \"STATEMENT\": \"m dv_x/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_x\"], \"ROLE\": \"EOM(v_x)\", \"EQUATION\": \"m*D(v_x,t)=0\"}, {\"NAME\": \"EOM_Z\", \"STATEMENT\": \"m dv_z/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_z\"], \"ROLE\": \"EOM(v_z)\", \"EQUATION\": \"m*D(v_z,t)=0\"}], \"ASSUMPTION\": [{\"NAME\": \"point_mass\", \"PROPOSITION\": \"the body is treated as a point mass\", \"REFS\": [\"m\"]}]}, \"BIND\": {\"HEIGHT\": [\"z\"], \"MASS\": [\"m\"], \"UP_VELOCITY\": [\"v_z\"]}, \"VALUES\": {\"h_max\": {\"VALUE\": \"100\", \"UNIT\": \"m\"}}, \"ANSWERS\": {}}, {\"NAME\": \"TABLE\", \"TPK\": {\"DOF\": [{\"NAME\": \"t\", \"DIMENSION\": \"T1\"}, {\"NAME\": \"x\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"z\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"v_x\", \"DIMENSION\": \"L1 T-1\"}, {\"NAME\": \"v_z\", \"DIMENSION\": \"L1 T-1\"}], \"CONSTANT\": [{\"NAME\": \"m\", \"DIMENSION\": \"M1\"}], \"LAW\": [{\"NAME\": \"KIN_X\", \"STATEMENT\": \"dx/dt = v_x\", \"REFS\": [\"t\", \"v_x\", \"x\"], \"ROLE\": \"EOM(x)\", \"EQUATION\": \"D(x,t)=v_x\"}, {\"NAME\": \"KIN_Z\", \"STATEMENT\": \"dz/dt = v_z\", \"REFS\": [\"t\", \"v_z\", \"z\"], \"ROLE\": \"CONSTRAINT\", \"EQUATION\": \"D(z,t)=v_z\"}, {\"NAME\": \"EOM_X\", \"STATEMENT\": \"m dv_x/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_x\"], \"ROLE\": \"EOM(v_x)\", \"EQUATION\": \"m*D(v_x,t)=0\"}], \"CONSTRAINT\": [{\"NAME\": \"C_Z\", \"TARGET\": \"z\", \"ACTION\": \"FIX\", \"VALUE\": \"0\", \"UNIT\": \"m\", \"STATEMENT\": \"the puck stays on the table top, z = 0\"}, {\"NAME\": \"C_VZ\", \"TARGET\": \"v_z\", \"ACTION\": \"FIX\", \"VALUE\": \"0\", \"UNIT\": \"m s-1\", \"STATEMENT\": \"the puck has no vertical velocity\"}]}, \"BIND\": {\"HEIGHT\": [\"z\"], \"MASS\": [\"m\"], \"UP_VELOCITY\": [\"v_z\"]}, \"VALUES\": {\"h_max\": {\"VALUE\": \"1\", \"UNIT\": \"m\"}}, \"ANSWERS\": {\"FIXED:v_z\": \"YES\"}}]}",
"{\"ID\": \"MATH\", \"VERSION\": \"1.0.0\", \"TITLE\": \"The mathematical constant pi, as the CONSTANT pi_c\", \"SOURCE\": \"pi to 16 significant digits, 3.141592653589793, the nearest IEEE 754 binary64 value\", \"PREREQUISITES\": [], \"PARAMETERS\": [{\"NAME\": \"pi_c\", \"DIMENSION\": \"1\", \"SUPPLY\": \"DECLARED\", \"VALUE\": \"3.141592653589793\", \"UNIT\": \"1\", \"OVERRIDABLE\": \"NO\", \"LABEL\": \"pi, to 16 significant digits\"}], \"SUMS\": [], \"TERMS\": [], \"ASSUMPTIONS\": [], \"BOUNDARIES\": [], \"NOT_CHOSEN\": \"No mathematical constant: pi exists only if you declare it.\", \"NOT_INCLUDED\": [\"pi_c is pi rounded to 16 significant digits; no other mathematical constant is declared.\"], \"EXCLUDES\": [], \"INTERACTS_WITH\": [], \"TEST_BINDINGS\": [{\"NAME\": \"PROJECTILE_2D\", \"TPK\": {\"DOF\": [{\"NAME\": \"t\", \"DIMENSION\": \"T1\"}, {\"NAME\": \"x\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"z\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"v_x\", \"DIMENSION\": \"L1 T-1\"}, {\"NAME\": \"v_z\", \"DIMENSION\": \"L1 T-1\"}], \"CONSTANT\": [{\"NAME\": \"m\", \"DIMENSION\": \"M1\"}], \"LAW\": [{\"NAME\": \"KIN_X\", \"STATEMENT\": \"dx/dt = v_x\", \"REFS\": [\"t\", \"v_x\", \"x\"], \"ROLE\": \"EOM(x)\", \"EQUATION\": \"D(x,t)=v_x\"}, {\"NAME\": \"KIN_Z\", \"STATEMENT\": \"dz/dt = v_z\", \"REFS\": [\"t\", \"v_z\", \"z\"], \"ROLE\": \"EOM(z)\", \"EQUATION\": \"D(z,t)=v_z\"}, {\"NAME\": \"EOM_X\", \"STATEMENT\": \"m dv_x/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_x\"], \"ROLE\": \"EOM(v_x)\", \"EQUATION\": \"m*D(v_x,t)=0\"}, {\"NAME\": \"EOM_Z\", \"STATEMENT\": \"m dv_z/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_z\"], \"ROLE\": \"EOM(v_z)\", \"EQUATION\": \"m*D(v_z,t)=0\"}], \"ASSUMPTION\": [{\"NAME\": \"point_mass\", \"PROPOSITION\": \"the body is treated as a point mass\", \"REFS\": [\"m\"]}]}, \"BIND\": {}, \"VALUES\": {}, \"ANSWERS\": {}}]}"
]
},
"expected": "[\"REFUSED\",\"ANSWER ROUND 1: field CHOSEN has the wrong type\"]",
"fn": "interview_check",
"hand_checked": true,
"name": "I15 CHOSEN a word other than NONE"
},
{
"args": {
"answer": [
{
"AT": 4,
"CHOSEN": "NONE",
"COVERED": [
[
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[
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[
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]
}
],
"carried": [],
"claims": [
{
"ANSWERS": {},
"BIND": {
"HEIGHT": [
"z"
],
"MASS": [
"m"
],
"UP_VELOCITY": [
"v_z"
]
},
"DIGEST": "24877ccb5c8ec300d29ed82ce6650592f35cf8899a3d878ccce9c08d4c72c025",
"ID": "GRAV-UNIFORM",
"VALUES": {
"h_max": {
"UNIT": "m",
"VALUE": "100"
}
},
"VERSION": "1.0.0"
}
],
"lines": [
{
"ACT": "MODULE ADD",
"DATE": "2026-10-01",
"DIGEST": "5f3fe27b42378bce0830b0d0959f892f4a8e73b12b540ae877e39e6439d08b4d",
"ID": "AIR-LINEAR",
"VERSION": "1.0.0"
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{
"ACT": "MODULE ADD",
"DATE": "2026-10-01",
"DIGEST": "6fb53c3a6546151eead2bd6e72e9cf8334f3a2040ad0ee2f5b988ec96d6fc852",
"ID": "AIR-QUADRATIC",
"VERSION": "1.0.0"
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{
"ACT": "MODULE ADD",
"DATE": "2026-10-01",
"DIGEST": "24877ccb5c8ec300d29ed82ce6650592f35cf8899a3d878ccce9c08d4c72c025",
"ID": "GRAV-UNIFORM",
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{
"ACT": "MODULE ADD",
"DATE": "2026-10-01",
"DIGEST": "8f39a356f35527b901fcee012764590f0819c8ffdeccad4bc05195ce3d2e0bcf",
"ID": "MATH",
"VERSION": "1.0.0"
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"modules": [
"{\"ID\": \"AIR-LINEAR\", \"VERSION\": \"1.0.0\", \"TITLE\": \"Air resistance at sea level, linear in the speed (Stokes drag on a sphere)\", \"SOURCE\": \"ISO 2533:1975, Standard Atmosphere, sea-level values: density 1.225 kg m-3, dynamic viscosity 1.7894e-5 Pa s\", \"PREREQUISITES\": [{\"SLOT\": \"VELOCITY\", \"KIND\": \"DOF\", \"DIMENSION\": \"L1 T-1\", \"MIN\": 1, \"MAX\": 3, \"LABEL\": \"the velocity components of the body, one per axis\"}], \"PARAMETERS\": [{\"NAME\": \"rho_air\", \"DIMENSION\": \"L-3 M1\", \"SUPPLY\": \"DECLARED\", \"VALUE\": \"1.225\", \"UNIT\": \"kg m-3\", \"OVERRIDABLE\": \"NO\", \"LABEL\": \"the density of air at sea level\"}, {\"NAME\": \"mu_air\", \"DIMENSION\": \"L-1 M1 T-1\", \"SUPPLY\": \"DECLARED\", \"VALUE\": \"1.7894e-5\", \"UNIT\": \"Pa s\", \"OVERRIDABLE\": \"NO\", \"LABEL\": \"the dynamic viscosity of air at sea level\"}, {\"NAME\": \"pi_c\", \"DIMENSION\": \"1\", \"SUPPLY\": \"DECLARED\", \"VALUE\": \"3.141592653589793\", \"UNIT\": \"1\", \"OVERRIDABLE\": \"NO\", \"LABEL\": \"pi, to 16 significant digits\"}, {\"NAME\": \"R_s\", \"DIMENSION\": \"L1\", \"SUPPLY\": \"AUTHOR\", \"LABEL\": \"the radius of the sphere\"}], \"SUMS\": [{\"NAME\": \"SPEED2\", \"OVER\": \"VELOCITY\", \"EACH\": \"VELOCITY^2\"}], \"TERMS\": [{\"TARGET\": \"VELOCITY\", \"SIGN\": \"-\", \"EXPR\": \"6*pi_c*mu_air*R_s*VELOCITY\", \"LABEL\": \"the linear (Stokes) drag\"}], \"ASSUMPTIONS\": [{\"NAME\": \"air_still\", \"PROPOSITION\": \"the air is at rest in the frame of the body's velocity\", \"REFS\": [\"VELOCITY\"]}, {\"NAME\": \"air_uniform\", \"PROPOSITION\": \"the air density is uniform over the region of motion\", \"REFS\": [\"rho_air\"]}, {\"NAME\": \"drag_sphere\", \"PROPOSITION\": \"the body is a rigid sphere of radius R_s\", \"REFS\": [\"R_s\"]}], \"BOUNDARIES\": [{\"NAME\": \"drag_linear_regime\", \"PREDICATE\": \"2 rho_air |v| R_s / mu_air < 1: the regime of the linear law\", \"CONDITION\": \"mu_air != 0 and SPEED2 >= 0 and 2*rho_air*sqrt(SPEED2)*R_s/mu_air < 1\"}], \"NOT_CHOSEN\": \"No linear (Stokes) air resistance.\", \"NOT_INCLUDED\": [\"No wind: the air is at rest.\", \"No change of air density or viscosity with altitude or temperature.\", \"No drag outside the regime of the linear law.\"], \"EXCLUDES\": [], \"INTERACTS_WITH\": [], \"TEST_BINDINGS\": [{\"NAME\": \"PROJECTILE_2D\", \"TPK\": {\"DOF\": [{\"NAME\": \"t\", \"DIMENSION\": \"T1\"}, {\"NAME\": \"x\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"z\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"v_x\", \"DIMENSION\": \"L1 T-1\"}, {\"NAME\": \"v_z\", \"DIMENSION\": \"L1 T-1\"}], \"CONSTANT\": [{\"NAME\": \"m\", \"DIMENSION\": \"M1\"}], \"LAW\": [{\"NAME\": \"KIN_X\", \"STATEMENT\": \"dx/dt = v_x\", \"REFS\": [\"t\", \"v_x\", \"x\"], \"ROLE\": \"EOM(x)\", \"EQUATION\": \"D(x,t)=v_x\"}, {\"NAME\": \"KIN_Z\", \"STATEMENT\": \"dz/dt = v_z\", \"REFS\": [\"t\", \"v_z\", \"z\"], \"ROLE\": \"EOM(z)\", \"EQUATION\": \"D(z,t)=v_z\"}, {\"NAME\": \"EOM_X\", \"STATEMENT\": \"m dv_x/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_x\"], \"ROLE\": \"EOM(v_x)\", \"EQUATION\": \"m*D(v_x,t)=0\"}, {\"NAME\": \"EOM_Z\", \"STATEMENT\": \"m dv_z/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_z\"], \"ROLE\": \"EOM(v_z)\", \"EQUATION\": \"m*D(v_z,t)=0\"}], \"ASSUMPTION\": [{\"NAME\": \"point_mass\", \"PROPOSITION\": \"the body is treated as a point mass\", \"REFS\": [\"m\"]}]}, \"BIND\": {\"VELOCITY\": [\"v_x\", \"v_z\"]}, \"VALUES\": {\"R_s\": {}}, \"ANSWERS\": {}}]}",
"{\"ID\": \"AIR-QUADRATIC\", \"VERSION\": \"1.0.0\", \"TITLE\": \"Air resistance at sea level, quadratic in the speed\", \"SOURCE\": \"ISO 2533:1975, Standard Atmosphere, sea-level values: density 1.225 kg m-3, dynamic viscosity 1.7894e-5 Pa s\", \"PREREQUISITES\": [{\"SLOT\": \"VELOCITY\", \"KIND\": \"DOF\", \"DIMENSION\": \"L1 T-1\", \"MIN\": 1, \"MAX\": 3, \"LABEL\": \"the velocity components of the body, one per axis\"}], \"PARAMETERS\": [{\"NAME\": \"rho_air\", \"DIMENSION\": \"L-3 M1\", \"SUPPLY\": \"DECLARED\", \"VALUE\": \"1.225\", \"UNIT\": \"kg m-3\", \"OVERRIDABLE\": \"NO\", \"LABEL\": \"the density of air at sea level\"}, {\"NAME\": \"mu_air\", \"DIMENSION\": \"L-1 M1 T-1\", \"SUPPLY\": \"DECLARED\", \"VALUE\": \"1.7894e-5\", \"UNIT\": \"Pa s\", \"OVERRIDABLE\": \"NO\", \"LABEL\": \"the dynamic viscosity of air at sea level\"}, {\"NAME\": \"C_d\", \"DIMENSION\": \"1\", \"SUPPLY\": \"AUTHOR\", \"LABEL\": \"the drag coefficient of the body\"}, {\"NAME\": \"A_ref\", \"DIMENSION\": \"L2\", \"SUPPLY\": \"AUTHOR\", \"LABEL\": \"the reference area of the drag coefficient\"}, {\"NAME\": \"L_ref\", \"DIMENSION\": \"L1\", \"SUPPLY\": \"AUTHOR\", \"LABEL\": \"the reference length of the Reynolds number\"}], \"SUMS\": [{\"NAME\": \"SPEED2\", \"OVER\": \"VELOCITY\", \"EACH\": \"VELOCITY^2\"}], \"TERMS\": [{\"TARGET\": \"VELOCITY\", \"SIGN\": \"-\", \"EXPR\": \"0.5*rho_air*C_d*A_ref*sqrt(SPEED2)*VELOCITY\", \"LABEL\": \"the quadratic drag\"}], \"ASSUMPTIONS\": [{\"NAME\": \"air_still\", \"PROPOSITION\": \"the air is at rest in the frame of the body's velocity\", \"REFS\": [\"VELOCITY\"]}, {\"NAME\": \"air_uniform\", \"PROPOSITION\": \"the air density is uniform over the region of motion\", \"REFS\": [\"rho_air\"]}, {\"NAME\": \"drag_cd_constant\", \"PROPOSITION\": \"the drag coefficient C_d is constant over the motion\", \"REFS\": [\"C_d\"]}, {\"NAME\": \"drag_no_lift\", \"PROPOSITION\": \"the body experiences no lift force\", \"REFS\": [\"VELOCITY\"]}, {\"NAME\": \"drag_no_magnus\", \"PROPOSITION\": \"the body experiences no Magnus force\", \"REFS\": [\"VELOCITY\"]}], \"BOUNDARIES\": [{\"NAME\": \"drag_quadratic_regime\", \"PREDICATE\": \"1e3 < rho_air |v| L_ref / mu_air < 2e5: the Reynolds window of the quadratic law\", \"CONDITION\": \"mu_air != 0 and SPEED2 >= 0 and rho_air*sqrt(SPEED2)*L_ref/mu_air > 1000 and rho_air*sqrt(SPEED2)*L_ref/mu_air < 200000\"}], \"NOT_CHOSEN\": \"No quadratic air resistance.\", \"NOT_INCLUDED\": [\"No wind: the air is at rest.\", \"No change of air density or viscosity with altitude or temperature.\", \"No lift, Magnus or added-mass force.\", \"No drag outside the Reynolds window of the quadratic law.\"], \"EXCLUDES\": [\"AIR-LINEAR\"], \"INTERACTS_WITH\": [], \"TEST_BINDINGS\": [{\"NAME\": \"PROJECTILE_2D\", \"TPK\": {\"DOF\": [{\"NAME\": \"t\", \"DIMENSION\": \"T1\"}, {\"NAME\": \"x\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"z\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"v_x\", \"DIMENSION\": \"L1 T-1\"}, {\"NAME\": \"v_z\", \"DIMENSION\": \"L1 T-1\"}], \"CONSTANT\": [{\"NAME\": \"m\", \"DIMENSION\": \"M1\"}], \"LAW\": [{\"NAME\": \"KIN_X\", \"STATEMENT\": \"dx/dt = v_x\", \"REFS\": [\"t\", \"v_x\", \"x\"], \"ROLE\": \"EOM(x)\", \"EQUATION\": \"D(x,t)=v_x\"}, {\"NAME\": \"KIN_Z\", \"STATEMENT\": \"dz/dt = v_z\", \"REFS\": [\"t\", \"v_z\", \"z\"], \"ROLE\": \"EOM(z)\", \"EQUATION\": \"D(z,t)=v_z\"}, {\"NAME\": \"EOM_X\", \"STATEMENT\": \"m dv_x/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_x\"], \"ROLE\": \"EOM(v_x)\", \"EQUATION\": \"m*D(v_x,t)=0\"}, {\"NAME\": \"EOM_Z\", \"STATEMENT\": \"m dv_z/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_z\"], \"ROLE\": \"EOM(v_z)\", \"EQUATION\": \"m*D(v_z,t)=0\"}], \"ASSUMPTION\": [{\"NAME\": \"point_mass\", \"PROPOSITION\": \"the body is treated as a point mass\", \"REFS\": [\"m\"]}]}, \"BIND\": {\"VELOCITY\": [\"v_x\", \"v_z\"]}, \"VALUES\": {\"A_ref\": {}, \"C_d\": {}, \"L_ref\": {}}, \"ANSWERS\": {}}]}",
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it acts in this kernel only where one of your own laws states it.\", \"NO_LINE\": \"No buoyancy: the air's upthrust on the body is not included.\"}], \"TEST_BINDINGS\": [{\"NAME\": \"PROJECTILE_2D\", \"TPK\": {\"DOF\": [{\"NAME\": \"t\", \"DIMENSION\": \"T1\"}, {\"NAME\": \"x\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"z\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"v_x\", \"DIMENSION\": \"L1 T-1\"}, {\"NAME\": \"v_z\", \"DIMENSION\": \"L1 T-1\"}], \"CONSTANT\": [{\"NAME\": \"m\", \"DIMENSION\": \"M1\"}], \"LAW\": [{\"NAME\": \"KIN_X\", \"STATEMENT\": \"dx/dt = v_x\", \"REFS\": [\"t\", \"v_x\", \"x\"], \"ROLE\": \"EOM(x)\", \"EQUATION\": \"D(x,t)=v_x\"}, {\"NAME\": \"KIN_Z\", \"STATEMENT\": \"dz/dt = v_z\", \"REFS\": [\"t\", \"v_z\", \"z\"], \"ROLE\": \"EOM(z)\", \"EQUATION\": \"D(z,t)=v_z\"}, {\"NAME\": \"EOM_X\", \"STATEMENT\": \"m dv_x/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_x\"], \"ROLE\": \"EOM(v_x)\", \"EQUATION\": \"m*D(v_x,t)=0\"}, {\"NAME\": \"EOM_Z\", \"STATEMENT\": \"m dv_z/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_z\"], \"ROLE\": \"EOM(v_z)\", \"EQUATION\": \"m*D(v_z,t)=0\"}], \"ASSUMPTION\": [{\"NAME\": \"point_mass\", \"PROPOSITION\": \"the body is treated as a point mass\", \"REFS\": [\"m\"]}]}, \"BIND\": {\"HEIGHT\": [\"z\"], \"MASS\": [\"m\"], \"UP_VELOCITY\": [\"v_z\"]}, \"VALUES\": {\"h_max\": {\"VALUE\": \"100\", \"UNIT\": \"m\"}}, \"ANSWERS\": {}}, {\"NAME\": \"TABLE\", \"TPK\": {\"DOF\": [{\"NAME\": \"t\", \"DIMENSION\": \"T1\"}, {\"NAME\": \"x\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"z\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"v_x\", \"DIMENSION\": \"L1 T-1\"}, {\"NAME\": \"v_z\", \"DIMENSION\": \"L1 T-1\"}], \"CONSTANT\": [{\"NAME\": \"m\", \"DIMENSION\": \"M1\"}], \"LAW\": [{\"NAME\": \"KIN_X\", \"STATEMENT\": \"dx/dt = v_x\", \"REFS\": [\"t\", \"v_x\", \"x\"], \"ROLE\": \"EOM(x)\", \"EQUATION\": \"D(x,t)=v_x\"}, {\"NAME\": \"KIN_Z\", \"STATEMENT\": \"dz/dt = v_z\", \"REFS\": [\"t\", \"v_z\", \"z\"], \"ROLE\": \"CONSTRAINT\", \"EQUATION\": \"D(z,t)=v_z\"}, {\"NAME\": \"EOM_X\", \"STATEMENT\": \"m dv_x/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_x\"], \"ROLE\": \"EOM(v_x)\", \"EQUATION\": \"m*D(v_x,t)=0\"}], \"CONSTRAINT\": [{\"NAME\": \"C_Z\", \"TARGET\": \"z\", \"ACTION\": \"FIX\", \"VALUE\": \"0\", \"UNIT\": \"m\", \"STATEMENT\": \"the puck stays on the table top, z = 0\"}, {\"NAME\": \"C_VZ\", \"TARGET\": \"v_z\", \"ACTION\": \"FIX\", \"VALUE\": \"0\", \"UNIT\": \"m s-1\", \"STATEMENT\": \"the puck has no vertical velocity\"}]}, \"BIND\": {\"HEIGHT\": [\"z\"], \"MASS\": [\"m\"], \"UP_VELOCITY\": [\"v_z\"]}, \"VALUES\": {\"h_max\": {\"VALUE\": \"1\", \"UNIT\": \"m\"}}, \"ANSWERS\": {\"FIXED:v_z\": \"YES\"}}]}",
"{\"ID\": \"MATH\", \"VERSION\": \"1.0.0\", \"TITLE\": \"The mathematical constant pi, as the CONSTANT pi_c\", \"SOURCE\": \"pi to 16 significant digits, 3.141592653589793, the nearest IEEE 754 binary64 value\", \"PREREQUISITES\": [], \"PARAMETERS\": [{\"NAME\": \"pi_c\", \"DIMENSION\": \"1\", \"SUPPLY\": \"DECLARED\", \"VALUE\": \"3.141592653589793\", \"UNIT\": \"1\", \"OVERRIDABLE\": \"NO\", \"LABEL\": \"pi, to 16 significant digits\"}], \"SUMS\": [], \"TERMS\": [], \"ASSUMPTIONS\": [], \"BOUNDARIES\": [], \"NOT_CHOSEN\": \"No mathematical constant: pi exists only if you declare it.\", \"NOT_INCLUDED\": [\"pi_c is pi rounded to 16 significant digits; no other mathematical constant is declared.\"], \"EXCLUDES\": [], \"INTERACTS_WITH\": [], \"TEST_BINDINGS\": [{\"NAME\": \"PROJECTILE_2D\", \"TPK\": {\"DOF\": [{\"NAME\": \"t\", \"DIMENSION\": \"T1\"}, {\"NAME\": \"x\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"z\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"v_x\", \"DIMENSION\": \"L1 T-1\"}, {\"NAME\": \"v_z\", \"DIMENSION\": \"L1 T-1\"}], \"CONSTANT\": [{\"NAME\": \"m\", \"DIMENSION\": \"M1\"}], \"LAW\": [{\"NAME\": \"KIN_X\", \"STATEMENT\": \"dx/dt = v_x\", \"REFS\": [\"t\", \"v_x\", \"x\"], \"ROLE\": \"EOM(x)\", \"EQUATION\": \"D(x,t)=v_x\"}, {\"NAME\": \"KIN_Z\", \"STATEMENT\": \"dz/dt = v_z\", \"REFS\": [\"t\", \"v_z\", \"z\"], \"ROLE\": \"EOM(z)\", \"EQUATION\": \"D(z,t)=v_z\"}, {\"NAME\": \"EOM_X\", \"STATEMENT\": \"m dv_x/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_x\"], \"ROLE\": \"EOM(v_x)\", \"EQUATION\": \"m*D(v_x,t)=0\"}, {\"NAME\": \"EOM_Z\", \"STATEMENT\": \"m dv_z/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_z\"], \"ROLE\": \"EOM(v_z)\", \"EQUATION\": \"m*D(v_z,t)=0\"}], \"ASSUMPTION\": [{\"NAME\": \"point_mass\", \"PROPOSITION\": \"the body is treated as a point mass\", \"REFS\": [\"m\"]}]}, \"BIND\": {}, \"VALUES\": {}, \"ANSWERS\": {}}]}"
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{
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{
"ACT": "MODULE ADD",
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"{\"ID\": \"AIR-LINEAR\", \"VERSION\": \"1.0.0\", \"TITLE\": \"Air resistance at sea level, linear in the speed (Stokes drag on a sphere)\", \"SOURCE\": \"ISO 2533:1975, Standard Atmosphere, sea-level values: density 1.225 kg m-3, dynamic viscosity 1.7894e-5 Pa s\", \"PREREQUISITES\": [{\"SLOT\": \"VELOCITY\", \"KIND\": \"DOF\", \"DIMENSION\": \"L1 T-1\", \"MIN\": 1, \"MAX\": 3, \"LABEL\": \"the velocity components of the body, one per axis\"}], \"PARAMETERS\": [{\"NAME\": \"rho_air\", \"DIMENSION\": \"L-3 M1\", \"SUPPLY\": \"DECLARED\", \"VALUE\": \"1.225\", \"UNIT\": \"kg m-3\", \"OVERRIDABLE\": \"NO\", \"LABEL\": \"the density of air at sea level\"}, {\"NAME\": \"mu_air\", \"DIMENSION\": \"L-1 M1 T-1\", \"SUPPLY\": \"DECLARED\", \"VALUE\": \"1.7894e-5\", \"UNIT\": \"Pa s\", \"OVERRIDABLE\": \"NO\", \"LABEL\": \"the dynamic viscosity of air at sea level\"}, {\"NAME\": \"pi_c\", \"DIMENSION\": \"1\", \"SUPPLY\": \"DECLARED\", \"VALUE\": \"3.141592653589793\", \"UNIT\": \"1\", \"OVERRIDABLE\": \"NO\", \"LABEL\": \"pi, to 16 significant digits\"}, {\"NAME\": \"R_s\", \"DIMENSION\": \"L1\", \"SUPPLY\": \"AUTHOR\", \"LABEL\": \"the radius of the sphere\"}], \"SUMS\": [{\"NAME\": \"SPEED2\", \"OVER\": \"VELOCITY\", \"EACH\": \"VELOCITY^2\"}], \"TERMS\": [{\"TARGET\": \"VELOCITY\", \"SIGN\": \"-\", \"EXPR\": \"6*pi_c*mu_air*R_s*VELOCITY\", \"LABEL\": \"the linear (Stokes) drag\"}], \"ASSUMPTIONS\": [{\"NAME\": \"air_still\", \"PROPOSITION\": \"the air is at rest in the frame of the body's velocity\", \"REFS\": [\"VELOCITY\"]}, {\"NAME\": \"air_uniform\", \"PROPOSITION\": \"the air density is uniform over the region of motion\", \"REFS\": [\"rho_air\"]}, {\"NAME\": \"drag_sphere\", \"PROPOSITION\": \"the body is a rigid sphere of radius R_s\", \"REFS\": [\"R_s\"]}], \"BOUNDARIES\": [{\"NAME\": \"drag_linear_regime\", \"PREDICATE\": \"2 rho_air |v| R_s / mu_air < 1: the regime of the linear law\", \"CONDITION\": \"mu_air != 0 and SPEED2 >= 0 and 2*rho_air*sqrt(SPEED2)*R_s/mu_air < 1\"}], \"NOT_CHOSEN\": \"No linear (Stokes) air resistance.\", \"NOT_INCLUDED\": [\"No wind: the air is at rest.\", \"No change of air density or viscosity with altitude or temperature.\", \"No drag outside the regime of the linear law.\"], \"EXCLUDES\": [], \"INTERACTS_WITH\": [], \"TEST_BINDINGS\": [{\"NAME\": \"PROJECTILE_2D\", \"TPK\": {\"DOF\": [{\"NAME\": \"t\", \"DIMENSION\": \"T1\"}, {\"NAME\": \"x\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"z\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"v_x\", \"DIMENSION\": \"L1 T-1\"}, {\"NAME\": \"v_z\", \"DIMENSION\": \"L1 T-1\"}], \"CONSTANT\": [{\"NAME\": \"m\", \"DIMENSION\": \"M1\"}], \"LAW\": [{\"NAME\": \"KIN_X\", \"STATEMENT\": \"dx/dt = v_x\", \"REFS\": [\"t\", \"v_x\", \"x\"], \"ROLE\": \"EOM(x)\", \"EQUATION\": \"D(x,t)=v_x\"}, {\"NAME\": \"KIN_Z\", \"STATEMENT\": \"dz/dt = v_z\", \"REFS\": [\"t\", \"v_z\", \"z\"], \"ROLE\": \"EOM(z)\", \"EQUATION\": \"D(z,t)=v_z\"}, {\"NAME\": \"EOM_X\", \"STATEMENT\": \"m dv_x/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_x\"], \"ROLE\": \"EOM(v_x)\", \"EQUATION\": \"m*D(v_x,t)=0\"}, {\"NAME\": \"EOM_Z\", \"STATEMENT\": \"m dv_z/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_z\"], \"ROLE\": \"EOM(v_z)\", \"EQUATION\": \"m*D(v_z,t)=0\"}], \"ASSUMPTION\": [{\"NAME\": \"point_mass\", \"PROPOSITION\": \"the body is treated as a point mass\", \"REFS\": [\"m\"]}]}, \"BIND\": {\"VELOCITY\": [\"v_x\", \"v_z\"]}, \"VALUES\": {\"R_s\": {}}, \"ANSWERS\": {}}]}",
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it acts in this kernel only where one of your own laws states it.\", \"NO_LINE\": \"No buoyancy: the air's upthrust on the body is not included.\"}], \"TEST_BINDINGS\": [{\"NAME\": \"PROJECTILE_2D\", \"TPK\": {\"DOF\": [{\"NAME\": \"t\", \"DIMENSION\": \"T1\"}, {\"NAME\": \"x\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"z\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"v_x\", \"DIMENSION\": \"L1 T-1\"}, {\"NAME\": \"v_z\", \"DIMENSION\": \"L1 T-1\"}], \"CONSTANT\": [{\"NAME\": \"m\", \"DIMENSION\": \"M1\"}], \"LAW\": [{\"NAME\": \"KIN_X\", \"STATEMENT\": \"dx/dt = v_x\", \"REFS\": [\"t\", \"v_x\", \"x\"], \"ROLE\": \"EOM(x)\", \"EQUATION\": \"D(x,t)=v_x\"}, {\"NAME\": \"KIN_Z\", \"STATEMENT\": \"dz/dt = v_z\", \"REFS\": [\"t\", \"v_z\", \"z\"], \"ROLE\": \"EOM(z)\", \"EQUATION\": \"D(z,t)=v_z\"}, {\"NAME\": \"EOM_X\", \"STATEMENT\": \"m dv_x/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_x\"], \"ROLE\": \"EOM(v_x)\", \"EQUATION\": \"m*D(v_x,t)=0\"}, {\"NAME\": \"EOM_Z\", \"STATEMENT\": \"m dv_z/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_z\"], \"ROLE\": \"EOM(v_z)\", \"EQUATION\": \"m*D(v_z,t)=0\"}], \"ASSUMPTION\": [{\"NAME\": \"point_mass\", \"PROPOSITION\": \"the body is treated as a point mass\", \"REFS\": [\"m\"]}]}, \"BIND\": {\"HEIGHT\": [\"z\"], \"MASS\": [\"m\"], \"UP_VELOCITY\": [\"v_z\"]}, \"VALUES\": {\"h_max\": {\"VALUE\": \"100\", \"UNIT\": \"m\"}}, \"ANSWERS\": {}}, {\"NAME\": \"TABLE\", \"TPK\": {\"DOF\": [{\"NAME\": \"t\", \"DIMENSION\": \"T1\"}, {\"NAME\": \"x\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"z\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"v_x\", \"DIMENSION\": \"L1 T-1\"}, {\"NAME\": \"v_z\", \"DIMENSION\": \"L1 T-1\"}], \"CONSTANT\": [{\"NAME\": \"m\", \"DIMENSION\": \"M1\"}], \"LAW\": [{\"NAME\": \"KIN_X\", \"STATEMENT\": \"dx/dt = v_x\", \"REFS\": [\"t\", \"v_x\", \"x\"], \"ROLE\": \"EOM(x)\", \"EQUATION\": \"D(x,t)=v_x\"}, {\"NAME\": \"KIN_Z\", \"STATEMENT\": \"dz/dt = v_z\", \"REFS\": [\"t\", \"v_z\", \"z\"], \"ROLE\": \"CONSTRAINT\", \"EQUATION\": \"D(z,t)=v_z\"}, {\"NAME\": \"EOM_X\", \"STATEMENT\": \"m dv_x/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_x\"], \"ROLE\": \"EOM(v_x)\", \"EQUATION\": \"m*D(v_x,t)=0\"}], \"CONSTRAINT\": [{\"NAME\": \"C_Z\", \"TARGET\": \"z\", \"ACTION\": \"FIX\", \"VALUE\": \"0\", \"UNIT\": \"m\", \"STATEMENT\": \"the puck stays on the table top, z = 0\"}, {\"NAME\": \"C_VZ\", \"TARGET\": \"v_z\", \"ACTION\": \"FIX\", \"VALUE\": \"0\", \"UNIT\": \"m s-1\", \"STATEMENT\": \"the puck has no vertical velocity\"}]}, \"BIND\": {\"HEIGHT\": [\"z\"], \"MASS\": [\"m\"], \"UP_VELOCITY\": [\"v_z\"]}, \"VALUES\": {\"h_max\": {\"VALUE\": \"1\", \"UNIT\": \"m\"}}, \"ANSWERS\": {\"FIXED:v_z\": \"YES\"}}]}",
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{
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{
"ACT": "MODULE ADD",
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"modules": [
"{\"ID\": \"AIR-LINEAR\", \"VERSION\": \"1.0.0\", \"TITLE\": \"Air resistance at sea level, linear in the speed (Stokes drag on a sphere)\", \"SOURCE\": \"ISO 2533:1975, Standard Atmosphere, sea-level values: density 1.225 kg m-3, dynamic viscosity 1.7894e-5 Pa s\", \"PREREQUISITES\": [{\"SLOT\": \"VELOCITY\", \"KIND\": \"DOF\", \"DIMENSION\": \"L1 T-1\", \"MIN\": 1, \"MAX\": 3, \"LABEL\": \"the velocity components of the body, one per axis\"}], \"PARAMETERS\": [{\"NAME\": \"rho_air\", \"DIMENSION\": \"L-3 M1\", \"SUPPLY\": \"DECLARED\", \"VALUE\": \"1.225\", \"UNIT\": \"kg m-3\", \"OVERRIDABLE\": \"NO\", \"LABEL\": \"the density of air at sea level\"}, {\"NAME\": \"mu_air\", \"DIMENSION\": \"L-1 M1 T-1\", \"SUPPLY\": \"DECLARED\", \"VALUE\": \"1.7894e-5\", \"UNIT\": \"Pa s\", \"OVERRIDABLE\": \"NO\", \"LABEL\": \"the dynamic viscosity of air at sea level\"}, {\"NAME\": \"pi_c\", \"DIMENSION\": \"1\", \"SUPPLY\": \"DECLARED\", \"VALUE\": \"3.141592653589793\", \"UNIT\": \"1\", \"OVERRIDABLE\": \"NO\", \"LABEL\": \"pi, to 16 significant digits\"}, {\"NAME\": \"R_s\", \"DIMENSION\": \"L1\", \"SUPPLY\": \"AUTHOR\", \"LABEL\": \"the radius of the sphere\"}], \"SUMS\": [{\"NAME\": \"SPEED2\", \"OVER\": \"VELOCITY\", \"EACH\": \"VELOCITY^2\"}], \"TERMS\": [{\"TARGET\": \"VELOCITY\", \"SIGN\": \"-\", \"EXPR\": \"6*pi_c*mu_air*R_s*VELOCITY\", \"LABEL\": \"the linear (Stokes) drag\"}], \"ASSUMPTIONS\": [{\"NAME\": \"air_still\", \"PROPOSITION\": \"the air is at rest in the frame of the body's velocity\", \"REFS\": [\"VELOCITY\"]}, {\"NAME\": \"air_uniform\", \"PROPOSITION\": \"the air density is uniform over the region of motion\", \"REFS\": [\"rho_air\"]}, {\"NAME\": \"drag_sphere\", \"PROPOSITION\": \"the body is a rigid sphere of radius R_s\", \"REFS\": [\"R_s\"]}], \"BOUNDARIES\": [{\"NAME\": \"drag_linear_regime\", \"PREDICATE\": \"2 rho_air |v| R_s / mu_air < 1: the regime of the linear law\", \"CONDITION\": \"mu_air != 0 and SPEED2 >= 0 and 2*rho_air*sqrt(SPEED2)*R_s/mu_air < 1\"}], \"NOT_CHOSEN\": \"No linear (Stokes) air resistance.\", \"NOT_INCLUDED\": [\"No wind: the air is at rest.\", \"No change of air density or viscosity with altitude or temperature.\", \"No drag outside the regime of the linear law.\"], \"EXCLUDES\": [], \"INTERACTS_WITH\": [], \"TEST_BINDINGS\": [{\"NAME\": \"PROJECTILE_2D\", \"TPK\": {\"DOF\": [{\"NAME\": \"t\", \"DIMENSION\": \"T1\"}, {\"NAME\": \"x\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"z\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"v_x\", \"DIMENSION\": \"L1 T-1\"}, {\"NAME\": \"v_z\", \"DIMENSION\": \"L1 T-1\"}], \"CONSTANT\": [{\"NAME\": \"m\", \"DIMENSION\": \"M1\"}], \"LAW\": [{\"NAME\": \"KIN_X\", \"STATEMENT\": \"dx/dt = v_x\", \"REFS\": [\"t\", \"v_x\", \"x\"], \"ROLE\": \"EOM(x)\", \"EQUATION\": \"D(x,t)=v_x\"}, {\"NAME\": \"KIN_Z\", \"STATEMENT\": \"dz/dt = v_z\", \"REFS\": [\"t\", \"v_z\", \"z\"], \"ROLE\": \"EOM(z)\", \"EQUATION\": \"D(z,t)=v_z\"}, {\"NAME\": \"EOM_X\", \"STATEMENT\": \"m dv_x/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_x\"], \"ROLE\": \"EOM(v_x)\", \"EQUATION\": \"m*D(v_x,t)=0\"}, {\"NAME\": \"EOM_Z\", \"STATEMENT\": \"m dv_z/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_z\"], \"ROLE\": \"EOM(v_z)\", \"EQUATION\": \"m*D(v_z,t)=0\"}], \"ASSUMPTION\": [{\"NAME\": \"point_mass\", \"PROPOSITION\": \"the body is treated as a point mass\", \"REFS\": [\"m\"]}]}, \"BIND\": {\"VELOCITY\": [\"v_x\", \"v_z\"]}, \"VALUES\": {\"R_s\": {}}, \"ANSWERS\": {}}]}",
"{\"ID\": \"AIR-QUADRATIC\", \"VERSION\": \"1.0.0\", \"TITLE\": \"Air resistance at sea level, quadratic in the speed\", \"SOURCE\": \"ISO 2533:1975, Standard Atmosphere, sea-level values: density 1.225 kg m-3, dynamic viscosity 1.7894e-5 Pa s\", \"PREREQUISITES\": [{\"SLOT\": \"VELOCITY\", \"KIND\": \"DOF\", \"DIMENSION\": \"L1 T-1\", \"MIN\": 1, \"MAX\": 3, \"LABEL\": \"the velocity components of the body, one per axis\"}], \"PARAMETERS\": [{\"NAME\": \"rho_air\", \"DIMENSION\": \"L-3 M1\", \"SUPPLY\": \"DECLARED\", \"VALUE\": \"1.225\", \"UNIT\": \"kg m-3\", \"OVERRIDABLE\": \"NO\", \"LABEL\": \"the density of air at sea level\"}, {\"NAME\": \"mu_air\", \"DIMENSION\": \"L-1 M1 T-1\", \"SUPPLY\": \"DECLARED\", \"VALUE\": \"1.7894e-5\", \"UNIT\": \"Pa s\", \"OVERRIDABLE\": \"NO\", \"LABEL\": \"the dynamic viscosity of air at sea level\"}, {\"NAME\": \"C_d\", \"DIMENSION\": \"1\", \"SUPPLY\": \"AUTHOR\", \"LABEL\": \"the drag coefficient of the body\"}, {\"NAME\": \"A_ref\", \"DIMENSION\": \"L2\", \"SUPPLY\": \"AUTHOR\", \"LABEL\": \"the reference area of the drag coefficient\"}, {\"NAME\": \"L_ref\", \"DIMENSION\": \"L1\", \"SUPPLY\": \"AUTHOR\", \"LABEL\": \"the reference length of the Reynolds number\"}], \"SUMS\": [{\"NAME\": \"SPEED2\", \"OVER\": \"VELOCITY\", \"EACH\": \"VELOCITY^2\"}], \"TERMS\": [{\"TARGET\": \"VELOCITY\", \"SIGN\": \"-\", \"EXPR\": \"0.5*rho_air*C_d*A_ref*sqrt(SPEED2)*VELOCITY\", \"LABEL\": \"the quadratic drag\"}], \"ASSUMPTIONS\": [{\"NAME\": \"air_still\", \"PROPOSITION\": \"the air is at rest in the frame of the body's velocity\", \"REFS\": [\"VELOCITY\"]}, {\"NAME\": \"air_uniform\", \"PROPOSITION\": \"the air density is uniform over the region of motion\", \"REFS\": [\"rho_air\"]}, {\"NAME\": \"drag_cd_constant\", \"PROPOSITION\": \"the drag coefficient C_d is constant over the motion\", \"REFS\": [\"C_d\"]}, {\"NAME\": \"drag_no_lift\", \"PROPOSITION\": \"the body experiences no lift force\", \"REFS\": [\"VELOCITY\"]}, {\"NAME\": \"drag_no_magnus\", \"PROPOSITION\": \"the body experiences no Magnus force\", \"REFS\": [\"VELOCITY\"]}], \"BOUNDARIES\": [{\"NAME\": \"drag_quadratic_regime\", \"PREDICATE\": \"1e3 < rho_air |v| L_ref / mu_air < 2e5: the Reynolds window of the quadratic law\", \"CONDITION\": \"mu_air != 0 and SPEED2 >= 0 and rho_air*sqrt(SPEED2)*L_ref/mu_air > 1000 and rho_air*sqrt(SPEED2)*L_ref/mu_air < 200000\"}], \"NOT_CHOSEN\": \"No quadratic air resistance.\", \"NOT_INCLUDED\": [\"No wind: the air is at rest.\", \"No change of air density or viscosity with altitude or temperature.\", \"No lift, Magnus or added-mass force.\", \"No drag outside the Reynolds window of the quadratic law.\"], \"EXCLUDES\": [\"AIR-LINEAR\"], \"INTERACTS_WITH\": [], \"TEST_BINDINGS\": [{\"NAME\": \"PROJECTILE_2D\", \"TPK\": {\"DOF\": [{\"NAME\": \"t\", \"DIMENSION\": \"T1\"}, {\"NAME\": \"x\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"z\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"v_x\", \"DIMENSION\": \"L1 T-1\"}, {\"NAME\": \"v_z\", \"DIMENSION\": \"L1 T-1\"}], \"CONSTANT\": [{\"NAME\": \"m\", \"DIMENSION\": \"M1\"}], \"LAW\": [{\"NAME\": \"KIN_X\", \"STATEMENT\": \"dx/dt = v_x\", \"REFS\": [\"t\", \"v_x\", \"x\"], \"ROLE\": \"EOM(x)\", \"EQUATION\": \"D(x,t)=v_x\"}, {\"NAME\": \"KIN_Z\", \"STATEMENT\": \"dz/dt = v_z\", \"REFS\": [\"t\", \"v_z\", \"z\"], \"ROLE\": \"EOM(z)\", \"EQUATION\": \"D(z,t)=v_z\"}, {\"NAME\": \"EOM_X\", \"STATEMENT\": \"m dv_x/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_x\"], \"ROLE\": \"EOM(v_x)\", \"EQUATION\": \"m*D(v_x,t)=0\"}, {\"NAME\": \"EOM_Z\", \"STATEMENT\": \"m dv_z/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_z\"], \"ROLE\": \"EOM(v_z)\", \"EQUATION\": \"m*D(v_z,t)=0\"}], \"ASSUMPTION\": [{\"NAME\": \"point_mass\", \"PROPOSITION\": \"the body is treated as a point mass\", \"REFS\": [\"m\"]}]}, \"BIND\": {\"VELOCITY\": [\"v_x\", \"v_z\"]}, \"VALUES\": {\"A_ref\": {}, \"C_d\": {}, \"L_ref\": {}}, \"ANSWERS\": {}}]}",
"{\"ID\": \"GRAV-UNIFORM\", \"VERSION\": \"1.0.0\", \"TITLE\": \"Uniform gravity at the standard value g_n\", \"SOURCE\": \"g_n = 9.80665 m s-2, exact by definition: 3rd CGPM (1901), declaration on the unit of mass and on the definition of weight\", \"PREREQUISITES\": [{\"SLOT\": \"MASS\", \"KIND\": \"CONSTANT\", \"DIMENSION\": \"M1\", \"MIN\": 1, \"MAX\": 1, \"LABEL\": \"the mass of the body\"}, {\"SLOT\": \"UP_VELOCITY\", \"KIND\": \"DOF\", \"DIMENSION\": \"L1 T-1\", \"MIN\": 1, \"MAX\": 1, \"LABEL\": \"the velocity component pointing up; its equation of motion receives the weight\"}, {\"SLOT\": \"HEIGHT\", \"KIND\": \"DOF\", \"DIMENSION\": \"L1\", \"MIN\": 1, \"MAX\": 1, \"LABEL\": \"the position along the same upward axis\"}], \"PARAMETERS\": [{\"NAME\": \"g_n\", \"DIMENSION\": \"L1 T-2\", \"SUPPLY\": \"DECLARED\", \"VALUE\": \"9.80665\", \"UNIT\": \"m s-2\", \"OVERRIDABLE\": \"NO\", \"LABEL\": \"the standard acceleration of gravity\"}, {\"NAME\": \"h_max\", \"DIMENSION\": \"L1\", \"SUPPLY\": \"AUTHOR\", \"LABEL\": \"the largest height, above or below the origin, over which the field is taken as uniform\"}], \"SUMS\": [], \"TERMS\": [{\"TARGET\": \"UP_VELOCITY\", \"SIGN\": \"-\", \"EXPR\": \"MASS*g_n\", \"LABEL\": \"the weight\"}], \"ASSUMPTIONS\": [{\"NAME\": \"gravity_uniform\", \"PROPOSITION\": \"the gravitational field is uniform over the region abs({HEIGHT}) < h_max\", \"REFS\": [\"HEIGHT\", \"h_max\"]}, {\"NAME\": \"gravity_standard\", \"PROPOSITION\": \"the local gravitational acceleration equals the conventional standard value g_n\", \"REFS\": [\"g_n\"]}, {\"NAME\": \"frame_inertial\", \"PROPOSITION\": \"the frame in which {HEIGHT} is measured is treated as inertial\", \"REFS\": [\"HEIGHT\"]}], \"BOUNDARIES\": [{\"NAME\": \"gravity_region\", \"PREDICATE\": \"abs({HEIGHT}) < h_max\", \"CONDITION\": \"abs(HEIGHT) < h_max\"}], \"NOT_CHOSEN\": \"No gravity: no weight acts on any DOF.\", \"NOT_INCLUDED\": [\"No variation of gravity with height or latitude beyond what g_n contains.\", \"No Earth rotation (Coriolis or centrifugal force) beyond what g_n contains.\", \"No gravity of bodies other than the Earth.\"], \"EXCLUDES\": [], \"INTERACTS_WITH\": [{\"WITH\": \"AIR-*\", \"QUESTION_ID\": \"BUOYANCY\", \"QUESTION\": \"Does the air's buoyancy (upthrust) act on the body in the system you mean?\", \"YES_LINE\": \"Buoyancy acts (your answer): no module adds it; it acts in this kernel only where one of your own laws states it.\", \"NO_LINE\": \"No buoyancy: the air's upthrust on the body is not included.\"}], \"TEST_BINDINGS\": [{\"NAME\": \"PROJECTILE_2D\", \"TPK\": {\"DOF\": [{\"NAME\": \"t\", \"DIMENSION\": \"T1\"}, {\"NAME\": \"x\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"z\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"v_x\", \"DIMENSION\": \"L1 T-1\"}, {\"NAME\": \"v_z\", \"DIMENSION\": \"L1 T-1\"}], \"CONSTANT\": [{\"NAME\": \"m\", \"DIMENSION\": \"M1\"}], \"LAW\": [{\"NAME\": \"KIN_X\", \"STATEMENT\": \"dx/dt = v_x\", \"REFS\": [\"t\", \"v_x\", \"x\"], \"ROLE\": \"EOM(x)\", \"EQUATION\": \"D(x,t)=v_x\"}, {\"NAME\": \"KIN_Z\", \"STATEMENT\": \"dz/dt = v_z\", \"REFS\": [\"t\", \"v_z\", \"z\"], \"ROLE\": \"EOM(z)\", \"EQUATION\": \"D(z,t)=v_z\"}, {\"NAME\": \"EOM_X\", \"STATEMENT\": \"m dv_x/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_x\"], \"ROLE\": \"EOM(v_x)\", \"EQUATION\": \"m*D(v_x,t)=0\"}, {\"NAME\": \"EOM_Z\", \"STATEMENT\": \"m dv_z/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_z\"], \"ROLE\": \"EOM(v_z)\", \"EQUATION\": \"m*D(v_z,t)=0\"}], \"ASSUMPTION\": [{\"NAME\": \"point_mass\", \"PROPOSITION\": \"the body is treated as a point mass\", \"REFS\": [\"m\"]}]}, \"BIND\": {\"HEIGHT\": [\"z\"], \"MASS\": [\"m\"], \"UP_VELOCITY\": [\"v_z\"]}, \"VALUES\": {\"h_max\": {\"VALUE\": \"100\", \"UNIT\": \"m\"}}, \"ANSWERS\": {}}, {\"NAME\": \"TABLE\", \"TPK\": {\"DOF\": [{\"NAME\": \"t\", \"DIMENSION\": \"T1\"}, {\"NAME\": \"x\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"z\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"v_x\", \"DIMENSION\": \"L1 T-1\"}, {\"NAME\": \"v_z\", \"DIMENSION\": \"L1 T-1\"}], \"CONSTANT\": [{\"NAME\": \"m\", \"DIMENSION\": \"M1\"}], \"LAW\": [{\"NAME\": \"KIN_X\", \"STATEMENT\": \"dx/dt = v_x\", \"REFS\": [\"t\", \"v_x\", \"x\"], \"ROLE\": \"EOM(x)\", \"EQUATION\": \"D(x,t)=v_x\"}, {\"NAME\": \"KIN_Z\", \"STATEMENT\": \"dz/dt = v_z\", \"REFS\": [\"t\", \"v_z\", \"z\"], \"ROLE\": \"CONSTRAINT\", \"EQUATION\": \"D(z,t)=v_z\"}, {\"NAME\": \"EOM_X\", \"STATEMENT\": \"m dv_x/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_x\"], \"ROLE\": \"EOM(v_x)\", \"EQUATION\": \"m*D(v_x,t)=0\"}], \"CONSTRAINT\": [{\"NAME\": \"C_Z\", \"TARGET\": \"z\", \"ACTION\": \"FIX\", \"VALUE\": \"0\", \"UNIT\": \"m\", \"STATEMENT\": \"the puck stays on the table top, z = 0\"}, {\"NAME\": \"C_VZ\", \"TARGET\": \"v_z\", \"ACTION\": \"FIX\", \"VALUE\": \"0\", \"UNIT\": \"m s-1\", \"STATEMENT\": \"the puck has no vertical velocity\"}]}, \"BIND\": {\"HEIGHT\": [\"z\"], \"MASS\": [\"m\"], \"UP_VELOCITY\": [\"v_z\"]}, \"VALUES\": {\"h_max\": {\"VALUE\": \"1\", \"UNIT\": \"m\"}}, \"ANSWERS\": {\"FIXED:v_z\": \"YES\"}}]}",
"{\"ID\": \"MATH\", \"VERSION\": \"1.0.0\", \"TITLE\": \"The mathematical constant pi, as the CONSTANT pi_c\", \"SOURCE\": \"pi to 16 significant digits, 3.141592653589793, the nearest IEEE 754 binary64 value\", \"PREREQUISITES\": [], \"PARAMETERS\": [{\"NAME\": \"pi_c\", \"DIMENSION\": \"1\", \"SUPPLY\": \"DECLARED\", \"VALUE\": \"3.141592653589793\", \"UNIT\": \"1\", \"OVERRIDABLE\": \"NO\", \"LABEL\": \"pi, to 16 significant digits\"}], \"SUMS\": [], \"TERMS\": [], \"ASSUMPTIONS\": [], \"BOUNDARIES\": [], \"NOT_CHOSEN\": \"No mathematical constant: pi exists only if you declare it.\", \"NOT_INCLUDED\": [\"pi_c is pi rounded to 16 significant digits; no other mathematical constant is declared.\"], \"EXCLUDES\": [], \"INTERACTS_WITH\": [], \"TEST_BINDINGS\": [{\"NAME\": \"PROJECTILE_2D\", \"TPK\": {\"DOF\": [{\"NAME\": \"t\", \"DIMENSION\": \"T1\"}, {\"NAME\": \"x\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"z\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"v_x\", \"DIMENSION\": \"L1 T-1\"}, {\"NAME\": \"v_z\", \"DIMENSION\": \"L1 T-1\"}], \"CONSTANT\": [{\"NAME\": \"m\", \"DIMENSION\": \"M1\"}], \"LAW\": [{\"NAME\": \"KIN_X\", \"STATEMENT\": \"dx/dt = v_x\", \"REFS\": [\"t\", \"v_x\", \"x\"], \"ROLE\": \"EOM(x)\", \"EQUATION\": \"D(x,t)=v_x\"}, {\"NAME\": \"KIN_Z\", \"STATEMENT\": \"dz/dt = v_z\", \"REFS\": [\"t\", \"v_z\", \"z\"], \"ROLE\": \"EOM(z)\", \"EQUATION\": \"D(z,t)=v_z\"}, {\"NAME\": \"EOM_X\", \"STATEMENT\": \"m dv_x/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_x\"], \"ROLE\": \"EOM(v_x)\", \"EQUATION\": \"m*D(v_x,t)=0\"}, {\"NAME\": \"EOM_Z\", \"STATEMENT\": \"m dv_z/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_z\"], \"ROLE\": \"EOM(v_z)\", \"EQUATION\": \"m*D(v_z,t)=0\"}], \"ASSUMPTION\": [{\"NAME\": \"point_mass\", \"PROPOSITION\": \"the body is treated as a point mass\", \"REFS\": [\"m\"]}]}, \"BIND\": {}, \"VALUES\": {}, \"ANSWERS\": {}}]}",
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it acts in this kernel only where one of your own laws states it.\", \"NO_LINE\": \"No buoyancy: the air's upthrust on the body is not included.\"}], \"TEST_BINDINGS\": [{\"NAME\": \"PROJECTILE_2D\", \"TPK\": {\"DOF\": [{\"NAME\": \"t\", \"DIMENSION\": \"T1\"}, {\"NAME\": \"x\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"z\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"v_x\", \"DIMENSION\": \"L1 T-1\"}, {\"NAME\": \"v_z\", \"DIMENSION\": \"L1 T-1\"}], \"CONSTANT\": [{\"NAME\": \"m\", \"DIMENSION\": \"M1\"}], \"LAW\": [{\"NAME\": \"KIN_X\", \"STATEMENT\": \"dx/dt = v_x\", \"REFS\": [\"t\", \"v_x\", \"x\"], \"ROLE\": \"EOM(x)\", \"EQUATION\": \"D(x,t)=v_x\"}, {\"NAME\": \"KIN_Z\", \"STATEMENT\": \"dz/dt = v_z\", \"REFS\": [\"t\", \"v_z\", \"z\"], \"ROLE\": \"EOM(z)\", \"EQUATION\": \"D(z,t)=v_z\"}, {\"NAME\": \"EOM_X\", \"STATEMENT\": \"m dv_x/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_x\"], \"ROLE\": \"EOM(v_x)\", \"EQUATION\": \"m*D(v_x,t)=0\"}, {\"NAME\": \"EOM_Z\", \"STATEMENT\": \"m dv_z/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_z\"], \"ROLE\": \"EOM(v_z)\", \"EQUATION\": \"m*D(v_z,t)=0\"}], \"ASSUMPTION\": [{\"NAME\": \"point_mass\", \"PROPOSITION\": \"the body is treated as a point mass\", \"REFS\": [\"m\"]}]}, \"BIND\": {\"HEIGHT\": [\"z\"], \"MASS\": [\"m\"], \"UP_VELOCITY\": [\"v_z\"]}, \"VALUES\": {\"h_max\": {\"VALUE\": \"100\", \"UNIT\": \"m\"}}, \"ANSWERS\": {}}, {\"NAME\": \"TABLE\", \"TPK\": {\"DOF\": [{\"NAME\": \"t\", \"DIMENSION\": \"T1\"}, {\"NAME\": \"x\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"z\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"v_x\", \"DIMENSION\": \"L1 T-1\"}, {\"NAME\": \"v_z\", \"DIMENSION\": \"L1 T-1\"}], \"CONSTANT\": [{\"NAME\": \"m\", \"DIMENSION\": \"M1\"}], \"LAW\": [{\"NAME\": \"KIN_X\", \"STATEMENT\": \"dx/dt = v_x\", \"REFS\": [\"t\", \"v_x\", \"x\"], \"ROLE\": \"EOM(x)\", \"EQUATION\": \"D(x,t)=v_x\"}, {\"NAME\": \"KIN_Z\", \"STATEMENT\": \"dz/dt = v_z\", \"REFS\": [\"t\", \"v_z\", \"z\"], \"ROLE\": \"CONSTRAINT\", \"EQUATION\": \"D(z,t)=v_z\"}, {\"NAME\": \"EOM_X\", \"STATEMENT\": \"m dv_x/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_x\"], \"ROLE\": \"EOM(v_x)\", \"EQUATION\": \"m*D(v_x,t)=0\"}], \"CONSTRAINT\": [{\"NAME\": \"C_Z\", \"TARGET\": \"z\", \"ACTION\": \"FIX\", \"VALUE\": \"0\", \"UNIT\": \"m\", \"STATEMENT\": \"the puck stays on the table top, z = 0\"}, {\"NAME\": \"C_VZ\", \"TARGET\": \"v_z\", \"ACTION\": \"FIX\", \"VALUE\": \"0\", \"UNIT\": \"m s-1\", \"STATEMENT\": \"the puck has no vertical velocity\"}]}, \"BIND\": {\"HEIGHT\": [\"z\"], \"MASS\": [\"m\"], \"UP_VELOCITY\": [\"v_z\"]}, \"VALUES\": {\"h_max\": {\"VALUE\": \"1\", \"UNIT\": \"m\"}}, \"ANSWERS\": {\"FIXED:v_z\": \"YES\"}}]}"
]
},
"expected": "[\"OK\",[\"ASK\",[]],[\"CLAIMS\",[[\"GRAV-UNIFORM\",\"1.0.0\",\"PINNED\"]]]]",
"fn": "interview_check",
"hand_checked": true,
"name": "I18 a pinned claim whose version was SUPERSEDED after the answer: kept"
},
{
"args": {
"answer": [
{
"AT": 5,
"CHOSEN": [
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],
"COVERED": [
[
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[
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[
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[
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]
]
}
],
"carried": [],
"claims": [
{
"ANSWERS": {},
"BIND": {
"HEIGHT": [
"z"
],
"MASS": [
"m"
],
"UP_VELOCITY": [
"v_z"
]
},
"DIGEST": "24877ccb5c8ec300d29ed82ce6650592f35cf8899a3d878ccce9c08d4c72c025",
"ID": "GRAV-UNIFORM",
"VALUES": {
"h_max": {
"UNIT": "m",
"VALUE": "100"
}
},
"VERSION": "1.0.0"
}
],
"lines": [
{
"ACT": "MODULE ADD",
"DATE": "2026-10-01",
"DIGEST": "5f3fe27b42378bce0830b0d0959f892f4a8e73b12b540ae877e39e6439d08b4d",
"ID": "AIR-LINEAR",
"VERSION": "1.0.0"
},
{
"ACT": "MODULE ADD",
"DATE": "2026-10-01",
"DIGEST": "6fb53c3a6546151eead2bd6e72e9cf8334f3a2040ad0ee2f5b988ec96d6fc852",
"ID": "AIR-QUADRATIC",
"VERSION": "1.0.0"
},
{
"ACT": "MODULE ADD",
"DATE": "2026-10-01",
"DIGEST": "24877ccb5c8ec300d29ed82ce6650592f35cf8899a3d878ccce9c08d4c72c025",
"ID": "GRAV-UNIFORM",
"VERSION": "1.0.0"
},
{
"ACT": "MODULE ADD",
"DATE": "2026-10-01",
"DIGEST": "8f39a356f35527b901fcee012764590f0819c8ffdeccad4bc05195ce3d2e0bcf",
"ID": "MATH",
"VERSION": "1.0.0"
},
{
"ACT": "MODULE VERSION",
"DATE": "2026-10-02",
"DIGEST": "5be3923c28dc8f8ff910b033c2d17154f267f2a20fdb32c74a07293a37dfe338",
"ID": "GRAV-UNIFORM",
"VERSION": "1.1.0"
}
],
"modified": [],
"modules": [
"{\"ID\": \"AIR-LINEAR\", \"VERSION\": \"1.0.0\", \"TITLE\": \"Air resistance at sea level, linear in the speed (Stokes drag on a sphere)\", \"SOURCE\": \"ISO 2533:1975, Standard Atmosphere, sea-level values: density 1.225 kg m-3, dynamic viscosity 1.7894e-5 Pa s\", \"PREREQUISITES\": [{\"SLOT\": \"VELOCITY\", \"KIND\": \"DOF\", \"DIMENSION\": \"L1 T-1\", \"MIN\": 1, \"MAX\": 3, \"LABEL\": \"the velocity components of the body, one per axis\"}], \"PARAMETERS\": [{\"NAME\": \"rho_air\", \"DIMENSION\": \"L-3 M1\", \"SUPPLY\": \"DECLARED\", \"VALUE\": \"1.225\", \"UNIT\": \"kg m-3\", \"OVERRIDABLE\": \"NO\", \"LABEL\": \"the density of air at sea level\"}, {\"NAME\": \"mu_air\", \"DIMENSION\": \"L-1 M1 T-1\", \"SUPPLY\": \"DECLARED\", \"VALUE\": \"1.7894e-5\", \"UNIT\": \"Pa s\", \"OVERRIDABLE\": \"NO\", \"LABEL\": \"the dynamic viscosity of air at sea level\"}, {\"NAME\": \"pi_c\", \"DIMENSION\": \"1\", \"SUPPLY\": \"DECLARED\", \"VALUE\": \"3.141592653589793\", \"UNIT\": \"1\", \"OVERRIDABLE\": \"NO\", \"LABEL\": \"pi, to 16 significant digits\"}, {\"NAME\": \"R_s\", \"DIMENSION\": \"L1\", \"SUPPLY\": \"AUTHOR\", \"LABEL\": \"the radius of the sphere\"}], \"SUMS\": [{\"NAME\": \"SPEED2\", \"OVER\": \"VELOCITY\", \"EACH\": \"VELOCITY^2\"}], \"TERMS\": [{\"TARGET\": \"VELOCITY\", \"SIGN\": \"-\", \"EXPR\": \"6*pi_c*mu_air*R_s*VELOCITY\", \"LABEL\": \"the linear (Stokes) drag\"}], \"ASSUMPTIONS\": [{\"NAME\": \"air_still\", \"PROPOSITION\": \"the air is at rest in the frame of the body's velocity\", \"REFS\": [\"VELOCITY\"]}, {\"NAME\": \"air_uniform\", \"PROPOSITION\": \"the air density is uniform over the region of motion\", \"REFS\": [\"rho_air\"]}, {\"NAME\": \"drag_sphere\", \"PROPOSITION\": \"the body is a rigid sphere of radius R_s\", \"REFS\": [\"R_s\"]}], \"BOUNDARIES\": [{\"NAME\": \"drag_linear_regime\", \"PREDICATE\": \"2 rho_air |v| R_s / mu_air < 1: the regime of the linear law\", \"CONDITION\": \"mu_air != 0 and SPEED2 >= 0 and 2*rho_air*sqrt(SPEED2)*R_s/mu_air < 1\"}], \"NOT_CHOSEN\": \"No linear (Stokes) air resistance.\", \"NOT_INCLUDED\": [\"No wind: the air is at rest.\", \"No change of air density or viscosity with altitude or temperature.\", \"No drag outside the regime of the linear law.\"], \"EXCLUDES\": [], \"INTERACTS_WITH\": [], \"TEST_BINDINGS\": [{\"NAME\": \"PROJECTILE_2D\", \"TPK\": {\"DOF\": [{\"NAME\": \"t\", \"DIMENSION\": \"T1\"}, {\"NAME\": \"x\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"z\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"v_x\", \"DIMENSION\": \"L1 T-1\"}, {\"NAME\": \"v_z\", \"DIMENSION\": \"L1 T-1\"}], \"CONSTANT\": [{\"NAME\": \"m\", \"DIMENSION\": \"M1\"}], \"LAW\": [{\"NAME\": \"KIN_X\", \"STATEMENT\": \"dx/dt = v_x\", \"REFS\": [\"t\", \"v_x\", \"x\"], \"ROLE\": \"EOM(x)\", \"EQUATION\": \"D(x,t)=v_x\"}, {\"NAME\": \"KIN_Z\", \"STATEMENT\": \"dz/dt = v_z\", \"REFS\": [\"t\", \"v_z\", \"z\"], \"ROLE\": \"EOM(z)\", \"EQUATION\": \"D(z,t)=v_z\"}, {\"NAME\": \"EOM_X\", \"STATEMENT\": \"m dv_x/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_x\"], \"ROLE\": \"EOM(v_x)\", \"EQUATION\": \"m*D(v_x,t)=0\"}, {\"NAME\": \"EOM_Z\", \"STATEMENT\": \"m dv_z/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_z\"], \"ROLE\": \"EOM(v_z)\", \"EQUATION\": \"m*D(v_z,t)=0\"}], \"ASSUMPTION\": [{\"NAME\": \"point_mass\", \"PROPOSITION\": \"the body is treated as a point mass\", \"REFS\": [\"m\"]}]}, \"BIND\": {\"VELOCITY\": [\"v_x\", \"v_z\"]}, \"VALUES\": {\"R_s\": {}}, \"ANSWERS\": {}}]}",
"{\"ID\": \"AIR-QUADRATIC\", \"VERSION\": \"1.0.0\", \"TITLE\": \"Air resistance at sea level, quadratic in the speed\", \"SOURCE\": \"ISO 2533:1975, Standard Atmosphere, sea-level values: density 1.225 kg m-3, dynamic viscosity 1.7894e-5 Pa s\", \"PREREQUISITES\": [{\"SLOT\": \"VELOCITY\", \"KIND\": \"DOF\", \"DIMENSION\": \"L1 T-1\", \"MIN\": 1, \"MAX\": 3, \"LABEL\": \"the velocity components of the body, one per axis\"}], \"PARAMETERS\": [{\"NAME\": \"rho_air\", \"DIMENSION\": \"L-3 M1\", \"SUPPLY\": \"DECLARED\", \"VALUE\": \"1.225\", \"UNIT\": \"kg m-3\", \"OVERRIDABLE\": \"NO\", \"LABEL\": \"the density of air at sea level\"}, {\"NAME\": \"mu_air\", \"DIMENSION\": \"L-1 M1 T-1\", \"SUPPLY\": \"DECLARED\", \"VALUE\": \"1.7894e-5\", \"UNIT\": \"Pa s\", \"OVERRIDABLE\": \"NO\", \"LABEL\": \"the dynamic viscosity of air at sea level\"}, {\"NAME\": \"C_d\", \"DIMENSION\": \"1\", \"SUPPLY\": \"AUTHOR\", \"LABEL\": \"the drag coefficient of the body\"}, {\"NAME\": \"A_ref\", \"DIMENSION\": \"L2\", \"SUPPLY\": \"AUTHOR\", \"LABEL\": \"the reference area of the drag coefficient\"}, {\"NAME\": \"L_ref\", \"DIMENSION\": \"L1\", \"SUPPLY\": \"AUTHOR\", \"LABEL\": \"the reference length of the Reynolds number\"}], \"SUMS\": [{\"NAME\": \"SPEED2\", \"OVER\": \"VELOCITY\", \"EACH\": \"VELOCITY^2\"}], \"TERMS\": [{\"TARGET\": \"VELOCITY\", \"SIGN\": \"-\", \"EXPR\": \"0.5*rho_air*C_d*A_ref*sqrt(SPEED2)*VELOCITY\", \"LABEL\": \"the quadratic drag\"}], \"ASSUMPTIONS\": [{\"NAME\": \"air_still\", \"PROPOSITION\": \"the air is at rest in the frame of the body's velocity\", \"REFS\": [\"VELOCITY\"]}, {\"NAME\": \"air_uniform\", \"PROPOSITION\": \"the air density is uniform over the region of motion\", \"REFS\": [\"rho_air\"]}, {\"NAME\": \"drag_cd_constant\", \"PROPOSITION\": \"the drag coefficient C_d is constant over the motion\", \"REFS\": [\"C_d\"]}, {\"NAME\": \"drag_no_lift\", \"PROPOSITION\": \"the body experiences no lift force\", \"REFS\": [\"VELOCITY\"]}, {\"NAME\": \"drag_no_magnus\", \"PROPOSITION\": \"the body experiences no Magnus force\", \"REFS\": [\"VELOCITY\"]}], \"BOUNDARIES\": [{\"NAME\": \"drag_quadratic_regime\", \"PREDICATE\": \"1e3 < rho_air |v| L_ref / mu_air < 2e5: the Reynolds window of the quadratic law\", \"CONDITION\": \"mu_air != 0 and SPEED2 >= 0 and rho_air*sqrt(SPEED2)*L_ref/mu_air > 1000 and rho_air*sqrt(SPEED2)*L_ref/mu_air < 200000\"}], \"NOT_CHOSEN\": \"No quadratic air resistance.\", \"NOT_INCLUDED\": [\"No wind: the air is at rest.\", \"No change of air density or viscosity with altitude or temperature.\", \"No lift, Magnus or added-mass force.\", \"No drag outside the Reynolds window of the quadratic law.\"], \"EXCLUDES\": [\"AIR-LINEAR\"], \"INTERACTS_WITH\": [], \"TEST_BINDINGS\": [{\"NAME\": \"PROJECTILE_2D\", \"TPK\": {\"DOF\": [{\"NAME\": \"t\", \"DIMENSION\": \"T1\"}, {\"NAME\": \"x\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"z\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"v_x\", \"DIMENSION\": \"L1 T-1\"}, {\"NAME\": \"v_z\", \"DIMENSION\": \"L1 T-1\"}], \"CONSTANT\": [{\"NAME\": \"m\", \"DIMENSION\": \"M1\"}], \"LAW\": [{\"NAME\": \"KIN_X\", \"STATEMENT\": \"dx/dt = v_x\", \"REFS\": [\"t\", \"v_x\", \"x\"], \"ROLE\": \"EOM(x)\", \"EQUATION\": \"D(x,t)=v_x\"}, {\"NAME\": \"KIN_Z\", \"STATEMENT\": \"dz/dt = v_z\", \"REFS\": [\"t\", \"v_z\", \"z\"], \"ROLE\": \"EOM(z)\", \"EQUATION\": \"D(z,t)=v_z\"}, {\"NAME\": \"EOM_X\", \"STATEMENT\": \"m dv_x/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_x\"], \"ROLE\": \"EOM(v_x)\", \"EQUATION\": \"m*D(v_x,t)=0\"}, {\"NAME\": \"EOM_Z\", \"STATEMENT\": \"m dv_z/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_z\"], \"ROLE\": \"EOM(v_z)\", \"EQUATION\": \"m*D(v_z,t)=0\"}], \"ASSUMPTION\": [{\"NAME\": \"point_mass\", \"PROPOSITION\": \"the body is treated as a point mass\", \"REFS\": [\"m\"]}]}, \"BIND\": {\"VELOCITY\": [\"v_x\", \"v_z\"]}, \"VALUES\": {\"A_ref\": {}, \"C_d\": {}, \"L_ref\": {}}, \"ANSWERS\": {}}]}",
"{\"ID\": \"GRAV-UNIFORM\", \"VERSION\": \"1.0.0\", \"TITLE\": \"Uniform gravity at the standard value g_n\", \"SOURCE\": \"g_n = 9.80665 m s-2, exact by definition: 3rd CGPM (1901), declaration on the unit of mass and on the definition of weight\", \"PREREQUISITES\": [{\"SLOT\": \"MASS\", \"KIND\": \"CONSTANT\", \"DIMENSION\": \"M1\", \"MIN\": 1, \"MAX\": 1, \"LABEL\": \"the mass of the body\"}, {\"SLOT\": \"UP_VELOCITY\", \"KIND\": \"DOF\", \"DIMENSION\": \"L1 T-1\", \"MIN\": 1, \"MAX\": 1, \"LABEL\": \"the velocity component pointing up; its equation of motion receives the weight\"}, {\"SLOT\": \"HEIGHT\", \"KIND\": \"DOF\", \"DIMENSION\": \"L1\", \"MIN\": 1, \"MAX\": 1, \"LABEL\": \"the position along the same upward axis\"}], \"PARAMETERS\": [{\"NAME\": \"g_n\", \"DIMENSION\": \"L1 T-2\", \"SUPPLY\": \"DECLARED\", \"VALUE\": \"9.80665\", \"UNIT\": \"m s-2\", \"OVERRIDABLE\": \"NO\", \"LABEL\": \"the standard acceleration of gravity\"}, {\"NAME\": \"h_max\", \"DIMENSION\": \"L1\", \"SUPPLY\": \"AUTHOR\", \"LABEL\": \"the largest height, above or below the origin, over which the field is taken as uniform\"}], \"SUMS\": [], \"TERMS\": [{\"TARGET\": \"UP_VELOCITY\", \"SIGN\": \"-\", \"EXPR\": \"MASS*g_n\", \"LABEL\": \"the weight\"}], \"ASSUMPTIONS\": [{\"NAME\": \"gravity_uniform\", \"PROPOSITION\": \"the gravitational field is uniform over the region abs({HEIGHT}) < h_max\", \"REFS\": [\"HEIGHT\", \"h_max\"]}, {\"NAME\": \"gravity_standard\", \"PROPOSITION\": \"the local gravitational acceleration equals the conventional standard value g_n\", \"REFS\": [\"g_n\"]}, {\"NAME\": \"frame_inertial\", \"PROPOSITION\": \"the frame in which {HEIGHT} is measured is treated as inertial\", \"REFS\": [\"HEIGHT\"]}], \"BOUNDARIES\": [{\"NAME\": \"gravity_region\", \"PREDICATE\": \"abs({HEIGHT}) < h_max\", \"CONDITION\": \"abs(HEIGHT) < h_max\"}], \"NOT_CHOSEN\": \"No gravity: no weight acts on any DOF.\", \"NOT_INCLUDED\": [\"No variation of gravity with height or latitude beyond what g_n contains.\", \"No Earth rotation (Coriolis or centrifugal force) beyond what g_n contains.\", \"No gravity of bodies other than the Earth.\"], \"EXCLUDES\": [], \"INTERACTS_WITH\": [{\"WITH\": \"AIR-*\", \"QUESTION_ID\": \"BUOYANCY\", \"QUESTION\": \"Does the air's buoyancy (upthrust) act on the body in the system you mean?\", \"YES_LINE\": \"Buoyancy acts (your answer): no module adds it; it acts in this kernel only where one of your own laws states it.\", \"NO_LINE\": \"No buoyancy: the air's upthrust on the body is not included.\"}], \"TEST_BINDINGS\": [{\"NAME\": \"PROJECTILE_2D\", \"TPK\": {\"DOF\": [{\"NAME\": \"t\", \"DIMENSION\": \"T1\"}, {\"NAME\": \"x\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"z\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"v_x\", \"DIMENSION\": \"L1 T-1\"}, {\"NAME\": \"v_z\", \"DIMENSION\": \"L1 T-1\"}], \"CONSTANT\": [{\"NAME\": \"m\", \"DIMENSION\": \"M1\"}], \"LAW\": [{\"NAME\": \"KIN_X\", \"STATEMENT\": \"dx/dt = v_x\", \"REFS\": [\"t\", \"v_x\", \"x\"], \"ROLE\": \"EOM(x)\", \"EQUATION\": \"D(x,t)=v_x\"}, {\"NAME\": \"KIN_Z\", \"STATEMENT\": \"dz/dt = v_z\", \"REFS\": [\"t\", \"v_z\", \"z\"], \"ROLE\": \"EOM(z)\", \"EQUATION\": \"D(z,t)=v_z\"}, {\"NAME\": \"EOM_X\", \"STATEMENT\": \"m dv_x/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_x\"], \"ROLE\": \"EOM(v_x)\", \"EQUATION\": \"m*D(v_x,t)=0\"}, {\"NAME\": \"EOM_Z\", \"STATEMENT\": \"m dv_z/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_z\"], \"ROLE\": \"EOM(v_z)\", \"EQUATION\": \"m*D(v_z,t)=0\"}], \"ASSUMPTION\": [{\"NAME\": \"point_mass\", \"PROPOSITION\": \"the body is treated as a point mass\", \"REFS\": [\"m\"]}]}, \"BIND\": {\"HEIGHT\": [\"z\"], \"MASS\": [\"m\"], \"UP_VELOCITY\": [\"v_z\"]}, \"VALUES\": {\"h_max\": {\"VALUE\": \"100\", \"UNIT\": \"m\"}}, \"ANSWERS\": {}}, {\"NAME\": \"TABLE\", \"TPK\": {\"DOF\": [{\"NAME\": \"t\", \"DIMENSION\": \"T1\"}, {\"NAME\": \"x\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"z\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"v_x\", \"DIMENSION\": \"L1 T-1\"}, {\"NAME\": \"v_z\", \"DIMENSION\": \"L1 T-1\"}], \"CONSTANT\": [{\"NAME\": \"m\", \"DIMENSION\": \"M1\"}], \"LAW\": [{\"NAME\": \"KIN_X\", \"STATEMENT\": \"dx/dt = v_x\", \"REFS\": [\"t\", \"v_x\", \"x\"], \"ROLE\": \"EOM(x)\", \"EQUATION\": \"D(x,t)=v_x\"}, {\"NAME\": \"KIN_Z\", \"STATEMENT\": \"dz/dt = v_z\", \"REFS\": [\"t\", \"v_z\", \"z\"], \"ROLE\": \"CONSTRAINT\", \"EQUATION\": \"D(z,t)=v_z\"}, {\"NAME\": \"EOM_X\", \"STATEMENT\": \"m dv_x/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_x\"], \"ROLE\": \"EOM(v_x)\", \"EQUATION\": \"m*D(v_x,t)=0\"}], \"CONSTRAINT\": [{\"NAME\": \"C_Z\", \"TARGET\": \"z\", \"ACTION\": \"FIX\", \"VALUE\": \"0\", \"UNIT\": \"m\", \"STATEMENT\": \"the puck stays on the table top, z = 0\"}, {\"NAME\": \"C_VZ\", \"TARGET\": \"v_z\", \"ACTION\": \"FIX\", \"VALUE\": \"0\", \"UNIT\": \"m s-1\", \"STATEMENT\": \"the puck has no vertical velocity\"}]}, \"BIND\": {\"HEIGHT\": [\"z\"], \"MASS\": [\"m\"], \"UP_VELOCITY\": [\"v_z\"]}, \"VALUES\": {\"h_max\": {\"VALUE\": \"1\", \"UNIT\": \"m\"}}, \"ANSWERS\": {\"FIXED:v_z\": \"YES\"}}]}",
"{\"ID\": \"MATH\", \"VERSION\": \"1.0.0\", \"TITLE\": \"The mathematical constant pi, as the CONSTANT pi_c\", \"SOURCE\": \"pi to 16 significant digits, 3.141592653589793, the nearest IEEE 754 binary64 value\", \"PREREQUISITES\": [], \"PARAMETERS\": [{\"NAME\": \"pi_c\", \"DIMENSION\": \"1\", \"SUPPLY\": \"DECLARED\", \"VALUE\": \"3.141592653589793\", \"UNIT\": \"1\", \"OVERRIDABLE\": \"NO\", \"LABEL\": \"pi, to 16 significant digits\"}], \"SUMS\": [], \"TERMS\": [], \"ASSUMPTIONS\": [], \"BOUNDARIES\": [], \"NOT_CHOSEN\": \"No mathematical constant: pi exists only if you declare it.\", \"NOT_INCLUDED\": [\"pi_c is pi rounded to 16 significant digits; no other mathematical constant is declared.\"], \"EXCLUDES\": [], \"INTERACTS_WITH\": [], \"TEST_BINDINGS\": [{\"NAME\": \"PROJECTILE_2D\", \"TPK\": {\"DOF\": [{\"NAME\": \"t\", \"DIMENSION\": \"T1\"}, {\"NAME\": \"x\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"z\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"v_x\", \"DIMENSION\": \"L1 T-1\"}, {\"NAME\": \"v_z\", \"DIMENSION\": \"L1 T-1\"}], \"CONSTANT\": [{\"NAME\": \"m\", \"DIMENSION\": \"M1\"}], \"LAW\": [{\"NAME\": \"KIN_X\", \"STATEMENT\": \"dx/dt = v_x\", \"REFS\": [\"t\", \"v_x\", \"x\"], \"ROLE\": \"EOM(x)\", \"EQUATION\": \"D(x,t)=v_x\"}, {\"NAME\": \"KIN_Z\", \"STATEMENT\": \"dz/dt = v_z\", \"REFS\": [\"t\", \"v_z\", \"z\"], \"ROLE\": \"EOM(z)\", \"EQUATION\": \"D(z,t)=v_z\"}, {\"NAME\": \"EOM_X\", \"STATEMENT\": \"m dv_x/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_x\"], \"ROLE\": \"EOM(v_x)\", \"EQUATION\": \"m*D(v_x,t)=0\"}, {\"NAME\": \"EOM_Z\", \"STATEMENT\": \"m dv_z/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_z\"], \"ROLE\": \"EOM(v_z)\", \"EQUATION\": \"m*D(v_z,t)=0\"}], \"ASSUMPTION\": [{\"NAME\": \"point_mass\", \"PROPOSITION\": \"the body is treated as a point mass\", \"REFS\": [\"m\"]}]}, \"BIND\": {}, \"VALUES\": {}, \"ANSWERS\": {}}]}",
"{\"ID\": \"GRAV-UNIFORM\", \"VERSION\": \"1.1.0\", \"TITLE\": \"Uniform gravity at the standard value g_n (text revised)\", \"SOURCE\": \"g_n = 9.80665 m s-2, exact by definition: 3rd CGPM (1901), declaration on the unit of mass and on the definition of weight\", \"PREREQUISITES\": [{\"SLOT\": \"MASS\", \"KIND\": \"CONSTANT\", \"DIMENSION\": \"M1\", \"MIN\": 1, \"MAX\": 1, \"LABEL\": \"the mass of the body\"}, {\"SLOT\": \"UP_VELOCITY\", \"KIND\": \"DOF\", \"DIMENSION\": \"L1 T-1\", \"MIN\": 1, \"MAX\": 1, \"LABEL\": \"the velocity component pointing up; its equation of motion receives the weight\"}, {\"SLOT\": \"HEIGHT\", \"KIND\": \"DOF\", \"DIMENSION\": \"L1\", \"MIN\": 1, \"MAX\": 1, \"LABEL\": \"the position along the same upward axis\"}], \"PARAMETERS\": [{\"NAME\": \"g_n\", \"DIMENSION\": \"L1 T-2\", \"SUPPLY\": \"DECLARED\", \"VALUE\": \"9.80665\", \"UNIT\": \"m s-2\", \"OVERRIDABLE\": \"NO\", \"LABEL\": \"the standard acceleration of gravity\"}, {\"NAME\": \"h_max\", \"DIMENSION\": \"L1\", \"SUPPLY\": \"AUTHOR\", \"LABEL\": \"the largest height, above or below the origin, over which the field is taken as uniform\"}], \"SUMS\": [], \"TERMS\": [{\"TARGET\": \"UP_VELOCITY\", \"SIGN\": \"-\", \"EXPR\": \"MASS*g_n\", \"LABEL\": \"the weight\"}], \"ASSUMPTIONS\": [{\"NAME\": \"gravity_uniform\", \"PROPOSITION\": \"the gravitational field is uniform over the region abs({HEIGHT}) < h_max\", \"REFS\": [\"HEIGHT\", \"h_max\"]}, {\"NAME\": \"gravity_standard\", \"PROPOSITION\": \"the local gravitational acceleration equals the conventional standard value g_n\", \"REFS\": [\"g_n\"]}, {\"NAME\": \"frame_inertial\", \"PROPOSITION\": \"the frame in which {HEIGHT} is measured is treated as inertial\", \"REFS\": [\"HEIGHT\"]}], \"BOUNDARIES\": [{\"NAME\": \"gravity_region\", \"PREDICATE\": \"abs({HEIGHT}) < h_max\", \"CONDITION\": \"abs(HEIGHT) < h_max\"}], \"NOT_CHOSEN\": \"No gravity: no weight acts on any DOF.\", \"NOT_INCLUDED\": [\"No variation of gravity with height or latitude beyond what g_n contains.\", \"No Earth rotation (Coriolis or centrifugal force) beyond what g_n contains.\", \"No gravity of bodies other than the Earth.\"], \"EXCLUDES\": [], \"INTERACTS_WITH\": [{\"WITH\": \"AIR-*\", \"QUESTION_ID\": \"BUOYANCY\", \"QUESTION\": \"Does the air's buoyancy (upthrust) act on the body in the system you mean?\", \"YES_LINE\": \"Buoyancy acts (your answer): no module adds it; it acts in this kernel only where one of your own laws states it.\", \"NO_LINE\": \"No buoyancy: the air's upthrust on the body is not included.\"}], \"TEST_BINDINGS\": [{\"NAME\": \"PROJECTILE_2D\", \"TPK\": {\"DOF\": [{\"NAME\": \"t\", \"DIMENSION\": \"T1\"}, {\"NAME\": \"x\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"z\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"v_x\", \"DIMENSION\": \"L1 T-1\"}, {\"NAME\": \"v_z\", \"DIMENSION\": \"L1 T-1\"}], \"CONSTANT\": [{\"NAME\": \"m\", \"DIMENSION\": \"M1\"}], \"LAW\": [{\"NAME\": \"KIN_X\", \"STATEMENT\": \"dx/dt = v_x\", \"REFS\": [\"t\", \"v_x\", \"x\"], \"ROLE\": \"EOM(x)\", \"EQUATION\": \"D(x,t)=v_x\"}, {\"NAME\": \"KIN_Z\", \"STATEMENT\": \"dz/dt = v_z\", \"REFS\": [\"t\", \"v_z\", \"z\"], \"ROLE\": \"EOM(z)\", \"EQUATION\": \"D(z,t)=v_z\"}, {\"NAME\": \"EOM_X\", \"STATEMENT\": \"m dv_x/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_x\"], \"ROLE\": \"EOM(v_x)\", \"EQUATION\": \"m*D(v_x,t)=0\"}, {\"NAME\": \"EOM_Z\", \"STATEMENT\": \"m dv_z/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_z\"], \"ROLE\": \"EOM(v_z)\", \"EQUATION\": \"m*D(v_z,t)=0\"}], \"ASSUMPTION\": [{\"NAME\": \"point_mass\", \"PROPOSITION\": \"the body is treated as a point mass\", \"REFS\": [\"m\"]}]}, \"BIND\": {\"HEIGHT\": [\"z\"], \"MASS\": [\"m\"], \"UP_VELOCITY\": [\"v_z\"]}, \"VALUES\": {\"h_max\": {\"VALUE\": \"100\", \"UNIT\": \"m\"}}, \"ANSWERS\": {}}, {\"NAME\": \"TABLE\", \"TPK\": {\"DOF\": [{\"NAME\": \"t\", \"DIMENSION\": \"T1\"}, {\"NAME\": \"x\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"z\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"v_x\", \"DIMENSION\": \"L1 T-1\"}, {\"NAME\": \"v_z\", \"DIMENSION\": \"L1 T-1\"}], \"CONSTANT\": [{\"NAME\": \"m\", \"DIMENSION\": \"M1\"}], \"LAW\": [{\"NAME\": \"KIN_X\", \"STATEMENT\": \"dx/dt = v_x\", \"REFS\": [\"t\", \"v_x\", \"x\"], \"ROLE\": \"EOM(x)\", \"EQUATION\": \"D(x,t)=v_x\"}, {\"NAME\": \"KIN_Z\", \"STATEMENT\": \"dz/dt = v_z\", \"REFS\": [\"t\", \"v_z\", \"z\"], \"ROLE\": \"CONSTRAINT\", \"EQUATION\": \"D(z,t)=v_z\"}, {\"NAME\": \"EOM_X\", \"STATEMENT\": \"m dv_x/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_x\"], \"ROLE\": \"EOM(v_x)\", \"EQUATION\": \"m*D(v_x,t)=0\"}], \"CONSTRAINT\": [{\"NAME\": \"C_Z\", \"TARGET\": \"z\", \"ACTION\": \"FIX\", \"VALUE\": \"0\", \"UNIT\": \"m\", \"STATEMENT\": \"the puck stays on the table top, z = 0\"}, {\"NAME\": \"C_VZ\", \"TARGET\": \"v_z\", \"ACTION\": \"FIX\", \"VALUE\": \"0\", \"UNIT\": \"m s-1\", \"STATEMENT\": \"the puck has no vertical velocity\"}]}, \"BIND\": {\"HEIGHT\": [\"z\"], \"MASS\": [\"m\"], \"UP_VELOCITY\": [\"v_z\"]}, \"VALUES\": {\"h_max\": {\"VALUE\": \"1\", \"UNIT\": \"m\"}}, \"ANSWERS\": {\"FIXED:v_z\": \"YES\"}}]}"
]
},
"expected": "[\"REFUSED\",\"CLAIM GRAV-UNIFORM 1.0.0: not OFFERED when chosen (a new claim names the OFFERED version)\"]",
"fn": "interview_check",
"hand_checked": true,
"name": "I19 a new claim of a version not OFFERED is refused"
},
{
"args": {
"answer": [
{
"AT": 5,
"CHOSEN": [
"GRAV-UNIFORM"
],
"COVERED": [
[
"AIR-LINEAR",
"1.0.0",
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[
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{
"ANSWERS": {},
"BIND": {
"HEIGHT": [
"z"
],
"MASS": [
"m"
],
"UP_VELOCITY": [
"v_z"
]
},
"DIGEST": "24877ccb5c8ec300d29ed82ce6650592f35cf8899a3d878ccce9c08d4c72c025",
"ID": "GRAV-UNIFORM",
"VALUES": {
"h_max": {
"UNIT": "m",
"VALUE": "100"
}
},
"VERSION": "1.0.0"
}
],
"lines": [
{
"ACT": "MODULE ADD",
"DATE": "2026-10-01",
"DIGEST": "5f3fe27b42378bce0830b0d0959f892f4a8e73b12b540ae877e39e6439d08b4d",
"ID": "AIR-LINEAR",
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{
"ACT": "MODULE ADD",
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"DIGEST": "6fb53c3a6546151eead2bd6e72e9cf8334f3a2040ad0ee2f5b988ec96d6fc852",
"ID": "AIR-QUADRATIC",
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{
"ACT": "MODULE ADD",
"DATE": "2026-10-01",
"DIGEST": "24877ccb5c8ec300d29ed82ce6650592f35cf8899a3d878ccce9c08d4c72c025",
"ID": "GRAV-UNIFORM",
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{
"ACT": "MODULE ADD",
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{
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"DIGEST": "5be3923c28dc8f8ff910b033c2d17154f267f2a20fdb32c74a07293a37dfe338",
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"{\"ID\": \"AIR-LINEAR\", \"VERSION\": \"1.0.0\", \"TITLE\": \"Air resistance at sea level, linear in the speed (Stokes drag on a sphere)\", \"SOURCE\": \"ISO 2533:1975, Standard Atmosphere, sea-level values: density 1.225 kg m-3, dynamic viscosity 1.7894e-5 Pa s\", \"PREREQUISITES\": [{\"SLOT\": \"VELOCITY\", \"KIND\": \"DOF\", \"DIMENSION\": \"L1 T-1\", \"MIN\": 1, \"MAX\": 3, \"LABEL\": \"the velocity components of the body, one per axis\"}], \"PARAMETERS\": [{\"NAME\": \"rho_air\", \"DIMENSION\": \"L-3 M1\", \"SUPPLY\": \"DECLARED\", \"VALUE\": \"1.225\", \"UNIT\": \"kg m-3\", \"OVERRIDABLE\": \"NO\", \"LABEL\": \"the density of air at sea level\"}, {\"NAME\": \"mu_air\", \"DIMENSION\": \"L-1 M1 T-1\", \"SUPPLY\": \"DECLARED\", \"VALUE\": \"1.7894e-5\", \"UNIT\": \"Pa s\", \"OVERRIDABLE\": \"NO\", \"LABEL\": \"the dynamic viscosity of air at sea level\"}, {\"NAME\": \"pi_c\", \"DIMENSION\": \"1\", \"SUPPLY\": \"DECLARED\", \"VALUE\": \"3.141592653589793\", \"UNIT\": \"1\", \"OVERRIDABLE\": \"NO\", \"LABEL\": \"pi, to 16 significant digits\"}, {\"NAME\": \"R_s\", \"DIMENSION\": \"L1\", \"SUPPLY\": \"AUTHOR\", \"LABEL\": \"the radius of the sphere\"}], \"SUMS\": [{\"NAME\": \"SPEED2\", \"OVER\": \"VELOCITY\", \"EACH\": \"VELOCITY^2\"}], \"TERMS\": [{\"TARGET\": \"VELOCITY\", \"SIGN\": \"-\", \"EXPR\": \"6*pi_c*mu_air*R_s*VELOCITY\", \"LABEL\": \"the linear (Stokes) drag\"}], \"ASSUMPTIONS\": [{\"NAME\": \"air_still\", \"PROPOSITION\": \"the air is at rest in the frame of the body's velocity\", \"REFS\": [\"VELOCITY\"]}, {\"NAME\": \"air_uniform\", \"PROPOSITION\": \"the air density is uniform over the region of motion\", \"REFS\": [\"rho_air\"]}, {\"NAME\": \"drag_sphere\", \"PROPOSITION\": \"the body is a rigid sphere of radius R_s\", \"REFS\": [\"R_s\"]}], \"BOUNDARIES\": [{\"NAME\": \"drag_linear_regime\", \"PREDICATE\": \"2 rho_air |v| R_s / mu_air < 1: the regime of the linear law\", \"CONDITION\": \"mu_air != 0 and SPEED2 >= 0 and 2*rho_air*sqrt(SPEED2)*R_s/mu_air < 1\"}], \"NOT_CHOSEN\": \"No linear (Stokes) air resistance.\", \"NOT_INCLUDED\": [\"No wind: the air is at rest.\", \"No change of air density or viscosity with altitude or temperature.\", \"No drag outside the regime of the linear law.\"], \"EXCLUDES\": [], \"INTERACTS_WITH\": [], \"TEST_BINDINGS\": [{\"NAME\": \"PROJECTILE_2D\", \"TPK\": {\"DOF\": [{\"NAME\": \"t\", \"DIMENSION\": \"T1\"}, {\"NAME\": \"x\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"z\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"v_x\", \"DIMENSION\": \"L1 T-1\"}, {\"NAME\": \"v_z\", \"DIMENSION\": \"L1 T-1\"}], \"CONSTANT\": [{\"NAME\": \"m\", \"DIMENSION\": \"M1\"}], \"LAW\": [{\"NAME\": \"KIN_X\", \"STATEMENT\": \"dx/dt = v_x\", \"REFS\": [\"t\", \"v_x\", \"x\"], \"ROLE\": \"EOM(x)\", \"EQUATION\": \"D(x,t)=v_x\"}, {\"NAME\": \"KIN_Z\", \"STATEMENT\": \"dz/dt = v_z\", \"REFS\": [\"t\", \"v_z\", \"z\"], \"ROLE\": \"EOM(z)\", \"EQUATION\": \"D(z,t)=v_z\"}, {\"NAME\": \"EOM_X\", \"STATEMENT\": \"m dv_x/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_x\"], \"ROLE\": \"EOM(v_x)\", \"EQUATION\": \"m*D(v_x,t)=0\"}, {\"NAME\": \"EOM_Z\", \"STATEMENT\": \"m dv_z/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_z\"], \"ROLE\": \"EOM(v_z)\", \"EQUATION\": \"m*D(v_z,t)=0\"}], \"ASSUMPTION\": [{\"NAME\": \"point_mass\", \"PROPOSITION\": \"the body is treated as a point mass\", \"REFS\": [\"m\"]}]}, \"BIND\": {\"VELOCITY\": [\"v_x\", \"v_z\"]}, \"VALUES\": {\"R_s\": {}}, \"ANSWERS\": {}}]}",
"{\"ID\": \"AIR-QUADRATIC\", \"VERSION\": \"1.0.0\", \"TITLE\": \"Air resistance at sea level, quadratic in the speed\", \"SOURCE\": \"ISO 2533:1975, Standard Atmosphere, sea-level values: density 1.225 kg m-3, dynamic viscosity 1.7894e-5 Pa s\", \"PREREQUISITES\": [{\"SLOT\": \"VELOCITY\", \"KIND\": \"DOF\", \"DIMENSION\": \"L1 T-1\", \"MIN\": 1, \"MAX\": 3, \"LABEL\": \"the velocity components of the body, one per axis\"}], \"PARAMETERS\": [{\"NAME\": \"rho_air\", \"DIMENSION\": \"L-3 M1\", \"SUPPLY\": \"DECLARED\", \"VALUE\": \"1.225\", \"UNIT\": \"kg m-3\", \"OVERRIDABLE\": \"NO\", \"LABEL\": \"the density of air at sea level\"}, {\"NAME\": \"mu_air\", \"DIMENSION\": \"L-1 M1 T-1\", \"SUPPLY\": \"DECLARED\", \"VALUE\": \"1.7894e-5\", \"UNIT\": \"Pa s\", \"OVERRIDABLE\": \"NO\", \"LABEL\": \"the dynamic viscosity of air at sea level\"}, {\"NAME\": \"C_d\", \"DIMENSION\": \"1\", \"SUPPLY\": \"AUTHOR\", \"LABEL\": \"the drag coefficient of the body\"}, {\"NAME\": \"A_ref\", \"DIMENSION\": \"L2\", \"SUPPLY\": \"AUTHOR\", \"LABEL\": \"the reference area of the drag coefficient\"}, {\"NAME\": \"L_ref\", \"DIMENSION\": \"L1\", \"SUPPLY\": \"AUTHOR\", \"LABEL\": \"the reference length of the Reynolds number\"}], \"SUMS\": [{\"NAME\": \"SPEED2\", \"OVER\": \"VELOCITY\", \"EACH\": \"VELOCITY^2\"}], \"TERMS\": [{\"TARGET\": \"VELOCITY\", \"SIGN\": \"-\", \"EXPR\": \"0.5*rho_air*C_d*A_ref*sqrt(SPEED2)*VELOCITY\", \"LABEL\": \"the quadratic drag\"}], \"ASSUMPTIONS\": [{\"NAME\": \"air_still\", \"PROPOSITION\": \"the air is at rest in the frame of the body's velocity\", \"REFS\": [\"VELOCITY\"]}, {\"NAME\": \"air_uniform\", \"PROPOSITION\": \"the air density is uniform over the region of motion\", \"REFS\": [\"rho_air\"]}, {\"NAME\": \"drag_cd_constant\", \"PROPOSITION\": \"the drag coefficient C_d is constant over the motion\", \"REFS\": [\"C_d\"]}, {\"NAME\": \"drag_no_lift\", \"PROPOSITION\": \"the body experiences no lift force\", \"REFS\": [\"VELOCITY\"]}, {\"NAME\": \"drag_no_magnus\", \"PROPOSITION\": \"the body experiences no Magnus force\", \"REFS\": [\"VELOCITY\"]}], \"BOUNDARIES\": [{\"NAME\": \"drag_quadratic_regime\", \"PREDICATE\": \"1e3 < rho_air |v| L_ref / mu_air < 2e5: the Reynolds window of the quadratic law\", \"CONDITION\": \"mu_air != 0 and SPEED2 >= 0 and rho_air*sqrt(SPEED2)*L_ref/mu_air > 1000 and rho_air*sqrt(SPEED2)*L_ref/mu_air < 200000\"}], \"NOT_CHOSEN\": \"No quadratic air resistance.\", \"NOT_INCLUDED\": [\"No wind: the air is at rest.\", \"No change of air density or viscosity with altitude or temperature.\", \"No lift, Magnus or added-mass force.\", \"No drag outside the Reynolds window of the quadratic law.\"], \"EXCLUDES\": [\"AIR-LINEAR\"], \"INTERACTS_WITH\": [], \"TEST_BINDINGS\": [{\"NAME\": \"PROJECTILE_2D\", \"TPK\": {\"DOF\": [{\"NAME\": \"t\", \"DIMENSION\": \"T1\"}, {\"NAME\": \"x\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"z\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"v_x\", \"DIMENSION\": \"L1 T-1\"}, {\"NAME\": \"v_z\", \"DIMENSION\": \"L1 T-1\"}], \"CONSTANT\": [{\"NAME\": \"m\", \"DIMENSION\": \"M1\"}], \"LAW\": [{\"NAME\": \"KIN_X\", \"STATEMENT\": \"dx/dt = v_x\", \"REFS\": [\"t\", \"v_x\", \"x\"], \"ROLE\": \"EOM(x)\", \"EQUATION\": \"D(x,t)=v_x\"}, {\"NAME\": \"KIN_Z\", \"STATEMENT\": \"dz/dt = v_z\", \"REFS\": [\"t\", \"v_z\", \"z\"], \"ROLE\": \"EOM(z)\", \"EQUATION\": \"D(z,t)=v_z\"}, {\"NAME\": \"EOM_X\", \"STATEMENT\": \"m dv_x/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_x\"], \"ROLE\": \"EOM(v_x)\", \"EQUATION\": \"m*D(v_x,t)=0\"}, {\"NAME\": \"EOM_Z\", \"STATEMENT\": \"m dv_z/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_z\"], \"ROLE\": \"EOM(v_z)\", \"EQUATION\": \"m*D(v_z,t)=0\"}], \"ASSUMPTION\": [{\"NAME\": \"point_mass\", \"PROPOSITION\": \"the body is treated as a point mass\", \"REFS\": [\"m\"]}]}, \"BIND\": {\"VELOCITY\": [\"v_x\", \"v_z\"]}, \"VALUES\": {\"A_ref\": {}, \"C_d\": {}, \"L_ref\": {}}, \"ANSWERS\": {}}]}",
"{\"ID\": \"GRAV-UNIFORM\", \"VERSION\": \"1.0.0\", \"TITLE\": \"Uniform gravity at the standard value g_n\", \"SOURCE\": \"g_n = 9.80665 m s-2, exact by definition: 3rd CGPM (1901), declaration on the unit of mass and on the definition of weight\", \"PREREQUISITES\": [{\"SLOT\": \"MASS\", \"KIND\": \"CONSTANT\", \"DIMENSION\": \"M1\", \"MIN\": 1, \"MAX\": 1, \"LABEL\": \"the mass of the body\"}, {\"SLOT\": \"UP_VELOCITY\", \"KIND\": \"DOF\", \"DIMENSION\": \"L1 T-1\", \"MIN\": 1, \"MAX\": 1, \"LABEL\": \"the velocity component pointing up; its equation of motion receives the weight\"}, {\"SLOT\": \"HEIGHT\", \"KIND\": \"DOF\", \"DIMENSION\": \"L1\", \"MIN\": 1, \"MAX\": 1, \"LABEL\": \"the position along the same upward axis\"}], \"PARAMETERS\": [{\"NAME\": \"g_n\", \"DIMENSION\": \"L1 T-2\", \"SUPPLY\": \"DECLARED\", \"VALUE\": \"9.80665\", \"UNIT\": \"m s-2\", \"OVERRIDABLE\": \"NO\", \"LABEL\": \"the standard acceleration of gravity\"}, {\"NAME\": \"h_max\", \"DIMENSION\": \"L1\", \"SUPPLY\": \"AUTHOR\", \"LABEL\": \"the largest height, above or below the origin, over which the field is taken as uniform\"}], \"SUMS\": [], \"TERMS\": [{\"TARGET\": \"UP_VELOCITY\", \"SIGN\": \"-\", \"EXPR\": \"MASS*g_n\", \"LABEL\": \"the weight\"}], \"ASSUMPTIONS\": [{\"NAME\": \"gravity_uniform\", \"PROPOSITION\": \"the gravitational field is uniform over the region abs({HEIGHT}) < h_max\", \"REFS\": [\"HEIGHT\", \"h_max\"]}, {\"NAME\": \"gravity_standard\", \"PROPOSITION\": \"the local gravitational acceleration equals the conventional standard value g_n\", \"REFS\": [\"g_n\"]}, {\"NAME\": \"frame_inertial\", \"PROPOSITION\": \"the frame in which {HEIGHT} is measured is treated as inertial\", \"REFS\": [\"HEIGHT\"]}], \"BOUNDARIES\": [{\"NAME\": \"gravity_region\", \"PREDICATE\": \"abs({HEIGHT}) < h_max\", \"CONDITION\": \"abs(HEIGHT) < h_max\"}], \"NOT_CHOSEN\": \"No gravity: no weight acts on any DOF.\", \"NOT_INCLUDED\": [\"No variation of gravity with height or latitude beyond what g_n contains.\", \"No Earth rotation (Coriolis or centrifugal force) beyond what g_n contains.\", \"No gravity of bodies other than the Earth.\"], \"EXCLUDES\": [], \"INTERACTS_WITH\": [{\"WITH\": \"AIR-*\", \"QUESTION_ID\": \"BUOYANCY\", \"QUESTION\": \"Does the air's buoyancy (upthrust) act on the body in the system you mean?\", \"YES_LINE\": \"Buoyancy acts (your answer): no module adds it; it acts in this kernel only where one of your own laws states it.\", \"NO_LINE\": \"No buoyancy: the air's upthrust on the body is not included.\"}], \"TEST_BINDINGS\": [{\"NAME\": \"PROJECTILE_2D\", \"TPK\": {\"DOF\": [{\"NAME\": \"t\", \"DIMENSION\": \"T1\"}, {\"NAME\": \"x\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"z\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"v_x\", \"DIMENSION\": \"L1 T-1\"}, {\"NAME\": \"v_z\", \"DIMENSION\": \"L1 T-1\"}], \"CONSTANT\": [{\"NAME\": \"m\", \"DIMENSION\": \"M1\"}], \"LAW\": [{\"NAME\": \"KIN_X\", \"STATEMENT\": \"dx/dt = v_x\", \"REFS\": [\"t\", \"v_x\", \"x\"], \"ROLE\": \"EOM(x)\", \"EQUATION\": \"D(x,t)=v_x\"}, {\"NAME\": \"KIN_Z\", \"STATEMENT\": \"dz/dt = v_z\", \"REFS\": [\"t\", \"v_z\", \"z\"], \"ROLE\": \"EOM(z)\", \"EQUATION\": \"D(z,t)=v_z\"}, {\"NAME\": \"EOM_X\", \"STATEMENT\": \"m dv_x/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_x\"], \"ROLE\": \"EOM(v_x)\", \"EQUATION\": \"m*D(v_x,t)=0\"}, {\"NAME\": \"EOM_Z\", \"STATEMENT\": \"m dv_z/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_z\"], \"ROLE\": \"EOM(v_z)\", \"EQUATION\": \"m*D(v_z,t)=0\"}], \"ASSUMPTION\": [{\"NAME\": \"point_mass\", \"PROPOSITION\": \"the body is treated as a point mass\", \"REFS\": [\"m\"]}]}, \"BIND\": {\"HEIGHT\": [\"z\"], \"MASS\": [\"m\"], \"UP_VELOCITY\": [\"v_z\"]}, \"VALUES\": {\"h_max\": {\"VALUE\": \"100\", \"UNIT\": \"m\"}}, \"ANSWERS\": {}}, {\"NAME\": \"TABLE\", \"TPK\": {\"DOF\": [{\"NAME\": \"t\", \"DIMENSION\": \"T1\"}, {\"NAME\": \"x\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"z\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"v_x\", \"DIMENSION\": \"L1 T-1\"}, {\"NAME\": \"v_z\", \"DIMENSION\": \"L1 T-1\"}], \"CONSTANT\": [{\"NAME\": \"m\", \"DIMENSION\": \"M1\"}], \"LAW\": [{\"NAME\": \"KIN_X\", \"STATEMENT\": \"dx/dt = v_x\", \"REFS\": [\"t\", \"v_x\", \"x\"], \"ROLE\": \"EOM(x)\", \"EQUATION\": \"D(x,t)=v_x\"}, {\"NAME\": \"KIN_Z\", \"STATEMENT\": \"dz/dt = v_z\", \"REFS\": [\"t\", \"v_z\", \"z\"], \"ROLE\": \"CONSTRAINT\", \"EQUATION\": \"D(z,t)=v_z\"}, {\"NAME\": \"EOM_X\", \"STATEMENT\": \"m dv_x/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_x\"], \"ROLE\": \"EOM(v_x)\", \"EQUATION\": \"m*D(v_x,t)=0\"}], \"CONSTRAINT\": [{\"NAME\": \"C_Z\", \"TARGET\": \"z\", \"ACTION\": \"FIX\", \"VALUE\": \"0\", \"UNIT\": \"m\", \"STATEMENT\": \"the puck stays on the table top, z = 0\"}, {\"NAME\": \"C_VZ\", \"TARGET\": \"v_z\", \"ACTION\": \"FIX\", \"VALUE\": \"0\", \"UNIT\": \"m s-1\", \"STATEMENT\": \"the puck has no vertical velocity\"}]}, \"BIND\": {\"HEIGHT\": [\"z\"], \"MASS\": [\"m\"], \"UP_VELOCITY\": [\"v_z\"]}, \"VALUES\": {\"h_max\": {\"VALUE\": \"1\", \"UNIT\": \"m\"}}, \"ANSWERS\": {\"FIXED:v_z\": \"YES\"}}]}",
"{\"ID\": \"MATH\", \"VERSION\": \"1.0.0\", \"TITLE\": \"The mathematical constant pi, as the CONSTANT pi_c\", \"SOURCE\": \"pi to 16 significant digits, 3.141592653589793, the nearest IEEE 754 binary64 value\", \"PREREQUISITES\": [], \"PARAMETERS\": [{\"NAME\": \"pi_c\", \"DIMENSION\": \"1\", \"SUPPLY\": \"DECLARED\", \"VALUE\": \"3.141592653589793\", \"UNIT\": \"1\", \"OVERRIDABLE\": \"NO\", \"LABEL\": \"pi, to 16 significant digits\"}], \"SUMS\": [], \"TERMS\": [], \"ASSUMPTIONS\": [], \"BOUNDARIES\": [], \"NOT_CHOSEN\": \"No mathematical constant: pi exists only if you declare it.\", \"NOT_INCLUDED\": [\"pi_c is pi rounded to 16 significant digits; no other mathematical constant is declared.\"], \"EXCLUDES\": [], \"INTERACTS_WITH\": [], \"TEST_BINDINGS\": [{\"NAME\": \"PROJECTILE_2D\", \"TPK\": {\"DOF\": [{\"NAME\": \"t\", \"DIMENSION\": \"T1\"}, {\"NAME\": \"x\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"z\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"v_x\", \"DIMENSION\": \"L1 T-1\"}, {\"NAME\": \"v_z\", \"DIMENSION\": \"L1 T-1\"}], \"CONSTANT\": [{\"NAME\": \"m\", \"DIMENSION\": \"M1\"}], \"LAW\": [{\"NAME\": \"KIN_X\", \"STATEMENT\": \"dx/dt = v_x\", \"REFS\": [\"t\", \"v_x\", \"x\"], \"ROLE\": \"EOM(x)\", \"EQUATION\": \"D(x,t)=v_x\"}, {\"NAME\": \"KIN_Z\", \"STATEMENT\": \"dz/dt = v_z\", \"REFS\": [\"t\", \"v_z\", \"z\"], \"ROLE\": \"EOM(z)\", \"EQUATION\": \"D(z,t)=v_z\"}, {\"NAME\": \"EOM_X\", \"STATEMENT\": \"m dv_x/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_x\"], \"ROLE\": \"EOM(v_x)\", \"EQUATION\": \"m*D(v_x,t)=0\"}, {\"NAME\": \"EOM_Z\", \"STATEMENT\": \"m dv_z/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_z\"], \"ROLE\": \"EOM(v_z)\", \"EQUATION\": \"m*D(v_z,t)=0\"}], \"ASSUMPTION\": [{\"NAME\": \"point_mass\", \"PROPOSITION\": \"the body is treated as a point mass\", \"REFS\": [\"m\"]}]}, \"BIND\": {}, \"VALUES\": {}, \"ANSWERS\": {}}]}",
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it acts in this kernel only where one of your own laws states it.\", \"NO_LINE\": \"No buoyancy: the air's upthrust on the body is not included.\"}], \"TEST_BINDINGS\": [{\"NAME\": \"PROJECTILE_2D\", \"TPK\": {\"DOF\": [{\"NAME\": \"t\", \"DIMENSION\": \"T1\"}, {\"NAME\": \"x\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"z\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"v_x\", \"DIMENSION\": \"L1 T-1\"}, {\"NAME\": \"v_z\", \"DIMENSION\": \"L1 T-1\"}], \"CONSTANT\": [{\"NAME\": \"m\", \"DIMENSION\": \"M1\"}], \"LAW\": [{\"NAME\": \"KIN_X\", \"STATEMENT\": \"dx/dt = v_x\", \"REFS\": [\"t\", \"v_x\", \"x\"], \"ROLE\": \"EOM(x)\", \"EQUATION\": \"D(x,t)=v_x\"}, {\"NAME\": \"KIN_Z\", \"STATEMENT\": \"dz/dt = v_z\", \"REFS\": [\"t\", \"v_z\", \"z\"], \"ROLE\": \"EOM(z)\", \"EQUATION\": \"D(z,t)=v_z\"}, {\"NAME\": \"EOM_X\", \"STATEMENT\": \"m dv_x/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_x\"], \"ROLE\": \"EOM(v_x)\", \"EQUATION\": \"m*D(v_x,t)=0\"}, {\"NAME\": \"EOM_Z\", \"STATEMENT\": \"m dv_z/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_z\"], \"ROLE\": \"EOM(v_z)\", \"EQUATION\": \"m*D(v_z,t)=0\"}], \"ASSUMPTION\": [{\"NAME\": \"point_mass\", \"PROPOSITION\": \"the body is treated as a point mass\", \"REFS\": [\"m\"]}]}, \"BIND\": {\"HEIGHT\": [\"z\"], \"MASS\": [\"m\"], \"UP_VELOCITY\": [\"v_z\"]}, \"VALUES\": {\"h_max\": {\"VALUE\": \"100\", \"UNIT\": \"m\"}}, \"ANSWERS\": {}}, {\"NAME\": \"TABLE\", \"TPK\": {\"DOF\": [{\"NAME\": \"t\", \"DIMENSION\": \"T1\"}, {\"NAME\": \"x\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"z\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"v_x\", \"DIMENSION\": \"L1 T-1\"}, {\"NAME\": \"v_z\", \"DIMENSION\": \"L1 T-1\"}], \"CONSTANT\": [{\"NAME\": \"m\", \"DIMENSION\": \"M1\"}], \"LAW\": [{\"NAME\": \"KIN_X\", \"STATEMENT\": \"dx/dt = v_x\", \"REFS\": [\"t\", \"v_x\", \"x\"], \"ROLE\": \"EOM(x)\", \"EQUATION\": \"D(x,t)=v_x\"}, {\"NAME\": \"KIN_Z\", \"STATEMENT\": \"dz/dt = v_z\", \"REFS\": [\"t\", \"v_z\", \"z\"], \"ROLE\": \"CONSTRAINT\", \"EQUATION\": \"D(z,t)=v_z\"}, {\"NAME\": \"EOM_X\", \"STATEMENT\": \"m dv_x/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_x\"], \"ROLE\": \"EOM(v_x)\", \"EQUATION\": \"m*D(v_x,t)=0\"}], \"CONSTRAINT\": [{\"NAME\": \"C_Z\", \"TARGET\": \"z\", \"ACTION\": \"FIX\", \"VALUE\": \"0\", \"UNIT\": \"m\", \"STATEMENT\": \"the puck stays on the table top, z = 0\"}, {\"NAME\": \"C_VZ\", \"TARGET\": \"v_z\", \"ACTION\": \"FIX\", \"VALUE\": \"0\", \"UNIT\": \"m s-1\", \"STATEMENT\": \"the puck has no vertical velocity\"}]}, \"BIND\": {\"HEIGHT\": [\"z\"], \"MASS\": [\"m\"], \"UP_VELOCITY\": [\"v_z\"]}, \"VALUES\": {\"h_max\": {\"VALUE\": \"1\", \"UNIT\": \"m\"}}, \"ANSWERS\": {\"FIXED:v_z\": \"YES\"}}]}"
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{
"ACT": "MODULE ADD",
"DATE": "2026-10-01",
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"{\"ID\": \"AIR-LINEAR\", \"VERSION\": \"1.0.0\", \"TITLE\": \"Air resistance at sea level, linear in the speed (Stokes drag on a sphere)\", \"SOURCE\": \"ISO 2533:1975, Standard Atmosphere, sea-level values: density 1.225 kg m-3, dynamic viscosity 1.7894e-5 Pa s\", \"PREREQUISITES\": [{\"SLOT\": \"VELOCITY\", \"KIND\": \"DOF\", \"DIMENSION\": \"L1 T-1\", \"MIN\": 1, \"MAX\": 3, \"LABEL\": \"the velocity components of the body, one per axis\"}], \"PARAMETERS\": [{\"NAME\": \"rho_air\", \"DIMENSION\": \"L-3 M1\", \"SUPPLY\": \"DECLARED\", \"VALUE\": \"1.225\", \"UNIT\": \"kg m-3\", \"OVERRIDABLE\": \"NO\", \"LABEL\": \"the density of air at sea level\"}, {\"NAME\": \"mu_air\", \"DIMENSION\": \"L-1 M1 T-1\", \"SUPPLY\": \"DECLARED\", \"VALUE\": \"1.7894e-5\", \"UNIT\": \"Pa s\", \"OVERRIDABLE\": \"NO\", \"LABEL\": \"the dynamic viscosity of air at sea level\"}, {\"NAME\": \"pi_c\", \"DIMENSION\": \"1\", \"SUPPLY\": \"DECLARED\", \"VALUE\": \"3.141592653589793\", \"UNIT\": \"1\", \"OVERRIDABLE\": \"NO\", \"LABEL\": \"pi, to 16 significant digits\"}, {\"NAME\": \"R_s\", \"DIMENSION\": \"L1\", \"SUPPLY\": \"AUTHOR\", \"LABEL\": \"the radius of the sphere\"}], \"SUMS\": [{\"NAME\": \"SPEED2\", \"OVER\": \"VELOCITY\", \"EACH\": \"VELOCITY^2\"}], \"TERMS\": [{\"TARGET\": \"VELOCITY\", \"SIGN\": \"-\", \"EXPR\": \"6*pi_c*mu_air*R_s*VELOCITY\", \"LABEL\": \"the linear (Stokes) drag\"}], \"ASSUMPTIONS\": [{\"NAME\": \"air_still\", \"PROPOSITION\": \"the air is at rest in the frame of the body's velocity\", \"REFS\": [\"VELOCITY\"]}, {\"NAME\": \"air_uniform\", \"PROPOSITION\": \"the air density is uniform over the region of motion\", \"REFS\": [\"rho_air\"]}, {\"NAME\": \"drag_sphere\", \"PROPOSITION\": \"the body is a rigid sphere of radius R_s\", \"REFS\": [\"R_s\"]}], \"BOUNDARIES\": [{\"NAME\": \"drag_linear_regime\", \"PREDICATE\": \"2 rho_air |v| R_s / mu_air < 1: the regime of the linear law\", \"CONDITION\": \"mu_air != 0 and SPEED2 >= 0 and 2*rho_air*sqrt(SPEED2)*R_s/mu_air < 1\"}], \"NOT_CHOSEN\": \"No linear (Stokes) air resistance.\", \"NOT_INCLUDED\": [\"No wind: the air is at rest.\", \"No change of air density or viscosity with altitude or temperature.\", \"No drag outside the regime of the linear law.\"], \"EXCLUDES\": [], \"INTERACTS_WITH\": [], \"TEST_BINDINGS\": [{\"NAME\": \"PROJECTILE_2D\", \"TPK\": {\"DOF\": [{\"NAME\": \"t\", \"DIMENSION\": \"T1\"}, {\"NAME\": \"x\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"z\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"v_x\", \"DIMENSION\": \"L1 T-1\"}, {\"NAME\": \"v_z\", \"DIMENSION\": \"L1 T-1\"}], \"CONSTANT\": [{\"NAME\": \"m\", \"DIMENSION\": \"M1\"}], \"LAW\": [{\"NAME\": \"KIN_X\", \"STATEMENT\": \"dx/dt = v_x\", \"REFS\": [\"t\", \"v_x\", \"x\"], \"ROLE\": \"EOM(x)\", \"EQUATION\": \"D(x,t)=v_x\"}, {\"NAME\": \"KIN_Z\", \"STATEMENT\": \"dz/dt = v_z\", \"REFS\": [\"t\", \"v_z\", \"z\"], \"ROLE\": \"EOM(z)\", \"EQUATION\": \"D(z,t)=v_z\"}, {\"NAME\": \"EOM_X\", \"STATEMENT\": \"m dv_x/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_x\"], \"ROLE\": \"EOM(v_x)\", \"EQUATION\": \"m*D(v_x,t)=0\"}, {\"NAME\": \"EOM_Z\", \"STATEMENT\": \"m dv_z/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_z\"], \"ROLE\": \"EOM(v_z)\", \"EQUATION\": \"m*D(v_z,t)=0\"}], \"ASSUMPTION\": [{\"NAME\": \"point_mass\", \"PROPOSITION\": \"the body is treated as a point mass\", \"REFS\": [\"m\"]}]}, \"BIND\": {\"VELOCITY\": [\"v_x\", \"v_z\"]}, \"VALUES\": {\"R_s\": {}}, \"ANSWERS\": {}}]}",
"{\"ID\": \"AIR-QUADRATIC\", \"VERSION\": \"1.0.0\", \"TITLE\": \"Air resistance at sea level, quadratic in the speed\", \"SOURCE\": \"ISO 2533:1975, Standard Atmosphere, sea-level values: density 1.225 kg m-3, dynamic viscosity 1.7894e-5 Pa s\", \"PREREQUISITES\": [{\"SLOT\": \"VELOCITY\", \"KIND\": \"DOF\", \"DIMENSION\": \"L1 T-1\", \"MIN\": 1, \"MAX\": 3, \"LABEL\": \"the velocity components of the body, one per axis\"}], \"PARAMETERS\": [{\"NAME\": \"rho_air\", \"DIMENSION\": \"L-3 M1\", \"SUPPLY\": \"DECLARED\", \"VALUE\": \"1.225\", \"UNIT\": \"kg m-3\", \"OVERRIDABLE\": \"NO\", \"LABEL\": \"the density of air at sea level\"}, {\"NAME\": \"mu_air\", \"DIMENSION\": \"L-1 M1 T-1\", \"SUPPLY\": \"DECLARED\", \"VALUE\": \"1.7894e-5\", \"UNIT\": \"Pa s\", \"OVERRIDABLE\": \"NO\", \"LABEL\": \"the dynamic viscosity of air at sea level\"}, {\"NAME\": \"C_d\", \"DIMENSION\": \"1\", \"SUPPLY\": \"AUTHOR\", \"LABEL\": \"the drag coefficient of the body\"}, {\"NAME\": \"A_ref\", \"DIMENSION\": \"L2\", \"SUPPLY\": \"AUTHOR\", \"LABEL\": \"the reference area of the drag coefficient\"}, {\"NAME\": \"L_ref\", \"DIMENSION\": \"L1\", \"SUPPLY\": \"AUTHOR\", \"LABEL\": \"the reference length of the Reynolds number\"}], \"SUMS\": [{\"NAME\": \"SPEED2\", \"OVER\": \"VELOCITY\", \"EACH\": \"VELOCITY^2\"}], \"TERMS\": [{\"TARGET\": \"VELOCITY\", \"SIGN\": \"-\", \"EXPR\": \"0.5*rho_air*C_d*A_ref*sqrt(SPEED2)*VELOCITY\", \"LABEL\": \"the quadratic drag\"}], \"ASSUMPTIONS\": [{\"NAME\": \"air_still\", \"PROPOSITION\": \"the air is at rest in the frame of the body's velocity\", \"REFS\": [\"VELOCITY\"]}, {\"NAME\": \"air_uniform\", \"PROPOSITION\": \"the air density is uniform over the region of motion\", \"REFS\": [\"rho_air\"]}, {\"NAME\": \"drag_cd_constant\", \"PROPOSITION\": \"the drag coefficient C_d is constant over the motion\", \"REFS\": [\"C_d\"]}, {\"NAME\": \"drag_no_lift\", \"PROPOSITION\": \"the body experiences no lift force\", \"REFS\": [\"VELOCITY\"]}, {\"NAME\": \"drag_no_magnus\", \"PROPOSITION\": \"the body experiences no Magnus force\", \"REFS\": [\"VELOCITY\"]}], \"BOUNDARIES\": [{\"NAME\": \"drag_quadratic_regime\", \"PREDICATE\": \"1e3 < rho_air |v| L_ref / mu_air < 2e5: the Reynolds window of the quadratic law\", \"CONDITION\": \"mu_air != 0 and SPEED2 >= 0 and rho_air*sqrt(SPEED2)*L_ref/mu_air > 1000 and rho_air*sqrt(SPEED2)*L_ref/mu_air < 200000\"}], \"NOT_CHOSEN\": \"No quadratic air resistance.\", \"NOT_INCLUDED\": [\"No wind: the air is at rest.\", \"No change of air density or viscosity with altitude or temperature.\", \"No lift, Magnus or added-mass force.\", \"No drag outside the Reynolds window of the quadratic law.\"], \"EXCLUDES\": [\"AIR-LINEAR\"], \"INTERACTS_WITH\": [], \"TEST_BINDINGS\": [{\"NAME\": \"PROJECTILE_2D\", \"TPK\": {\"DOF\": [{\"NAME\": \"t\", \"DIMENSION\": \"T1\"}, {\"NAME\": \"x\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"z\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"v_x\", \"DIMENSION\": \"L1 T-1\"}, {\"NAME\": \"v_z\", \"DIMENSION\": \"L1 T-1\"}], \"CONSTANT\": [{\"NAME\": \"m\", \"DIMENSION\": \"M1\"}], \"LAW\": [{\"NAME\": \"KIN_X\", \"STATEMENT\": \"dx/dt = v_x\", \"REFS\": [\"t\", \"v_x\", \"x\"], \"ROLE\": \"EOM(x)\", \"EQUATION\": \"D(x,t)=v_x\"}, {\"NAME\": \"KIN_Z\", \"STATEMENT\": \"dz/dt = v_z\", \"REFS\": [\"t\", \"v_z\", \"z\"], \"ROLE\": \"EOM(z)\", \"EQUATION\": \"D(z,t)=v_z\"}, {\"NAME\": \"EOM_X\", \"STATEMENT\": \"m dv_x/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_x\"], \"ROLE\": \"EOM(v_x)\", \"EQUATION\": \"m*D(v_x,t)=0\"}, {\"NAME\": \"EOM_Z\", \"STATEMENT\": \"m dv_z/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_z\"], \"ROLE\": \"EOM(v_z)\", \"EQUATION\": \"m*D(v_z,t)=0\"}], \"ASSUMPTION\": [{\"NAME\": \"point_mass\", \"PROPOSITION\": \"the body is treated as a point mass\", \"REFS\": [\"m\"]}]}, \"BIND\": {\"VELOCITY\": [\"v_x\", \"v_z\"]}, \"VALUES\": {\"A_ref\": {}, \"C_d\": {}, \"L_ref\": {}}, \"ANSWERS\": {}}]}",
"{\"ID\": \"GRAV-UNIFORM\", \"VERSION\": \"1.0.0\", \"TITLE\": \"Uniform gravity at the standard value g_n\", \"SOURCE\": \"g_n = 9.80665 m s-2, exact by definition: 3rd CGPM (1901), declaration on the unit of mass and on the definition of weight\", \"PREREQUISITES\": [{\"SLOT\": \"MASS\", \"KIND\": \"CONSTANT\", \"DIMENSION\": \"M1\", \"MIN\": 1, \"MAX\": 1, \"LABEL\": \"the mass of the body\"}, {\"SLOT\": \"UP_VELOCITY\", \"KIND\": \"DOF\", \"DIMENSION\": \"L1 T-1\", \"MIN\": 1, \"MAX\": 1, \"LABEL\": \"the velocity component pointing up; its equation of motion receives the weight\"}, {\"SLOT\": \"HEIGHT\", \"KIND\": \"DOF\", \"DIMENSION\": \"L1\", \"MIN\": 1, \"MAX\": 1, \"LABEL\": \"the position along the same upward axis\"}], \"PARAMETERS\": [{\"NAME\": \"g_n\", \"DIMENSION\": \"L1 T-2\", \"SUPPLY\": \"DECLARED\", \"VALUE\": \"9.80665\", \"UNIT\": \"m s-2\", \"OVERRIDABLE\": \"NO\", \"LABEL\": \"the standard acceleration of gravity\"}, {\"NAME\": \"h_max\", \"DIMENSION\": \"L1\", \"SUPPLY\": \"AUTHOR\", \"LABEL\": \"the largest height, above or below the origin, over which the field is taken as uniform\"}], \"SUMS\": [], \"TERMS\": [{\"TARGET\": \"UP_VELOCITY\", \"SIGN\": \"-\", \"EXPR\": \"MASS*g_n\", \"LABEL\": \"the weight\"}], \"ASSUMPTIONS\": [{\"NAME\": \"gravity_uniform\", \"PROPOSITION\": \"the gravitational field is uniform over the region abs({HEIGHT}) < h_max\", \"REFS\": [\"HEIGHT\", \"h_max\"]}, {\"NAME\": \"gravity_standard\", \"PROPOSITION\": \"the local gravitational acceleration equals the conventional standard value g_n\", \"REFS\": [\"g_n\"]}, {\"NAME\": \"frame_inertial\", \"PROPOSITION\": \"the frame in which {HEIGHT} is measured is treated as inertial\", \"REFS\": [\"HEIGHT\"]}], \"BOUNDARIES\": [{\"NAME\": \"gravity_region\", \"PREDICATE\": \"abs({HEIGHT}) < h_max\", \"CONDITION\": \"abs(HEIGHT) < h_max\"}], \"NOT_CHOSEN\": \"No gravity: no weight acts on any DOF.\", \"NOT_INCLUDED\": [\"No variation of gravity with height or latitude beyond what g_n contains.\", \"No Earth rotation (Coriolis or centrifugal force) beyond what g_n contains.\", \"No gravity of bodies other than the Earth.\"], \"EXCLUDES\": [], \"INTERACTS_WITH\": [{\"WITH\": \"AIR-*\", \"QUESTION_ID\": \"BUOYANCY\", \"QUESTION\": \"Does the air's buoyancy (upthrust) act on the body in the system you mean?\", \"YES_LINE\": \"Buoyancy acts (your answer): no module adds it; it acts in this kernel only where one of your own laws states it.\", \"NO_LINE\": \"No buoyancy: the air's upthrust on the body is not included.\"}], \"TEST_BINDINGS\": [{\"NAME\": \"PROJECTILE_2D\", \"TPK\": {\"DOF\": [{\"NAME\": \"t\", \"DIMENSION\": \"T1\"}, {\"NAME\": \"x\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"z\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"v_x\", \"DIMENSION\": \"L1 T-1\"}, {\"NAME\": \"v_z\", \"DIMENSION\": \"L1 T-1\"}], \"CONSTANT\": [{\"NAME\": \"m\", \"DIMENSION\": \"M1\"}], \"LAW\": [{\"NAME\": \"KIN_X\", \"STATEMENT\": \"dx/dt = v_x\", \"REFS\": [\"t\", \"v_x\", \"x\"], \"ROLE\": \"EOM(x)\", \"EQUATION\": \"D(x,t)=v_x\"}, {\"NAME\": \"KIN_Z\", \"STATEMENT\": \"dz/dt = v_z\", \"REFS\": [\"t\", \"v_z\", \"z\"], \"ROLE\": \"EOM(z)\", \"EQUATION\": \"D(z,t)=v_z\"}, {\"NAME\": \"EOM_X\", \"STATEMENT\": \"m dv_x/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_x\"], \"ROLE\": \"EOM(v_x)\", \"EQUATION\": \"m*D(v_x,t)=0\"}, {\"NAME\": \"EOM_Z\", \"STATEMENT\": \"m dv_z/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_z\"], \"ROLE\": \"EOM(v_z)\", \"EQUATION\": \"m*D(v_z,t)=0\"}], \"ASSUMPTION\": [{\"NAME\": \"point_mass\", \"PROPOSITION\": \"the body is treated as a point mass\", \"REFS\": [\"m\"]}]}, \"BIND\": {\"HEIGHT\": [\"z\"], \"MASS\": [\"m\"], \"UP_VELOCITY\": [\"v_z\"]}, \"VALUES\": {\"h_max\": {\"VALUE\": \"100\", \"UNIT\": \"m\"}}, \"ANSWERS\": {}}, {\"NAME\": \"TABLE\", \"TPK\": {\"DOF\": [{\"NAME\": \"t\", \"DIMENSION\": \"T1\"}, {\"NAME\": \"x\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"z\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"v_x\", \"DIMENSION\": \"L1 T-1\"}, {\"NAME\": \"v_z\", \"DIMENSION\": \"L1 T-1\"}], \"CONSTANT\": [{\"NAME\": \"m\", \"DIMENSION\": \"M1\"}], \"LAW\": [{\"NAME\": \"KIN_X\", \"STATEMENT\": \"dx/dt = v_x\", \"REFS\": [\"t\", \"v_x\", \"x\"], \"ROLE\": \"EOM(x)\", \"EQUATION\": \"D(x,t)=v_x\"}, {\"NAME\": \"KIN_Z\", \"STATEMENT\": \"dz/dt = v_z\", \"REFS\": [\"t\", \"v_z\", \"z\"], \"ROLE\": \"CONSTRAINT\", \"EQUATION\": \"D(z,t)=v_z\"}, {\"NAME\": \"EOM_X\", \"STATEMENT\": \"m dv_x/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_x\"], \"ROLE\": \"EOM(v_x)\", \"EQUATION\": \"m*D(v_x,t)=0\"}], \"CONSTRAINT\": [{\"NAME\": \"C_Z\", \"TARGET\": \"z\", \"ACTION\": \"FIX\", \"VALUE\": \"0\", \"UNIT\": \"m\", \"STATEMENT\": \"the puck stays on the table top, z = 0\"}, {\"NAME\": \"C_VZ\", \"TARGET\": \"v_z\", \"ACTION\": \"FIX\", \"VALUE\": \"0\", \"UNIT\": \"m s-1\", \"STATEMENT\": \"the puck has no vertical velocity\"}]}, \"BIND\": {\"HEIGHT\": [\"z\"], \"MASS\": [\"m\"], \"UP_VELOCITY\": [\"v_z\"]}, \"VALUES\": {\"h_max\": {\"VALUE\": \"1\", \"UNIT\": \"m\"}}, \"ANSWERS\": {\"FIXED:v_z\": \"YES\"}}]}",
"{\"ID\": \"MATH\", \"VERSION\": \"1.0.0\", \"TITLE\": \"The mathematical constant pi, as the CONSTANT pi_c\", \"SOURCE\": \"pi to 16 significant digits, 3.141592653589793, the nearest IEEE 754 binary64 value\", \"PREREQUISITES\": [], \"PARAMETERS\": [{\"NAME\": \"pi_c\", \"DIMENSION\": \"1\", \"SUPPLY\": \"DECLARED\", \"VALUE\": \"3.141592653589793\", \"UNIT\": \"1\", \"OVERRIDABLE\": \"NO\", \"LABEL\": \"pi, to 16 significant digits\"}], \"SUMS\": [], \"TERMS\": [], \"ASSUMPTIONS\": [], \"BOUNDARIES\": [], \"NOT_CHOSEN\": \"No mathematical constant: pi exists only if you declare it.\", \"NOT_INCLUDED\": [\"pi_c is pi rounded to 16 significant digits; no other mathematical constant is declared.\"], \"EXCLUDES\": [], \"INTERACTS_WITH\": [], \"TEST_BINDINGS\": [{\"NAME\": \"PROJECTILE_2D\", \"TPK\": {\"DOF\": [{\"NAME\": \"t\", \"DIMENSION\": \"T1\"}, {\"NAME\": \"x\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"z\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"v_x\", \"DIMENSION\": \"L1 T-1\"}, {\"NAME\": \"v_z\", \"DIMENSION\": \"L1 T-1\"}], \"CONSTANT\": [{\"NAME\": \"m\", \"DIMENSION\": \"M1\"}], \"LAW\": [{\"NAME\": \"KIN_X\", \"STATEMENT\": \"dx/dt = v_x\", \"REFS\": [\"t\", \"v_x\", \"x\"], \"ROLE\": \"EOM(x)\", \"EQUATION\": \"D(x,t)=v_x\"}, {\"NAME\": \"KIN_Z\", \"STATEMENT\": \"dz/dt = v_z\", \"REFS\": [\"t\", \"v_z\", \"z\"], \"ROLE\": \"EOM(z)\", \"EQUATION\": \"D(z,t)=v_z\"}, {\"NAME\": \"EOM_X\", \"STATEMENT\": \"m dv_x/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_x\"], \"ROLE\": \"EOM(v_x)\", \"EQUATION\": \"m*D(v_x,t)=0\"}, {\"NAME\": \"EOM_Z\", \"STATEMENT\": \"m dv_z/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_z\"], \"ROLE\": \"EOM(v_z)\", \"EQUATION\": \"m*D(v_z,t)=0\"}], \"ASSUMPTION\": [{\"NAME\": \"point_mass\", \"PROPOSITION\": \"the body is treated as a point mass\", \"REFS\": [\"m\"]}]}, \"BIND\": {}, \"VALUES\": {}, \"ANSWERS\": {}}]}"
]
},
"expected": "[\"OK\",[\"ASK\",[]],[\"CLAIMS\",[[\"MATH\",\"1.0.0\",\"CARRIED\"]]]]",
"fn": "interview_check",
"hand_checked": true,
"name": "I21 a carried claim of an ID no longer offered"
},
{
"args": {
"answer": [
{
"AT": 5,
"CHOSEN": "NONE",
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]
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{
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"lines": [
{
"ACT": "MODULE ADD",
"DATE": "2026-10-01",
"DIGEST": "5f3fe27b42378bce0830b0d0959f892f4a8e73b12b540ae877e39e6439d08b4d",
"ID": "AIR-LINEAR",
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{
"ACT": "MODULE ADD",
"DATE": "2026-10-01",
"DIGEST": "6fb53c3a6546151eead2bd6e72e9cf8334f3a2040ad0ee2f5b988ec96d6fc852",
"ID": "AIR-QUADRATIC",
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{
"ACT": "MODULE ADD",
"DATE": "2026-10-01",
"DIGEST": "24877ccb5c8ec300d29ed82ce6650592f35cf8899a3d878ccce9c08d4c72c025",
"ID": "GRAV-UNIFORM",
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{
"ACT": "MODULE ADD",
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"DIGEST": "8f39a356f35527b901fcee012764590f0819c8ffdeccad4bc05195ce3d2e0bcf",
"ID": "MATH",
"VERSION": "1.0.0"
},
{
"ACT": "MODULE RETIRE",
"DATE": "2026-10-02",
"ID": "MATH",
"VERSION": "1.0.0"
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"modules": [
"{\"ID\": \"AIR-LINEAR\", \"VERSION\": \"1.0.0\", \"TITLE\": \"Air resistance at sea level, linear in the speed (Stokes drag on a sphere)\", \"SOURCE\": \"ISO 2533:1975, Standard Atmosphere, sea-level values: density 1.225 kg m-3, dynamic viscosity 1.7894e-5 Pa s\", \"PREREQUISITES\": [{\"SLOT\": \"VELOCITY\", \"KIND\": \"DOF\", \"DIMENSION\": \"L1 T-1\", \"MIN\": 1, \"MAX\": 3, \"LABEL\": \"the velocity components of the body, one per axis\"}], \"PARAMETERS\": [{\"NAME\": \"rho_air\", \"DIMENSION\": \"L-3 M1\", \"SUPPLY\": \"DECLARED\", \"VALUE\": \"1.225\", \"UNIT\": \"kg m-3\", \"OVERRIDABLE\": \"NO\", \"LABEL\": \"the density of air at sea level\"}, {\"NAME\": \"mu_air\", \"DIMENSION\": \"L-1 M1 T-1\", \"SUPPLY\": \"DECLARED\", \"VALUE\": \"1.7894e-5\", \"UNIT\": \"Pa s\", \"OVERRIDABLE\": \"NO\", \"LABEL\": \"the dynamic viscosity of air at sea level\"}, {\"NAME\": \"pi_c\", \"DIMENSION\": \"1\", \"SUPPLY\": \"DECLARED\", \"VALUE\": \"3.141592653589793\", \"UNIT\": \"1\", \"OVERRIDABLE\": \"NO\", \"LABEL\": \"pi, to 16 significant digits\"}, {\"NAME\": \"R_s\", \"DIMENSION\": \"L1\", \"SUPPLY\": \"AUTHOR\", \"LABEL\": \"the radius of the sphere\"}], \"SUMS\": [{\"NAME\": \"SPEED2\", \"OVER\": \"VELOCITY\", \"EACH\": \"VELOCITY^2\"}], \"TERMS\": [{\"TARGET\": \"VELOCITY\", \"SIGN\": \"-\", \"EXPR\": \"6*pi_c*mu_air*R_s*VELOCITY\", \"LABEL\": \"the linear (Stokes) drag\"}], \"ASSUMPTIONS\": [{\"NAME\": \"air_still\", \"PROPOSITION\": \"the air is at rest in the frame of the body's velocity\", \"REFS\": [\"VELOCITY\"]}, {\"NAME\": \"air_uniform\", \"PROPOSITION\": \"the air density is uniform over the region of motion\", \"REFS\": [\"rho_air\"]}, {\"NAME\": \"drag_sphere\", \"PROPOSITION\": \"the body is a rigid sphere of radius R_s\", \"REFS\": [\"R_s\"]}], \"BOUNDARIES\": [{\"NAME\": \"drag_linear_regime\", \"PREDICATE\": \"2 rho_air |v| R_s / mu_air < 1: the regime of the linear law\", \"CONDITION\": \"mu_air != 0 and SPEED2 >= 0 and 2*rho_air*sqrt(SPEED2)*R_s/mu_air < 1\"}], \"NOT_CHOSEN\": \"No linear (Stokes) air resistance.\", \"NOT_INCLUDED\": [\"No wind: the air is at rest.\", \"No change of air density or viscosity with altitude or temperature.\", \"No drag outside the regime of the linear law.\"], \"EXCLUDES\": [], \"INTERACTS_WITH\": [], \"TEST_BINDINGS\": [{\"NAME\": \"PROJECTILE_2D\", \"TPK\": {\"DOF\": [{\"NAME\": \"t\", \"DIMENSION\": \"T1\"}, {\"NAME\": \"x\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"z\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"v_x\", \"DIMENSION\": \"L1 T-1\"}, {\"NAME\": \"v_z\", \"DIMENSION\": \"L1 T-1\"}], \"CONSTANT\": [{\"NAME\": \"m\", \"DIMENSION\": \"M1\"}], \"LAW\": [{\"NAME\": \"KIN_X\", \"STATEMENT\": \"dx/dt = v_x\", \"REFS\": [\"t\", \"v_x\", \"x\"], \"ROLE\": \"EOM(x)\", \"EQUATION\": \"D(x,t)=v_x\"}, {\"NAME\": \"KIN_Z\", \"STATEMENT\": \"dz/dt = v_z\", \"REFS\": [\"t\", \"v_z\", \"z\"], \"ROLE\": \"EOM(z)\", \"EQUATION\": \"D(z,t)=v_z\"}, {\"NAME\": \"EOM_X\", \"STATEMENT\": \"m dv_x/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_x\"], \"ROLE\": \"EOM(v_x)\", \"EQUATION\": \"m*D(v_x,t)=0\"}, {\"NAME\": \"EOM_Z\", \"STATEMENT\": \"m dv_z/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_z\"], \"ROLE\": \"EOM(v_z)\", \"EQUATION\": \"m*D(v_z,t)=0\"}], \"ASSUMPTION\": [{\"NAME\": \"point_mass\", \"PROPOSITION\": \"the body is treated as a point mass\", \"REFS\": [\"m\"]}]}, \"BIND\": {\"VELOCITY\": [\"v_x\", \"v_z\"]}, \"VALUES\": {\"R_s\": {}}, \"ANSWERS\": {}}]}",
"{\"ID\": \"AIR-QUADRATIC\", \"VERSION\": \"1.0.0\", \"TITLE\": \"Air resistance at sea level, quadratic in the speed\", \"SOURCE\": \"ISO 2533:1975, Standard Atmosphere, sea-level values: density 1.225 kg m-3, dynamic viscosity 1.7894e-5 Pa s\", \"PREREQUISITES\": [{\"SLOT\": \"VELOCITY\", \"KIND\": \"DOF\", \"DIMENSION\": \"L1 T-1\", \"MIN\": 1, \"MAX\": 3, \"LABEL\": \"the velocity components of the body, one per axis\"}], \"PARAMETERS\": [{\"NAME\": \"rho_air\", \"DIMENSION\": \"L-3 M1\", \"SUPPLY\": \"DECLARED\", \"VALUE\": \"1.225\", \"UNIT\": \"kg m-3\", \"OVERRIDABLE\": \"NO\", \"LABEL\": \"the density of air at sea level\"}, {\"NAME\": \"mu_air\", \"DIMENSION\": \"L-1 M1 T-1\", \"SUPPLY\": \"DECLARED\", \"VALUE\": \"1.7894e-5\", \"UNIT\": \"Pa s\", \"OVERRIDABLE\": \"NO\", \"LABEL\": \"the dynamic viscosity of air at sea level\"}, {\"NAME\": \"C_d\", \"DIMENSION\": \"1\", \"SUPPLY\": \"AUTHOR\", \"LABEL\": \"the drag coefficient of the body\"}, {\"NAME\": \"A_ref\", \"DIMENSION\": \"L2\", \"SUPPLY\": \"AUTHOR\", \"LABEL\": \"the reference area of the drag coefficient\"}, {\"NAME\": \"L_ref\", \"DIMENSION\": \"L1\", \"SUPPLY\": \"AUTHOR\", \"LABEL\": \"the reference length of the Reynolds number\"}], \"SUMS\": [{\"NAME\": \"SPEED2\", \"OVER\": \"VELOCITY\", \"EACH\": \"VELOCITY^2\"}], \"TERMS\": [{\"TARGET\": \"VELOCITY\", \"SIGN\": \"-\", \"EXPR\": \"0.5*rho_air*C_d*A_ref*sqrt(SPEED2)*VELOCITY\", \"LABEL\": \"the quadratic drag\"}], \"ASSUMPTIONS\": [{\"NAME\": \"air_still\", \"PROPOSITION\": \"the air is at rest in the frame of the body's velocity\", \"REFS\": [\"VELOCITY\"]}, {\"NAME\": \"air_uniform\", \"PROPOSITION\": \"the air density is uniform over the region of motion\", \"REFS\": [\"rho_air\"]}, {\"NAME\": \"drag_cd_constant\", \"PROPOSITION\": \"the drag coefficient C_d is constant over the motion\", \"REFS\": [\"C_d\"]}, {\"NAME\": \"drag_no_lift\", \"PROPOSITION\": \"the body experiences no lift force\", \"REFS\": [\"VELOCITY\"]}, {\"NAME\": \"drag_no_magnus\", \"PROPOSITION\": \"the body experiences no Magnus force\", \"REFS\": [\"VELOCITY\"]}], \"BOUNDARIES\": [{\"NAME\": \"drag_quadratic_regime\", \"PREDICATE\": \"1e3 < rho_air |v| L_ref / mu_air < 2e5: the Reynolds window of the quadratic law\", \"CONDITION\": \"mu_air != 0 and SPEED2 >= 0 and rho_air*sqrt(SPEED2)*L_ref/mu_air > 1000 and rho_air*sqrt(SPEED2)*L_ref/mu_air < 200000\"}], \"NOT_CHOSEN\": \"No quadratic air resistance.\", \"NOT_INCLUDED\": [\"No wind: the air is at rest.\", \"No change of air density or viscosity with altitude or temperature.\", \"No lift, Magnus or added-mass force.\", \"No drag outside the Reynolds window of the quadratic law.\"], \"EXCLUDES\": [\"AIR-LINEAR\"], \"INTERACTS_WITH\": [], \"TEST_BINDINGS\": [{\"NAME\": \"PROJECTILE_2D\", \"TPK\": {\"DOF\": [{\"NAME\": \"t\", \"DIMENSION\": \"T1\"}, {\"NAME\": \"x\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"z\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"v_x\", \"DIMENSION\": \"L1 T-1\"}, {\"NAME\": \"v_z\", \"DIMENSION\": \"L1 T-1\"}], \"CONSTANT\": [{\"NAME\": \"m\", \"DIMENSION\": \"M1\"}], \"LAW\": [{\"NAME\": \"KIN_X\", \"STATEMENT\": \"dx/dt = v_x\", \"REFS\": [\"t\", \"v_x\", \"x\"], \"ROLE\": \"EOM(x)\", \"EQUATION\": \"D(x,t)=v_x\"}, {\"NAME\": \"KIN_Z\", \"STATEMENT\": \"dz/dt = v_z\", \"REFS\": [\"t\", \"v_z\", \"z\"], \"ROLE\": \"EOM(z)\", \"EQUATION\": \"D(z,t)=v_z\"}, {\"NAME\": \"EOM_X\", \"STATEMENT\": \"m dv_x/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_x\"], \"ROLE\": \"EOM(v_x)\", \"EQUATION\": \"m*D(v_x,t)=0\"}, {\"NAME\": \"EOM_Z\", \"STATEMENT\": \"m dv_z/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_z\"], \"ROLE\": \"EOM(v_z)\", \"EQUATION\": \"m*D(v_z,t)=0\"}], \"ASSUMPTION\": [{\"NAME\": \"point_mass\", \"PROPOSITION\": \"the body is treated as a point mass\", \"REFS\": [\"m\"]}]}, \"BIND\": {\"VELOCITY\": [\"v_x\", \"v_z\"]}, \"VALUES\": {\"A_ref\": {}, \"C_d\": {}, \"L_ref\": {}}, \"ANSWERS\": {}}]}",
"{\"ID\": \"GRAV-UNIFORM\", \"VERSION\": \"1.0.0\", \"TITLE\": \"Uniform gravity at the standard value g_n\", \"SOURCE\": \"g_n = 9.80665 m s-2, exact by definition: 3rd CGPM (1901), declaration on the unit of mass and on the definition of weight\", \"PREREQUISITES\": [{\"SLOT\": \"MASS\", \"KIND\": \"CONSTANT\", \"DIMENSION\": \"M1\", \"MIN\": 1, \"MAX\": 1, \"LABEL\": \"the mass of the body\"}, {\"SLOT\": \"UP_VELOCITY\", \"KIND\": \"DOF\", \"DIMENSION\": \"L1 T-1\", \"MIN\": 1, \"MAX\": 1, \"LABEL\": \"the velocity component pointing up; its equation of motion receives the weight\"}, {\"SLOT\": \"HEIGHT\", \"KIND\": \"DOF\", \"DIMENSION\": \"L1\", \"MIN\": 1, \"MAX\": 1, \"LABEL\": \"the position along the same upward axis\"}], \"PARAMETERS\": [{\"NAME\": \"g_n\", \"DIMENSION\": \"L1 T-2\", \"SUPPLY\": \"DECLARED\", \"VALUE\": \"9.80665\", \"UNIT\": \"m s-2\", \"OVERRIDABLE\": \"NO\", \"LABEL\": \"the standard acceleration of gravity\"}, {\"NAME\": \"h_max\", \"DIMENSION\": \"L1\", \"SUPPLY\": \"AUTHOR\", \"LABEL\": \"the largest height, above or below the origin, over which the field is taken as uniform\"}], \"SUMS\": [], \"TERMS\": [{\"TARGET\": \"UP_VELOCITY\", \"SIGN\": \"-\", \"EXPR\": \"MASS*g_n\", \"LABEL\": \"the weight\"}], \"ASSUMPTIONS\": [{\"NAME\": \"gravity_uniform\", \"PROPOSITION\": \"the gravitational field is uniform over the region abs({HEIGHT}) < h_max\", \"REFS\": [\"HEIGHT\", \"h_max\"]}, {\"NAME\": \"gravity_standard\", \"PROPOSITION\": \"the local gravitational acceleration equals the conventional standard value g_n\", \"REFS\": [\"g_n\"]}, {\"NAME\": \"frame_inertial\", \"PROPOSITION\": \"the frame in which {HEIGHT} is measured is treated as inertial\", \"REFS\": [\"HEIGHT\"]}], \"BOUNDARIES\": [{\"NAME\": \"gravity_region\", \"PREDICATE\": \"abs({HEIGHT}) < h_max\", \"CONDITION\": \"abs(HEIGHT) < h_max\"}], \"NOT_CHOSEN\": \"No gravity: no weight acts on any DOF.\", \"NOT_INCLUDED\": [\"No variation of gravity with height or latitude beyond what g_n contains.\", \"No Earth rotation (Coriolis or centrifugal force) beyond what g_n contains.\", \"No gravity of bodies other than the Earth.\"], \"EXCLUDES\": [], \"INTERACTS_WITH\": [{\"WITH\": \"AIR-*\", \"QUESTION_ID\": \"BUOYANCY\", \"QUESTION\": \"Does the air's buoyancy (upthrust) act on the body in the system you mean?\", \"YES_LINE\": \"Buoyancy acts (your answer): no module adds it; it acts in this kernel only where one of your own laws states it.\", \"NO_LINE\": \"No buoyancy: the air's upthrust on the body is not included.\"}], \"TEST_BINDINGS\": [{\"NAME\": \"PROJECTILE_2D\", \"TPK\": {\"DOF\": [{\"NAME\": \"t\", \"DIMENSION\": \"T1\"}, {\"NAME\": \"x\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"z\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"v_x\", \"DIMENSION\": \"L1 T-1\"}, {\"NAME\": \"v_z\", \"DIMENSION\": \"L1 T-1\"}], \"CONSTANT\": [{\"NAME\": \"m\", \"DIMENSION\": \"M1\"}], \"LAW\": [{\"NAME\": \"KIN_X\", \"STATEMENT\": \"dx/dt = v_x\", \"REFS\": [\"t\", \"v_x\", \"x\"], \"ROLE\": \"EOM(x)\", \"EQUATION\": \"D(x,t)=v_x\"}, {\"NAME\": \"KIN_Z\", \"STATEMENT\": \"dz/dt = v_z\", \"REFS\": [\"t\", \"v_z\", \"z\"], \"ROLE\": \"EOM(z)\", \"EQUATION\": \"D(z,t)=v_z\"}, {\"NAME\": \"EOM_X\", \"STATEMENT\": \"m dv_x/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_x\"], \"ROLE\": \"EOM(v_x)\", \"EQUATION\": \"m*D(v_x,t)=0\"}, {\"NAME\": \"EOM_Z\", \"STATEMENT\": \"m dv_z/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_z\"], \"ROLE\": \"EOM(v_z)\", \"EQUATION\": \"m*D(v_z,t)=0\"}], \"ASSUMPTION\": [{\"NAME\": \"point_mass\", \"PROPOSITION\": \"the body is treated as a point mass\", \"REFS\": [\"m\"]}]}, \"BIND\": {\"HEIGHT\": [\"z\"], \"MASS\": [\"m\"], \"UP_VELOCITY\": [\"v_z\"]}, \"VALUES\": {\"h_max\": {\"VALUE\": \"100\", \"UNIT\": \"m\"}}, \"ANSWERS\": {}}, {\"NAME\": \"TABLE\", \"TPK\": {\"DOF\": [{\"NAME\": \"t\", \"DIMENSION\": \"T1\"}, {\"NAME\": \"x\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"z\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"v_x\", \"DIMENSION\": \"L1 T-1\"}, {\"NAME\": \"v_z\", \"DIMENSION\": \"L1 T-1\"}], \"CONSTANT\": [{\"NAME\": \"m\", \"DIMENSION\": \"M1\"}], \"LAW\": [{\"NAME\": \"KIN_X\", \"STATEMENT\": \"dx/dt = v_x\", \"REFS\": [\"t\", \"v_x\", \"x\"], \"ROLE\": \"EOM(x)\", \"EQUATION\": \"D(x,t)=v_x\"}, {\"NAME\": \"KIN_Z\", \"STATEMENT\": \"dz/dt = v_z\", \"REFS\": [\"t\", \"v_z\", \"z\"], \"ROLE\": \"CONSTRAINT\", \"EQUATION\": \"D(z,t)=v_z\"}, {\"NAME\": \"EOM_X\", \"STATEMENT\": \"m dv_x/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_x\"], \"ROLE\": \"EOM(v_x)\", \"EQUATION\": \"m*D(v_x,t)=0\"}], \"CONSTRAINT\": [{\"NAME\": \"C_Z\", \"TARGET\": \"z\", \"ACTION\": \"FIX\", \"VALUE\": \"0\", \"UNIT\": \"m\", \"STATEMENT\": \"the puck stays on the table top, z = 0\"}, {\"NAME\": \"C_VZ\", \"TARGET\": \"v_z\", \"ACTION\": \"FIX\", \"VALUE\": \"0\", \"UNIT\": \"m s-1\", \"STATEMENT\": \"the puck has no vertical velocity\"}]}, \"BIND\": {\"HEIGHT\": [\"z\"], \"MASS\": [\"m\"], \"UP_VELOCITY\": [\"v_z\"]}, \"VALUES\": {\"h_max\": {\"VALUE\": \"1\", \"UNIT\": \"m\"}}, \"ANSWERS\": {\"FIXED:v_z\": \"YES\"}}]}",
"{\"ID\": \"MATH\", \"VERSION\": \"1.0.0\", \"TITLE\": \"The mathematical constant pi, as the CONSTANT pi_c\", \"SOURCE\": \"pi to 16 significant digits, 3.141592653589793, the nearest IEEE 754 binary64 value\", \"PREREQUISITES\": [], \"PARAMETERS\": [{\"NAME\": \"pi_c\", \"DIMENSION\": \"1\", \"SUPPLY\": \"DECLARED\", \"VALUE\": \"3.141592653589793\", \"UNIT\": \"1\", \"OVERRIDABLE\": \"NO\", \"LABEL\": \"pi, to 16 significant digits\"}], \"SUMS\": [], \"TERMS\": [], \"ASSUMPTIONS\": [], \"BOUNDARIES\": [], \"NOT_CHOSEN\": \"No mathematical constant: pi exists only if you declare it.\", \"NOT_INCLUDED\": [\"pi_c is pi rounded to 16 significant digits; no other mathematical constant is declared.\"], \"EXCLUDES\": [], \"INTERACTS_WITH\": [], \"TEST_BINDINGS\": [{\"NAME\": \"PROJECTILE_2D\", \"TPK\": {\"DOF\": [{\"NAME\": \"t\", \"DIMENSION\": \"T1\"}, {\"NAME\": \"x\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"z\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"v_x\", \"DIMENSION\": \"L1 T-1\"}, {\"NAME\": \"v_z\", \"DIMENSION\": \"L1 T-1\"}], \"CONSTANT\": [{\"NAME\": \"m\", \"DIMENSION\": \"M1\"}], \"LAW\": [{\"NAME\": \"KIN_X\", \"STATEMENT\": \"dx/dt = v_x\", \"REFS\": [\"t\", \"v_x\", \"x\"], \"ROLE\": \"EOM(x)\", \"EQUATION\": \"D(x,t)=v_x\"}, {\"NAME\": \"KIN_Z\", \"STATEMENT\": \"dz/dt = v_z\", \"REFS\": [\"t\", \"v_z\", \"z\"], \"ROLE\": \"EOM(z)\", \"EQUATION\": \"D(z,t)=v_z\"}, {\"NAME\": \"EOM_X\", \"STATEMENT\": \"m dv_x/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_x\"], \"ROLE\": \"EOM(v_x)\", \"EQUATION\": \"m*D(v_x,t)=0\"}, {\"NAME\": \"EOM_Z\", \"STATEMENT\": \"m dv_z/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_z\"], \"ROLE\": \"EOM(v_z)\", \"EQUATION\": \"m*D(v_z,t)=0\"}], \"ASSUMPTION\": [{\"NAME\": \"point_mass\", \"PROPOSITION\": \"the body is treated as a point mass\", \"REFS\": [\"m\"]}]}, \"BIND\": {}, \"VALUES\": {}, \"ANSWERS\": {}}]}"
]
},
"expected": "[\"REFUSED\",\"CLAIM MATH 1.0.0: MATH is not in the answer\"]",
"fn": "interview_check",
"hand_checked": true,
"name": "I22 the same claim not carried"
},
{
"args": {
"answer": [
{
"AT": 4,
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{
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{
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"lines": [
{
"ACT": "MODULE ADD",
"DATE": "2026-10-01",
"DIGEST": "5f3fe27b42378bce0830b0d0959f892f4a8e73b12b540ae877e39e6439d08b4d",
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{
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{
"ACT": "MODULE ADD",
"DATE": "2026-10-01",
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{
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"modules": [
"{\"ID\": \"AIR-LINEAR\", \"VERSION\": \"1.0.0\", \"TITLE\": \"Air resistance at sea level, linear in the speed (Stokes drag on a sphere)\", \"SOURCE\": \"ISO 2533:1975, Standard Atmosphere, sea-level values: density 1.225 kg m-3, dynamic viscosity 1.7894e-5 Pa s\", \"PREREQUISITES\": [{\"SLOT\": \"VELOCITY\", \"KIND\": \"DOF\", \"DIMENSION\": \"L1 T-1\", \"MIN\": 1, \"MAX\": 3, \"LABEL\": \"the velocity components of the body, one per axis\"}], \"PARAMETERS\": [{\"NAME\": \"rho_air\", \"DIMENSION\": \"L-3 M1\", \"SUPPLY\": \"DECLARED\", \"VALUE\": \"1.225\", \"UNIT\": \"kg m-3\", \"OVERRIDABLE\": \"NO\", \"LABEL\": \"the density of air at sea level\"}, {\"NAME\": \"mu_air\", \"DIMENSION\": \"L-1 M1 T-1\", \"SUPPLY\": \"DECLARED\", \"VALUE\": \"1.7894e-5\", \"UNIT\": \"Pa s\", \"OVERRIDABLE\": \"NO\", \"LABEL\": \"the dynamic viscosity of air at sea level\"}, {\"NAME\": \"pi_c\", \"DIMENSION\": \"1\", \"SUPPLY\": \"DECLARED\", \"VALUE\": \"3.141592653589793\", \"UNIT\": \"1\", \"OVERRIDABLE\": \"NO\", \"LABEL\": \"pi, to 16 significant digits\"}, {\"NAME\": \"R_s\", \"DIMENSION\": \"L1\", \"SUPPLY\": \"AUTHOR\", \"LABEL\": \"the radius of the sphere\"}], \"SUMS\": [{\"NAME\": \"SPEED2\", \"OVER\": \"VELOCITY\", \"EACH\": \"VELOCITY^2\"}], \"TERMS\": [{\"TARGET\": \"VELOCITY\", \"SIGN\": \"-\", \"EXPR\": \"6*pi_c*mu_air*R_s*VELOCITY\", \"LABEL\": \"the linear (Stokes) drag\"}], \"ASSUMPTIONS\": [{\"NAME\": \"air_still\", \"PROPOSITION\": \"the air is at rest in the frame of the body's velocity\", \"REFS\": [\"VELOCITY\"]}, {\"NAME\": \"air_uniform\", \"PROPOSITION\": \"the air density is uniform over the region of motion\", \"REFS\": [\"rho_air\"]}, {\"NAME\": \"drag_sphere\", \"PROPOSITION\": \"the body is a rigid sphere of radius R_s\", \"REFS\": [\"R_s\"]}], \"BOUNDARIES\": [{\"NAME\": \"drag_linear_regime\", \"PREDICATE\": \"2 rho_air |v| R_s / mu_air < 1: the regime of the linear law\", \"CONDITION\": \"mu_air != 0 and SPEED2 >= 0 and 2*rho_air*sqrt(SPEED2)*R_s/mu_air < 1\"}], \"NOT_CHOSEN\": \"No linear (Stokes) air resistance.\", \"NOT_INCLUDED\": [\"No wind: the air is at rest.\", \"No change of air density or viscosity with altitude or temperature.\", \"No drag outside the regime of the linear law.\"], \"EXCLUDES\": [], \"INTERACTS_WITH\": [], \"TEST_BINDINGS\": [{\"NAME\": \"PROJECTILE_2D\", \"TPK\": {\"DOF\": [{\"NAME\": \"t\", \"DIMENSION\": \"T1\"}, {\"NAME\": \"x\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"z\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"v_x\", \"DIMENSION\": \"L1 T-1\"}, {\"NAME\": \"v_z\", \"DIMENSION\": \"L1 T-1\"}], \"CONSTANT\": [{\"NAME\": \"m\", \"DIMENSION\": \"M1\"}], \"LAW\": [{\"NAME\": \"KIN_X\", \"STATEMENT\": \"dx/dt = v_x\", \"REFS\": [\"t\", \"v_x\", \"x\"], \"ROLE\": \"EOM(x)\", \"EQUATION\": \"D(x,t)=v_x\"}, {\"NAME\": \"KIN_Z\", \"STATEMENT\": \"dz/dt = v_z\", \"REFS\": [\"t\", \"v_z\", \"z\"], \"ROLE\": \"EOM(z)\", \"EQUATION\": \"D(z,t)=v_z\"}, {\"NAME\": \"EOM_X\", \"STATEMENT\": \"m dv_x/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_x\"], \"ROLE\": \"EOM(v_x)\", \"EQUATION\": \"m*D(v_x,t)=0\"}, {\"NAME\": \"EOM_Z\", \"STATEMENT\": \"m dv_z/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_z\"], \"ROLE\": \"EOM(v_z)\", \"EQUATION\": \"m*D(v_z,t)=0\"}], \"ASSUMPTION\": [{\"NAME\": \"point_mass\", \"PROPOSITION\": \"the body is treated as a point mass\", \"REFS\": [\"m\"]}]}, \"BIND\": {\"VELOCITY\": [\"v_x\", \"v_z\"]}, \"VALUES\": {\"R_s\": {}}, \"ANSWERS\": {}}]}",
"{\"ID\": \"AIR-QUADRATIC\", \"VERSION\": \"1.0.0\", \"TITLE\": \"Air resistance at sea level, quadratic in the speed\", \"SOURCE\": \"ISO 2533:1975, Standard Atmosphere, sea-level values: density 1.225 kg m-3, dynamic viscosity 1.7894e-5 Pa s\", \"PREREQUISITES\": [{\"SLOT\": \"VELOCITY\", \"KIND\": \"DOF\", \"DIMENSION\": \"L1 T-1\", \"MIN\": 1, \"MAX\": 3, \"LABEL\": \"the velocity components of the body, one per axis\"}], \"PARAMETERS\": [{\"NAME\": \"rho_air\", \"DIMENSION\": \"L-3 M1\", \"SUPPLY\": \"DECLARED\", \"VALUE\": \"1.225\", \"UNIT\": \"kg m-3\", \"OVERRIDABLE\": \"NO\", \"LABEL\": \"the density of air at sea level\"}, {\"NAME\": \"mu_air\", \"DIMENSION\": \"L-1 M1 T-1\", \"SUPPLY\": \"DECLARED\", \"VALUE\": \"1.7894e-5\", \"UNIT\": \"Pa s\", \"OVERRIDABLE\": \"NO\", \"LABEL\": \"the dynamic viscosity of air at sea level\"}, {\"NAME\": \"C_d\", \"DIMENSION\": \"1\", \"SUPPLY\": \"AUTHOR\", \"LABEL\": \"the drag coefficient of the body\"}, {\"NAME\": \"A_ref\", \"DIMENSION\": \"L2\", \"SUPPLY\": \"AUTHOR\", \"LABEL\": \"the reference area of the drag coefficient\"}, {\"NAME\": \"L_ref\", \"DIMENSION\": \"L1\", \"SUPPLY\": \"AUTHOR\", \"LABEL\": \"the reference length of the Reynolds number\"}], \"SUMS\": [{\"NAME\": \"SPEED2\", \"OVER\": \"VELOCITY\", \"EACH\": \"VELOCITY^2\"}], \"TERMS\": [{\"TARGET\": \"VELOCITY\", \"SIGN\": \"-\", \"EXPR\": \"0.5*rho_air*C_d*A_ref*sqrt(SPEED2)*VELOCITY\", \"LABEL\": \"the quadratic drag\"}], \"ASSUMPTIONS\": [{\"NAME\": \"air_still\", \"PROPOSITION\": \"the air is at rest in the frame of the body's velocity\", \"REFS\": [\"VELOCITY\"]}, {\"NAME\": \"air_uniform\", \"PROPOSITION\": \"the air density is uniform over the region of motion\", \"REFS\": [\"rho_air\"]}, {\"NAME\": \"drag_cd_constant\", \"PROPOSITION\": \"the drag coefficient C_d is constant over the motion\", \"REFS\": [\"C_d\"]}, {\"NAME\": \"drag_no_lift\", \"PROPOSITION\": \"the body experiences no lift force\", \"REFS\": [\"VELOCITY\"]}, {\"NAME\": \"drag_no_magnus\", \"PROPOSITION\": \"the body experiences no Magnus force\", \"REFS\": [\"VELOCITY\"]}], \"BOUNDARIES\": [{\"NAME\": \"drag_quadratic_regime\", \"PREDICATE\": \"1e3 < rho_air |v| L_ref / mu_air < 2e5: the Reynolds window of the quadratic law\", \"CONDITION\": \"mu_air != 0 and SPEED2 >= 0 and rho_air*sqrt(SPEED2)*L_ref/mu_air > 1000 and rho_air*sqrt(SPEED2)*L_ref/mu_air < 200000\"}], \"NOT_CHOSEN\": \"No quadratic air resistance.\", \"NOT_INCLUDED\": [\"No wind: the air is at rest.\", \"No change of air density or viscosity with altitude or temperature.\", \"No lift, Magnus or added-mass force.\", \"No drag outside the Reynolds window of the quadratic law.\"], \"EXCLUDES\": [\"AIR-LINEAR\"], \"INTERACTS_WITH\": [], \"TEST_BINDINGS\": [{\"NAME\": \"PROJECTILE_2D\", \"TPK\": {\"DOF\": [{\"NAME\": \"t\", \"DIMENSION\": \"T1\"}, {\"NAME\": \"x\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"z\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"v_x\", \"DIMENSION\": \"L1 T-1\"}, {\"NAME\": \"v_z\", \"DIMENSION\": \"L1 T-1\"}], \"CONSTANT\": [{\"NAME\": \"m\", \"DIMENSION\": \"M1\"}], \"LAW\": [{\"NAME\": \"KIN_X\", \"STATEMENT\": \"dx/dt = v_x\", \"REFS\": [\"t\", \"v_x\", \"x\"], \"ROLE\": \"EOM(x)\", \"EQUATION\": \"D(x,t)=v_x\"}, {\"NAME\": \"KIN_Z\", \"STATEMENT\": \"dz/dt = v_z\", \"REFS\": [\"t\", \"v_z\", \"z\"], \"ROLE\": \"EOM(z)\", \"EQUATION\": \"D(z,t)=v_z\"}, {\"NAME\": \"EOM_X\", \"STATEMENT\": \"m dv_x/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_x\"], \"ROLE\": \"EOM(v_x)\", \"EQUATION\": \"m*D(v_x,t)=0\"}, {\"NAME\": \"EOM_Z\", \"STATEMENT\": \"m dv_z/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_z\"], \"ROLE\": \"EOM(v_z)\", \"EQUATION\": \"m*D(v_z,t)=0\"}], \"ASSUMPTION\": [{\"NAME\": \"point_mass\", \"PROPOSITION\": \"the body is treated as a point mass\", \"REFS\": [\"m\"]}]}, \"BIND\": {\"VELOCITY\": [\"v_x\", \"v_z\"]}, \"VALUES\": {\"A_ref\": {}, \"C_d\": {}, \"L_ref\": {}}, \"ANSWERS\": {}}]}",
"{\"ID\": \"GRAV-UNIFORM\", \"VERSION\": \"1.0.0\", \"TITLE\": \"Uniform gravity at the standard value g_n\", \"SOURCE\": \"g_n = 9.80665 m s-2, exact by definition: 3rd CGPM (1901), declaration on the unit of mass and on the definition of weight\", \"PREREQUISITES\": [{\"SLOT\": \"MASS\", \"KIND\": \"CONSTANT\", \"DIMENSION\": \"M1\", \"MIN\": 1, \"MAX\": 1, \"LABEL\": \"the mass of the body\"}, {\"SLOT\": \"UP_VELOCITY\", \"KIND\": \"DOF\", \"DIMENSION\": \"L1 T-1\", \"MIN\": 1, \"MAX\": 1, \"LABEL\": \"the velocity component pointing up; its equation of motion receives the weight\"}, {\"SLOT\": \"HEIGHT\", \"KIND\": \"DOF\", \"DIMENSION\": \"L1\", \"MIN\": 1, \"MAX\": 1, \"LABEL\": \"the position along the same upward axis\"}], \"PARAMETERS\": [{\"NAME\": \"g_n\", \"DIMENSION\": \"L1 T-2\", \"SUPPLY\": \"DECLARED\", \"VALUE\": \"9.80665\", \"UNIT\": \"m s-2\", \"OVERRIDABLE\": \"NO\", \"LABEL\": \"the standard acceleration of gravity\"}, {\"NAME\": \"h_max\", \"DIMENSION\": \"L1\", \"SUPPLY\": \"AUTHOR\", \"LABEL\": \"the largest height, above or below the origin, over which the field is taken as uniform\"}], \"SUMS\": [], \"TERMS\": [{\"TARGET\": \"UP_VELOCITY\", \"SIGN\": \"-\", \"EXPR\": \"MASS*g_n\", \"LABEL\": \"the weight\"}], \"ASSUMPTIONS\": [{\"NAME\": \"gravity_uniform\", \"PROPOSITION\": \"the gravitational field is uniform over the region abs({HEIGHT}) < h_max\", \"REFS\": [\"HEIGHT\", \"h_max\"]}, {\"NAME\": \"gravity_standard\", \"PROPOSITION\": \"the local gravitational acceleration equals the conventional standard value g_n\", \"REFS\": [\"g_n\"]}, {\"NAME\": \"frame_inertial\", \"PROPOSITION\": \"the frame in which {HEIGHT} is measured is treated as inertial\", \"REFS\": [\"HEIGHT\"]}], \"BOUNDARIES\": [{\"NAME\": \"gravity_region\", \"PREDICATE\": \"abs({HEIGHT}) < h_max\", \"CONDITION\": \"abs(HEIGHT) < h_max\"}], \"NOT_CHOSEN\": \"No gravity: no weight acts on any DOF.\", \"NOT_INCLUDED\": [\"No variation of gravity with height or latitude beyond what g_n contains.\", \"No Earth rotation (Coriolis or centrifugal force) beyond what g_n contains.\", \"No gravity of bodies other than the Earth.\"], \"EXCLUDES\": [], \"INTERACTS_WITH\": [{\"WITH\": \"AIR-*\", \"QUESTION_ID\": \"BUOYANCY\", \"QUESTION\": \"Does the air's buoyancy (upthrust) act on the body in the system you mean?\", \"YES_LINE\": \"Buoyancy acts (your answer): no module adds it; it acts in this kernel only where one of your own laws states it.\", \"NO_LINE\": \"No buoyancy: the air's upthrust on the body is not included.\"}], \"TEST_BINDINGS\": [{\"NAME\": \"PROJECTILE_2D\", \"TPK\": {\"DOF\": [{\"NAME\": \"t\", \"DIMENSION\": \"T1\"}, {\"NAME\": \"x\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"z\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"v_x\", \"DIMENSION\": \"L1 T-1\"}, {\"NAME\": \"v_z\", \"DIMENSION\": \"L1 T-1\"}], \"CONSTANT\": [{\"NAME\": \"m\", \"DIMENSION\": \"M1\"}], \"LAW\": [{\"NAME\": \"KIN_X\", \"STATEMENT\": \"dx/dt = v_x\", \"REFS\": [\"t\", \"v_x\", \"x\"], \"ROLE\": \"EOM(x)\", \"EQUATION\": \"D(x,t)=v_x\"}, {\"NAME\": \"KIN_Z\", \"STATEMENT\": \"dz/dt = v_z\", \"REFS\": [\"t\", \"v_z\", \"z\"], \"ROLE\": \"EOM(z)\", \"EQUATION\": \"D(z,t)=v_z\"}, {\"NAME\": \"EOM_X\", \"STATEMENT\": \"m dv_x/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_x\"], \"ROLE\": \"EOM(v_x)\", \"EQUATION\": \"m*D(v_x,t)=0\"}, {\"NAME\": \"EOM_Z\", \"STATEMENT\": \"m dv_z/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_z\"], \"ROLE\": \"EOM(v_z)\", \"EQUATION\": \"m*D(v_z,t)=0\"}], \"ASSUMPTION\": [{\"NAME\": \"point_mass\", \"PROPOSITION\": \"the body is treated as a point mass\", \"REFS\": [\"m\"]}]}, \"BIND\": {\"HEIGHT\": [\"z\"], \"MASS\": [\"m\"], \"UP_VELOCITY\": [\"v_z\"]}, \"VALUES\": {\"h_max\": {\"VALUE\": \"100\", \"UNIT\": \"m\"}}, \"ANSWERS\": {}}, {\"NAME\": \"TABLE\", \"TPK\": {\"DOF\": [{\"NAME\": \"t\", \"DIMENSION\": \"T1\"}, {\"NAME\": \"x\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"z\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"v_x\", \"DIMENSION\": \"L1 T-1\"}, {\"NAME\": \"v_z\", \"DIMENSION\": \"L1 T-1\"}], \"CONSTANT\": [{\"NAME\": \"m\", \"DIMENSION\": \"M1\"}], \"LAW\": [{\"NAME\": \"KIN_X\", \"STATEMENT\": \"dx/dt = v_x\", \"REFS\": [\"t\", \"v_x\", \"x\"], \"ROLE\": \"EOM(x)\", \"EQUATION\": \"D(x,t)=v_x\"}, {\"NAME\": \"KIN_Z\", \"STATEMENT\": \"dz/dt = v_z\", \"REFS\": [\"t\", \"v_z\", \"z\"], \"ROLE\": \"CONSTRAINT\", \"EQUATION\": \"D(z,t)=v_z\"}, {\"NAME\": \"EOM_X\", \"STATEMENT\": \"m dv_x/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_x\"], \"ROLE\": \"EOM(v_x)\", \"EQUATION\": \"m*D(v_x,t)=0\"}], \"CONSTRAINT\": [{\"NAME\": \"C_Z\", \"TARGET\": \"z\", \"ACTION\": \"FIX\", \"VALUE\": \"0\", \"UNIT\": \"m\", \"STATEMENT\": \"the puck stays on the table top, z = 0\"}, {\"NAME\": \"C_VZ\", \"TARGET\": \"v_z\", \"ACTION\": \"FIX\", \"VALUE\": \"0\", \"UNIT\": \"m s-1\", \"STATEMENT\": \"the puck has no vertical velocity\"}]}, \"BIND\": {\"HEIGHT\": [\"z\"], \"MASS\": [\"m\"], \"UP_VELOCITY\": [\"v_z\"]}, \"VALUES\": {\"h_max\": {\"VALUE\": \"1\", \"UNIT\": \"m\"}}, \"ANSWERS\": {\"FIXED:v_z\": \"YES\"}}]}",
"{\"ID\": \"MATH\", \"VERSION\": \"1.0.0\", \"TITLE\": \"The mathematical constant pi, as the CONSTANT pi_c\", \"SOURCE\": \"pi to 16 significant digits, 3.141592653589793, the nearest IEEE 754 binary64 value\", \"PREREQUISITES\": [], \"PARAMETERS\": [{\"NAME\": \"pi_c\", \"DIMENSION\": \"1\", \"SUPPLY\": \"DECLARED\", \"VALUE\": \"3.141592653589793\", \"UNIT\": \"1\", \"OVERRIDABLE\": \"NO\", \"LABEL\": \"pi, to 16 significant digits\"}], \"SUMS\": [], \"TERMS\": [], \"ASSUMPTIONS\": [], \"BOUNDARIES\": [], \"NOT_CHOSEN\": \"No mathematical constant: pi exists only if you declare it.\", \"NOT_INCLUDED\": [\"pi_c is pi rounded to 16 significant digits; no other mathematical constant is declared.\"], \"EXCLUDES\": [], \"INTERACTS_WITH\": [], \"TEST_BINDINGS\": [{\"NAME\": \"PROJECTILE_2D\", \"TPK\": {\"DOF\": [{\"NAME\": \"t\", \"DIMENSION\": \"T1\"}, {\"NAME\": \"x\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"z\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"v_x\", \"DIMENSION\": \"L1 T-1\"}, {\"NAME\": \"v_z\", \"DIMENSION\": \"L1 T-1\"}], \"CONSTANT\": [{\"NAME\": \"m\", \"DIMENSION\": \"M1\"}], \"LAW\": [{\"NAME\": \"KIN_X\", \"STATEMENT\": \"dx/dt = v_x\", \"REFS\": [\"t\", \"v_x\", \"x\"], \"ROLE\": \"EOM(x)\", \"EQUATION\": \"D(x,t)=v_x\"}, {\"NAME\": \"KIN_Z\", \"STATEMENT\": \"dz/dt = v_z\", \"REFS\": [\"t\", \"v_z\", \"z\"], \"ROLE\": \"EOM(z)\", \"EQUATION\": \"D(z,t)=v_z\"}, {\"NAME\": \"EOM_X\", \"STATEMENT\": \"m dv_x/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_x\"], \"ROLE\": \"EOM(v_x)\", \"EQUATION\": \"m*D(v_x,t)=0\"}, {\"NAME\": \"EOM_Z\", \"STATEMENT\": \"m dv_z/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_z\"], \"ROLE\": \"EOM(v_z)\", \"EQUATION\": \"m*D(v_z,t)=0\"}], \"ASSUMPTION\": [{\"NAME\": \"point_mass\", \"PROPOSITION\": \"the body is treated as a point mass\", \"REFS\": [\"m\"]}]}, \"BIND\": {}, \"VALUES\": {}, \"ANSWERS\": {}}]}"
]
},
"expected": "[\"REFUSED\",\"CLAIMS: AIR-LINEAR 1.0.0 and AIR-QUADRATIC 1.0.0 exclude each other (EXCLUDES)\"]",
"fn": "interview_check",
"hand_checked": true,
"name": "I23 two excluding modules chosen"
},
{
"args": {
"answer": [
{
"AT": 4,
"CHOSEN": [
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"GRAV-UNIFORM"
],
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]
}
],
"carried": [],
"claims": [
{
"ANSWERS": {},
"BIND": {
"HEIGHT": [
"z"
],
"MASS": [
"m"
],
"UP_VELOCITY": [
"v_z"
]
},
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"ID": "GRAV-UNIFORM",
"VALUES": {
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"UNIT": "m",
"VALUE": "100"
}
},
"VERSION": "1.0.0"
},
{
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"v_x",
"v_z"
]
},
"DIGEST": "6fb53c3a6546151eead2bd6e72e9cf8334f3a2040ad0ee2f5b988ec96d6fc852",
"ID": "AIR-QUADRATIC",
"VALUES": {
"A_ref": {},
"C_d": {},
"L_ref": {}
},
"VERSION": "1.0.0"
}
],
"lines": [
{
"ACT": "MODULE ADD",
"DATE": "2026-10-01",
"DIGEST": "5f3fe27b42378bce0830b0d0959f892f4a8e73b12b540ae877e39e6439d08b4d",
"ID": "AIR-LINEAR",
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{
"ACT": "MODULE ADD",
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"DIGEST": "6fb53c3a6546151eead2bd6e72e9cf8334f3a2040ad0ee2f5b988ec96d6fc852",
"ID": "AIR-QUADRATIC",
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{
"ACT": "MODULE ADD",
"DATE": "2026-10-01",
"DIGEST": "24877ccb5c8ec300d29ed82ce6650592f35cf8899a3d878ccce9c08d4c72c025",
"ID": "GRAV-UNIFORM",
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{
"ACT": "MODULE ADD",
"DATE": "2026-10-01",
"DIGEST": "8f39a356f35527b901fcee012764590f0819c8ffdeccad4bc05195ce3d2e0bcf",
"ID": "MATH",
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"modules": [
"{\"ID\": \"AIR-LINEAR\", \"VERSION\": \"1.0.0\", \"TITLE\": \"Air resistance at sea level, linear in the speed (Stokes drag on a sphere)\", \"SOURCE\": \"ISO 2533:1975, Standard Atmosphere, sea-level values: density 1.225 kg m-3, dynamic viscosity 1.7894e-5 Pa s\", \"PREREQUISITES\": [{\"SLOT\": \"VELOCITY\", \"KIND\": \"DOF\", \"DIMENSION\": \"L1 T-1\", \"MIN\": 1, \"MAX\": 3, \"LABEL\": \"the velocity components of the body, one per axis\"}], \"PARAMETERS\": [{\"NAME\": \"rho_air\", \"DIMENSION\": \"L-3 M1\", \"SUPPLY\": \"DECLARED\", \"VALUE\": \"1.225\", \"UNIT\": \"kg m-3\", \"OVERRIDABLE\": \"NO\", \"LABEL\": \"the density of air at sea level\"}, {\"NAME\": \"mu_air\", \"DIMENSION\": \"L-1 M1 T-1\", \"SUPPLY\": \"DECLARED\", \"VALUE\": \"1.7894e-5\", \"UNIT\": \"Pa s\", \"OVERRIDABLE\": \"NO\", \"LABEL\": \"the dynamic viscosity of air at sea level\"}, {\"NAME\": \"pi_c\", \"DIMENSION\": \"1\", \"SUPPLY\": \"DECLARED\", \"VALUE\": \"3.141592653589793\", \"UNIT\": \"1\", \"OVERRIDABLE\": \"NO\", \"LABEL\": \"pi, to 16 significant digits\"}, {\"NAME\": \"R_s\", \"DIMENSION\": \"L1\", \"SUPPLY\": \"AUTHOR\", \"LABEL\": \"the radius of the sphere\"}], \"SUMS\": [{\"NAME\": \"SPEED2\", \"OVER\": \"VELOCITY\", \"EACH\": \"VELOCITY^2\"}], \"TERMS\": [{\"TARGET\": \"VELOCITY\", \"SIGN\": \"-\", \"EXPR\": \"6*pi_c*mu_air*R_s*VELOCITY\", \"LABEL\": \"the linear (Stokes) drag\"}], \"ASSUMPTIONS\": [{\"NAME\": \"air_still\", \"PROPOSITION\": \"the air is at rest in the frame of the body's velocity\", \"REFS\": [\"VELOCITY\"]}, {\"NAME\": \"air_uniform\", \"PROPOSITION\": \"the air density is uniform over the region of motion\", \"REFS\": [\"rho_air\"]}, {\"NAME\": \"drag_sphere\", \"PROPOSITION\": \"the body is a rigid sphere of radius R_s\", \"REFS\": [\"R_s\"]}], \"BOUNDARIES\": [{\"NAME\": \"drag_linear_regime\", \"PREDICATE\": \"2 rho_air |v| R_s / mu_air < 1: the regime of the linear law\", \"CONDITION\": \"mu_air != 0 and SPEED2 >= 0 and 2*rho_air*sqrt(SPEED2)*R_s/mu_air < 1\"}], \"NOT_CHOSEN\": \"No linear (Stokes) air resistance.\", \"NOT_INCLUDED\": [\"No wind: the air is at rest.\", \"No change of air density or viscosity with altitude or temperature.\", \"No drag outside the regime of the linear law.\"], \"EXCLUDES\": [], \"INTERACTS_WITH\": [], \"TEST_BINDINGS\": [{\"NAME\": \"PROJECTILE_2D\", \"TPK\": {\"DOF\": [{\"NAME\": \"t\", \"DIMENSION\": \"T1\"}, {\"NAME\": \"x\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"z\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"v_x\", \"DIMENSION\": \"L1 T-1\"}, {\"NAME\": \"v_z\", \"DIMENSION\": \"L1 T-1\"}], \"CONSTANT\": [{\"NAME\": \"m\", \"DIMENSION\": \"M1\"}], \"LAW\": [{\"NAME\": \"KIN_X\", \"STATEMENT\": \"dx/dt = v_x\", \"REFS\": [\"t\", \"v_x\", \"x\"], \"ROLE\": \"EOM(x)\", \"EQUATION\": \"D(x,t)=v_x\"}, {\"NAME\": \"KIN_Z\", \"STATEMENT\": \"dz/dt = v_z\", \"REFS\": [\"t\", \"v_z\", \"z\"], \"ROLE\": \"EOM(z)\", \"EQUATION\": \"D(z,t)=v_z\"}, {\"NAME\": \"EOM_X\", \"STATEMENT\": \"m dv_x/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_x\"], \"ROLE\": \"EOM(v_x)\", \"EQUATION\": \"m*D(v_x,t)=0\"}, {\"NAME\": \"EOM_Z\", \"STATEMENT\": \"m dv_z/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_z\"], \"ROLE\": \"EOM(v_z)\", \"EQUATION\": \"m*D(v_z,t)=0\"}], \"ASSUMPTION\": [{\"NAME\": \"point_mass\", \"PROPOSITION\": \"the body is treated as a point mass\", \"REFS\": [\"m\"]}]}, \"BIND\": {\"VELOCITY\": [\"v_x\", \"v_z\"]}, \"VALUES\": {\"R_s\": {}}, \"ANSWERS\": {}}]}",
"{\"ID\": \"AIR-QUADRATIC\", \"VERSION\": \"1.0.0\", \"TITLE\": \"Air resistance at sea level, quadratic in the speed\", \"SOURCE\": \"ISO 2533:1975, Standard Atmosphere, sea-level values: density 1.225 kg m-3, dynamic viscosity 1.7894e-5 Pa s\", \"PREREQUISITES\": [{\"SLOT\": \"VELOCITY\", \"KIND\": \"DOF\", \"DIMENSION\": \"L1 T-1\", \"MIN\": 1, \"MAX\": 3, \"LABEL\": \"the velocity components of the body, one per axis\"}], \"PARAMETERS\": [{\"NAME\": \"rho_air\", \"DIMENSION\": \"L-3 M1\", \"SUPPLY\": \"DECLARED\", \"VALUE\": \"1.225\", \"UNIT\": \"kg m-3\", \"OVERRIDABLE\": \"NO\", \"LABEL\": \"the density of air at sea level\"}, {\"NAME\": \"mu_air\", \"DIMENSION\": \"L-1 M1 T-1\", \"SUPPLY\": \"DECLARED\", \"VALUE\": \"1.7894e-5\", \"UNIT\": \"Pa s\", \"OVERRIDABLE\": \"NO\", \"LABEL\": \"the dynamic viscosity of air at sea level\"}, {\"NAME\": \"C_d\", \"DIMENSION\": \"1\", \"SUPPLY\": \"AUTHOR\", \"LABEL\": \"the drag coefficient of the body\"}, {\"NAME\": \"A_ref\", \"DIMENSION\": \"L2\", \"SUPPLY\": \"AUTHOR\", \"LABEL\": \"the reference area of the drag coefficient\"}, {\"NAME\": \"L_ref\", \"DIMENSION\": \"L1\", \"SUPPLY\": \"AUTHOR\", \"LABEL\": \"the reference length of the Reynolds number\"}], \"SUMS\": [{\"NAME\": \"SPEED2\", \"OVER\": \"VELOCITY\", \"EACH\": \"VELOCITY^2\"}], \"TERMS\": [{\"TARGET\": \"VELOCITY\", \"SIGN\": \"-\", \"EXPR\": \"0.5*rho_air*C_d*A_ref*sqrt(SPEED2)*VELOCITY\", \"LABEL\": \"the quadratic drag\"}], \"ASSUMPTIONS\": [{\"NAME\": \"air_still\", \"PROPOSITION\": \"the air is at rest in the frame of the body's velocity\", \"REFS\": [\"VELOCITY\"]}, {\"NAME\": \"air_uniform\", \"PROPOSITION\": \"the air density is uniform over the region of motion\", \"REFS\": [\"rho_air\"]}, {\"NAME\": \"drag_cd_constant\", \"PROPOSITION\": \"the drag coefficient C_d is constant over the motion\", \"REFS\": [\"C_d\"]}, {\"NAME\": \"drag_no_lift\", \"PROPOSITION\": \"the body experiences no lift force\", \"REFS\": [\"VELOCITY\"]}, {\"NAME\": \"drag_no_magnus\", \"PROPOSITION\": \"the body experiences no Magnus force\", \"REFS\": [\"VELOCITY\"]}], \"BOUNDARIES\": [{\"NAME\": \"drag_quadratic_regime\", \"PREDICATE\": \"1e3 < rho_air |v| L_ref / mu_air < 2e5: the Reynolds window of the quadratic law\", \"CONDITION\": \"mu_air != 0 and SPEED2 >= 0 and rho_air*sqrt(SPEED2)*L_ref/mu_air > 1000 and rho_air*sqrt(SPEED2)*L_ref/mu_air < 200000\"}], \"NOT_CHOSEN\": \"No quadratic air resistance.\", \"NOT_INCLUDED\": [\"No wind: the air is at rest.\", \"No change of air density or viscosity with altitude or temperature.\", \"No lift, Magnus or added-mass force.\", \"No drag outside the Reynolds window of the quadratic law.\"], \"EXCLUDES\": [\"AIR-LINEAR\"], \"INTERACTS_WITH\": [], \"TEST_BINDINGS\": [{\"NAME\": \"PROJECTILE_2D\", \"TPK\": {\"DOF\": [{\"NAME\": \"t\", \"DIMENSION\": \"T1\"}, {\"NAME\": \"x\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"z\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"v_x\", \"DIMENSION\": \"L1 T-1\"}, {\"NAME\": \"v_z\", \"DIMENSION\": \"L1 T-1\"}], \"CONSTANT\": [{\"NAME\": \"m\", \"DIMENSION\": \"M1\"}], \"LAW\": [{\"NAME\": \"KIN_X\", \"STATEMENT\": \"dx/dt = v_x\", \"REFS\": [\"t\", \"v_x\", \"x\"], \"ROLE\": \"EOM(x)\", \"EQUATION\": \"D(x,t)=v_x\"}, {\"NAME\": \"KIN_Z\", \"STATEMENT\": \"dz/dt = v_z\", \"REFS\": [\"t\", \"v_z\", \"z\"], \"ROLE\": \"EOM(z)\", \"EQUATION\": \"D(z,t)=v_z\"}, {\"NAME\": \"EOM_X\", \"STATEMENT\": \"m dv_x/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_x\"], \"ROLE\": \"EOM(v_x)\", \"EQUATION\": \"m*D(v_x,t)=0\"}, {\"NAME\": \"EOM_Z\", \"STATEMENT\": \"m dv_z/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_z\"], \"ROLE\": \"EOM(v_z)\", \"EQUATION\": \"m*D(v_z,t)=0\"}], \"ASSUMPTION\": [{\"NAME\": \"point_mass\", \"PROPOSITION\": \"the body is treated as a point mass\", \"REFS\": [\"m\"]}]}, \"BIND\": {\"VELOCITY\": [\"v_x\", \"v_z\"]}, \"VALUES\": {\"A_ref\": {}, \"C_d\": {}, \"L_ref\": {}}, \"ANSWERS\": {}}]}",
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it acts in this kernel only where one of your own laws states it.\", \"NO_LINE\": \"No buoyancy: the air's upthrust on the body is not included.\"}], \"TEST_BINDINGS\": [{\"NAME\": \"PROJECTILE_2D\", \"TPK\": {\"DOF\": [{\"NAME\": \"t\", \"DIMENSION\": \"T1\"}, {\"NAME\": \"x\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"z\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"v_x\", \"DIMENSION\": \"L1 T-1\"}, {\"NAME\": \"v_z\", \"DIMENSION\": \"L1 T-1\"}], \"CONSTANT\": [{\"NAME\": \"m\", \"DIMENSION\": \"M1\"}], \"LAW\": [{\"NAME\": \"KIN_X\", \"STATEMENT\": \"dx/dt = v_x\", \"REFS\": [\"t\", \"v_x\", \"x\"], \"ROLE\": \"EOM(x)\", \"EQUATION\": \"D(x,t)=v_x\"}, {\"NAME\": \"KIN_Z\", \"STATEMENT\": \"dz/dt = v_z\", \"REFS\": [\"t\", \"v_z\", \"z\"], \"ROLE\": \"EOM(z)\", \"EQUATION\": \"D(z,t)=v_z\"}, {\"NAME\": \"EOM_X\", \"STATEMENT\": \"m dv_x/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_x\"], \"ROLE\": \"EOM(v_x)\", \"EQUATION\": \"m*D(v_x,t)=0\"}, {\"NAME\": \"EOM_Z\", \"STATEMENT\": \"m dv_z/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_z\"], \"ROLE\": \"EOM(v_z)\", \"EQUATION\": \"m*D(v_z,t)=0\"}], \"ASSUMPTION\": [{\"NAME\": \"point_mass\", \"PROPOSITION\": \"the body is treated as a point mass\", \"REFS\": [\"m\"]}]}, \"BIND\": {\"HEIGHT\": [\"z\"], \"MASS\": [\"m\"], \"UP_VELOCITY\": [\"v_z\"]}, \"VALUES\": {\"h_max\": {\"VALUE\": \"100\", \"UNIT\": \"m\"}}, \"ANSWERS\": {}}, {\"NAME\": \"TABLE\", \"TPK\": {\"DOF\": [{\"NAME\": \"t\", \"DIMENSION\": \"T1\"}, {\"NAME\": \"x\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"z\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"v_x\", \"DIMENSION\": \"L1 T-1\"}, {\"NAME\": \"v_z\", \"DIMENSION\": \"L1 T-1\"}], \"CONSTANT\": [{\"NAME\": \"m\", \"DIMENSION\": \"M1\"}], \"LAW\": [{\"NAME\": \"KIN_X\", \"STATEMENT\": \"dx/dt = v_x\", \"REFS\": [\"t\", \"v_x\", \"x\"], \"ROLE\": \"EOM(x)\", \"EQUATION\": \"D(x,t)=v_x\"}, {\"NAME\": \"KIN_Z\", \"STATEMENT\": \"dz/dt = v_z\", \"REFS\": [\"t\", \"v_z\", \"z\"], \"ROLE\": \"CONSTRAINT\", \"EQUATION\": \"D(z,t)=v_z\"}, {\"NAME\": \"EOM_X\", \"STATEMENT\": \"m dv_x/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_x\"], \"ROLE\": \"EOM(v_x)\", \"EQUATION\": \"m*D(v_x,t)=0\"}], \"CONSTRAINT\": [{\"NAME\": \"C_Z\", \"TARGET\": \"z\", \"ACTION\": \"FIX\", \"VALUE\": \"0\", \"UNIT\": \"m\", \"STATEMENT\": \"the puck stays on the table top, z = 0\"}, {\"NAME\": \"C_VZ\", \"TARGET\": \"v_z\", \"ACTION\": \"FIX\", \"VALUE\": \"0\", \"UNIT\": \"m s-1\", \"STATEMENT\": \"the puck has no vertical velocity\"}]}, \"BIND\": {\"HEIGHT\": [\"z\"], \"MASS\": [\"m\"], \"UP_VELOCITY\": [\"v_z\"]}, \"VALUES\": {\"h_max\": {\"VALUE\": \"1\", \"UNIT\": \"m\"}}, \"ANSWERS\": {\"FIXED:v_z\": \"YES\"}}]}",
"{\"ID\": \"MATH\", \"VERSION\": \"1.0.0\", \"TITLE\": \"The mathematical constant pi, as the CONSTANT pi_c\", \"SOURCE\": \"pi to 16 significant digits, 3.141592653589793, the nearest IEEE 754 binary64 value\", \"PREREQUISITES\": [], \"PARAMETERS\": [{\"NAME\": \"pi_c\", \"DIMENSION\": \"1\", \"SUPPLY\": \"DECLARED\", \"VALUE\": \"3.141592653589793\", \"UNIT\": \"1\", \"OVERRIDABLE\": \"NO\", \"LABEL\": \"pi, to 16 significant digits\"}], \"SUMS\": [], \"TERMS\": [], \"ASSUMPTIONS\": [], \"BOUNDARIES\": [], \"NOT_CHOSEN\": \"No mathematical constant: pi exists only if you declare it.\", \"NOT_INCLUDED\": [\"pi_c is pi rounded to 16 significant digits; no other mathematical constant is declared.\"], \"EXCLUDES\": [], \"INTERACTS_WITH\": [], \"TEST_BINDINGS\": [{\"NAME\": \"PROJECTILE_2D\", \"TPK\": {\"DOF\": [{\"NAME\": \"t\", \"DIMENSION\": \"T1\"}, {\"NAME\": \"x\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"z\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"v_x\", \"DIMENSION\": \"L1 T-1\"}, {\"NAME\": \"v_z\", \"DIMENSION\": \"L1 T-1\"}], \"CONSTANT\": [{\"NAME\": \"m\", \"DIMENSION\": \"M1\"}], \"LAW\": [{\"NAME\": \"KIN_X\", \"STATEMENT\": \"dx/dt = v_x\", \"REFS\": [\"t\", \"v_x\", \"x\"], \"ROLE\": \"EOM(x)\", \"EQUATION\": \"D(x,t)=v_x\"}, {\"NAME\": \"KIN_Z\", \"STATEMENT\": \"dz/dt = v_z\", \"REFS\": [\"t\", \"v_z\", \"z\"], \"ROLE\": \"EOM(z)\", \"EQUATION\": \"D(z,t)=v_z\"}, {\"NAME\": \"EOM_X\", \"STATEMENT\": \"m dv_x/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_x\"], \"ROLE\": \"EOM(v_x)\", \"EQUATION\": \"m*D(v_x,t)=0\"}, {\"NAME\": \"EOM_Z\", \"STATEMENT\": \"m dv_z/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_z\"], \"ROLE\": \"EOM(v_z)\", \"EQUATION\": \"m*D(v_z,t)=0\"}], \"ASSUMPTION\": [{\"NAME\": \"point_mass\", \"PROPOSITION\": \"the body is treated as a point mass\", \"REFS\": [\"m\"]}]}, \"BIND\": {}, \"VALUES\": {}, \"ANSWERS\": {}}]}"
]
},
"expected": "[\"REFUSED\",\"CLAIM GRAV-UNIFORM 1.0.0: question BUOYANCY is not answered\"]",
"fn": "interview_check",
"hand_checked": true,
"name": "I24 the buoyancy question unanswered"
},
{
"args": {
"answer": [
{
"AT": 4,
"CHOSEN": [
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"claims": [
{
"ANSWERS": {
"BUOYANCY": "NO"
},
"BIND": {
"HEIGHT": [
"z"
],
"MASS": [
"m"
],
"UP_VELOCITY": [
"v_z"
]
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"DIGEST": "24877ccb5c8ec300d29ed82ce6650592f35cf8899a3d878ccce9c08d4c72c025",
"ID": "GRAV-UNIFORM",
"VALUES": {
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"UNIT": "m",
"VALUE": "100"
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},
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"lines": [
{
"ACT": "MODULE ADD",
"DATE": "2026-10-01",
"DIGEST": "5f3fe27b42378bce0830b0d0959f892f4a8e73b12b540ae877e39e6439d08b4d",
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{
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"DIGEST": "6fb53c3a6546151eead2bd6e72e9cf8334f3a2040ad0ee2f5b988ec96d6fc852",
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{
"ACT": "MODULE ADD",
"DATE": "2026-10-01",
"DIGEST": "24877ccb5c8ec300d29ed82ce6650592f35cf8899a3d878ccce9c08d4c72c025",
"ID": "GRAV-UNIFORM",
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{
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"{\"ID\": \"AIR-LINEAR\", \"VERSION\": \"1.0.0\", \"TITLE\": \"Air resistance at sea level, linear in the speed (Stokes drag on a sphere)\", \"SOURCE\": \"ISO 2533:1975, Standard Atmosphere, sea-level values: density 1.225 kg m-3, dynamic viscosity 1.7894e-5 Pa s\", \"PREREQUISITES\": [{\"SLOT\": \"VELOCITY\", \"KIND\": \"DOF\", \"DIMENSION\": \"L1 T-1\", \"MIN\": 1, \"MAX\": 3, \"LABEL\": \"the velocity components of the body, one per axis\"}], \"PARAMETERS\": [{\"NAME\": \"rho_air\", \"DIMENSION\": \"L-3 M1\", \"SUPPLY\": \"DECLARED\", \"VALUE\": \"1.225\", \"UNIT\": \"kg m-3\", \"OVERRIDABLE\": \"NO\", \"LABEL\": \"the density of air at sea level\"}, {\"NAME\": \"mu_air\", \"DIMENSION\": \"L-1 M1 T-1\", \"SUPPLY\": \"DECLARED\", \"VALUE\": \"1.7894e-5\", \"UNIT\": \"Pa s\", \"OVERRIDABLE\": \"NO\", \"LABEL\": \"the dynamic viscosity of air at sea level\"}, {\"NAME\": \"pi_c\", \"DIMENSION\": \"1\", \"SUPPLY\": \"DECLARED\", \"VALUE\": \"3.141592653589793\", \"UNIT\": \"1\", \"OVERRIDABLE\": \"NO\", \"LABEL\": \"pi, to 16 significant digits\"}, {\"NAME\": \"R_s\", \"DIMENSION\": \"L1\", \"SUPPLY\": \"AUTHOR\", \"LABEL\": \"the radius of the sphere\"}], \"SUMS\": [{\"NAME\": \"SPEED2\", \"OVER\": \"VELOCITY\", \"EACH\": \"VELOCITY^2\"}], \"TERMS\": [{\"TARGET\": \"VELOCITY\", \"SIGN\": \"-\", \"EXPR\": \"6*pi_c*mu_air*R_s*VELOCITY\", \"LABEL\": \"the linear (Stokes) drag\"}], \"ASSUMPTIONS\": [{\"NAME\": \"air_still\", \"PROPOSITION\": \"the air is at rest in the frame of the body's velocity\", \"REFS\": [\"VELOCITY\"]}, {\"NAME\": \"air_uniform\", \"PROPOSITION\": \"the air density is uniform over the region of motion\", \"REFS\": [\"rho_air\"]}, {\"NAME\": \"drag_sphere\", \"PROPOSITION\": \"the body is a rigid sphere of radius R_s\", \"REFS\": [\"R_s\"]}], \"BOUNDARIES\": [{\"NAME\": \"drag_linear_regime\", \"PREDICATE\": \"2 rho_air |v| R_s / mu_air < 1: the regime of the linear law\", \"CONDITION\": \"mu_air != 0 and SPEED2 >= 0 and 2*rho_air*sqrt(SPEED2)*R_s/mu_air < 1\"}], \"NOT_CHOSEN\": \"No linear (Stokes) air resistance.\", \"NOT_INCLUDED\": [\"No wind: the air is at rest.\", \"No change of air density or viscosity with altitude or temperature.\", \"No drag outside the regime of the linear law.\"], \"EXCLUDES\": [], \"INTERACTS_WITH\": [], \"TEST_BINDINGS\": [{\"NAME\": \"PROJECTILE_2D\", \"TPK\": {\"DOF\": [{\"NAME\": \"t\", \"DIMENSION\": \"T1\"}, {\"NAME\": \"x\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"z\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"v_x\", \"DIMENSION\": \"L1 T-1\"}, {\"NAME\": \"v_z\", \"DIMENSION\": \"L1 T-1\"}], \"CONSTANT\": [{\"NAME\": \"m\", \"DIMENSION\": \"M1\"}], \"LAW\": [{\"NAME\": \"KIN_X\", \"STATEMENT\": \"dx/dt = v_x\", \"REFS\": [\"t\", \"v_x\", \"x\"], \"ROLE\": \"EOM(x)\", \"EQUATION\": \"D(x,t)=v_x\"}, {\"NAME\": \"KIN_Z\", \"STATEMENT\": \"dz/dt = v_z\", \"REFS\": [\"t\", \"v_z\", \"z\"], \"ROLE\": \"EOM(z)\", \"EQUATION\": \"D(z,t)=v_z\"}, {\"NAME\": \"EOM_X\", \"STATEMENT\": \"m dv_x/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_x\"], \"ROLE\": \"EOM(v_x)\", \"EQUATION\": \"m*D(v_x,t)=0\"}, {\"NAME\": \"EOM_Z\", \"STATEMENT\": \"m dv_z/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_z\"], \"ROLE\": \"EOM(v_z)\", \"EQUATION\": \"m*D(v_z,t)=0\"}], \"ASSUMPTION\": [{\"NAME\": \"point_mass\", \"PROPOSITION\": \"the body is treated as a point mass\", \"REFS\": [\"m\"]}]}, \"BIND\": {\"VELOCITY\": [\"v_x\", \"v_z\"]}, \"VALUES\": {\"R_s\": {}}, \"ANSWERS\": {}}]}",
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it acts in this kernel only where one of your own laws states it.\", \"NO_LINE\": \"No buoyancy: the air's upthrust on the body is not included.\"}], \"TEST_BINDINGS\": [{\"NAME\": \"PROJECTILE_2D\", \"TPK\": {\"DOF\": [{\"NAME\": \"t\", \"DIMENSION\": \"T1\"}, {\"NAME\": \"x\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"z\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"v_x\", \"DIMENSION\": \"L1 T-1\"}, {\"NAME\": \"v_z\", \"DIMENSION\": \"L1 T-1\"}], \"CONSTANT\": [{\"NAME\": \"m\", \"DIMENSION\": \"M1\"}], \"LAW\": [{\"NAME\": \"KIN_X\", \"STATEMENT\": \"dx/dt = v_x\", \"REFS\": [\"t\", \"v_x\", \"x\"], \"ROLE\": \"EOM(x)\", \"EQUATION\": \"D(x,t)=v_x\"}, {\"NAME\": \"KIN_Z\", \"STATEMENT\": \"dz/dt = v_z\", \"REFS\": [\"t\", \"v_z\", \"z\"], \"ROLE\": \"EOM(z)\", \"EQUATION\": \"D(z,t)=v_z\"}, {\"NAME\": \"EOM_X\", \"STATEMENT\": \"m dv_x/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_x\"], \"ROLE\": \"EOM(v_x)\", \"EQUATION\": \"m*D(v_x,t)=0\"}, {\"NAME\": \"EOM_Z\", \"STATEMENT\": \"m dv_z/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_z\"], \"ROLE\": \"EOM(v_z)\", \"EQUATION\": \"m*D(v_z,t)=0\"}], \"ASSUMPTION\": [{\"NAME\": \"point_mass\", \"PROPOSITION\": \"the body is treated as a point mass\", \"REFS\": [\"m\"]}]}, \"BIND\": {\"HEIGHT\": [\"z\"], \"MASS\": [\"m\"], \"UP_VELOCITY\": [\"v_z\"]}, \"VALUES\": {\"h_max\": {\"VALUE\": \"100\", \"UNIT\": \"m\"}}, \"ANSWERS\": {}}, {\"NAME\": \"TABLE\", \"TPK\": {\"DOF\": [{\"NAME\": \"t\", \"DIMENSION\": \"T1\"}, {\"NAME\": \"x\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"z\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"v_x\", \"DIMENSION\": \"L1 T-1\"}, {\"NAME\": \"v_z\", \"DIMENSION\": \"L1 T-1\"}], \"CONSTANT\": [{\"NAME\": \"m\", \"DIMENSION\": \"M1\"}], \"LAW\": [{\"NAME\": \"KIN_X\", \"STATEMENT\": \"dx/dt = v_x\", \"REFS\": [\"t\", \"v_x\", \"x\"], \"ROLE\": \"EOM(x)\", \"EQUATION\": \"D(x,t)=v_x\"}, {\"NAME\": \"KIN_Z\", \"STATEMENT\": \"dz/dt = v_z\", \"REFS\": [\"t\", \"v_z\", \"z\"], \"ROLE\": \"CONSTRAINT\", \"EQUATION\": \"D(z,t)=v_z\"}, {\"NAME\": \"EOM_X\", \"STATEMENT\": \"m dv_x/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_x\"], \"ROLE\": \"EOM(v_x)\", \"EQUATION\": \"m*D(v_x,t)=0\"}], \"CONSTRAINT\": [{\"NAME\": \"C_Z\", \"TARGET\": \"z\", \"ACTION\": \"FIX\", \"VALUE\": \"0\", \"UNIT\": \"m\", \"STATEMENT\": \"the puck stays on the table top, z = 0\"}, {\"NAME\": \"C_VZ\", \"TARGET\": \"v_z\", \"ACTION\": \"FIX\", \"VALUE\": \"0\", \"UNIT\": \"m s-1\", \"STATEMENT\": \"the puck has no vertical velocity\"}]}, \"BIND\": {\"HEIGHT\": [\"z\"], \"MASS\": [\"m\"], \"UP_VELOCITY\": [\"v_z\"]}, \"VALUES\": {\"h_max\": {\"VALUE\": \"1\", \"UNIT\": \"m\"}}, \"ANSWERS\": {\"FIXED:v_z\": \"YES\"}}]}",
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},
"expected": "[\"REFUSED\",\"CLAIM GRAV-UNIFORM 1.0.0: answer BUOYANCY answers no question raised\"]",
"fn": "interview_check",
"hand_checked": true,
"name": "I25 a buoyancy answer with no air module"
},
{
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"answer": [
{
"AT": 4,
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"claims": [
{
"ANSWERS": {
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"BIND": {
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"z"
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"MASS": [
"m"
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"lines": [
{
"ACT": "MODULE ADD",
"DATE": "2026-10-01",
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"{\"ID\": \"AIR-LINEAR\", \"VERSION\": \"1.0.0\", \"TITLE\": \"Air resistance at sea level, linear in the speed (Stokes drag on a sphere)\", \"SOURCE\": \"ISO 2533:1975, Standard Atmosphere, sea-level values: density 1.225 kg m-3, dynamic viscosity 1.7894e-5 Pa s\", \"PREREQUISITES\": [{\"SLOT\": \"VELOCITY\", \"KIND\": \"DOF\", \"DIMENSION\": \"L1 T-1\", \"MIN\": 1, \"MAX\": 3, \"LABEL\": \"the velocity components of the body, one per axis\"}], \"PARAMETERS\": [{\"NAME\": \"rho_air\", \"DIMENSION\": \"L-3 M1\", \"SUPPLY\": \"DECLARED\", \"VALUE\": \"1.225\", \"UNIT\": \"kg m-3\", \"OVERRIDABLE\": \"NO\", \"LABEL\": \"the density of air at sea level\"}, {\"NAME\": \"mu_air\", \"DIMENSION\": \"L-1 M1 T-1\", \"SUPPLY\": \"DECLARED\", \"VALUE\": \"1.7894e-5\", \"UNIT\": \"Pa s\", \"OVERRIDABLE\": \"NO\", \"LABEL\": \"the dynamic viscosity of air at sea level\"}, {\"NAME\": \"pi_c\", \"DIMENSION\": \"1\", \"SUPPLY\": \"DECLARED\", \"VALUE\": \"3.141592653589793\", \"UNIT\": \"1\", \"OVERRIDABLE\": \"NO\", \"LABEL\": \"pi, to 16 significant digits\"}, {\"NAME\": \"R_s\", \"DIMENSION\": \"L1\", \"SUPPLY\": \"AUTHOR\", \"LABEL\": \"the radius of the sphere\"}], \"SUMS\": [{\"NAME\": \"SPEED2\", \"OVER\": \"VELOCITY\", \"EACH\": \"VELOCITY^2\"}], \"TERMS\": [{\"TARGET\": \"VELOCITY\", \"SIGN\": \"-\", \"EXPR\": \"6*pi_c*mu_air*R_s*VELOCITY\", \"LABEL\": \"the linear (Stokes) drag\"}], \"ASSUMPTIONS\": [{\"NAME\": \"air_still\", \"PROPOSITION\": \"the air is at rest in the frame of the body's velocity\", \"REFS\": [\"VELOCITY\"]}, {\"NAME\": \"air_uniform\", \"PROPOSITION\": \"the air density is uniform over the region of motion\", \"REFS\": [\"rho_air\"]}, {\"NAME\": \"drag_sphere\", \"PROPOSITION\": \"the body is a rigid sphere of radius R_s\", \"REFS\": [\"R_s\"]}], \"BOUNDARIES\": [{\"NAME\": \"drag_linear_regime\", \"PREDICATE\": \"2 rho_air |v| R_s / mu_air < 1: the regime of the linear law\", \"CONDITION\": \"mu_air != 0 and SPEED2 >= 0 and 2*rho_air*sqrt(SPEED2)*R_s/mu_air < 1\"}], \"NOT_CHOSEN\": \"No linear (Stokes) air resistance.\", \"NOT_INCLUDED\": [\"No wind: the air is at rest.\", \"No change of air density or viscosity with altitude or temperature.\", \"No drag outside the regime of the linear law.\"], \"EXCLUDES\": [], \"INTERACTS_WITH\": [], \"TEST_BINDINGS\": [{\"NAME\": \"PROJECTILE_2D\", \"TPK\": {\"DOF\": [{\"NAME\": \"t\", \"DIMENSION\": \"T1\"}, {\"NAME\": \"x\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"z\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"v_x\", \"DIMENSION\": \"L1 T-1\"}, {\"NAME\": \"v_z\", \"DIMENSION\": \"L1 T-1\"}], \"CONSTANT\": [{\"NAME\": \"m\", \"DIMENSION\": \"M1\"}], \"LAW\": [{\"NAME\": \"KIN_X\", \"STATEMENT\": \"dx/dt = v_x\", \"REFS\": [\"t\", \"v_x\", \"x\"], \"ROLE\": \"EOM(x)\", \"EQUATION\": \"D(x,t)=v_x\"}, {\"NAME\": \"KIN_Z\", \"STATEMENT\": \"dz/dt = v_z\", \"REFS\": [\"t\", \"v_z\", \"z\"], \"ROLE\": \"EOM(z)\", \"EQUATION\": \"D(z,t)=v_z\"}, {\"NAME\": \"EOM_X\", \"STATEMENT\": \"m dv_x/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_x\"], \"ROLE\": \"EOM(v_x)\", \"EQUATION\": \"m*D(v_x,t)=0\"}, {\"NAME\": \"EOM_Z\", \"STATEMENT\": \"m dv_z/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_z\"], \"ROLE\": \"EOM(v_z)\", \"EQUATION\": \"m*D(v_z,t)=0\"}], \"ASSUMPTION\": [{\"NAME\": \"point_mass\", \"PROPOSITION\": \"the body is treated as a point mass\", \"REFS\": [\"m\"]}]}, \"BIND\": {\"VELOCITY\": [\"v_x\", \"v_z\"]}, \"VALUES\": {\"R_s\": {}}, \"ANSWERS\": {}}]}",
"{\"ID\": \"AIR-QUADRATIC\", \"VERSION\": \"1.0.0\", \"TITLE\": \"Air resistance at sea level, quadratic in the speed\", \"SOURCE\": \"ISO 2533:1975, Standard Atmosphere, sea-level values: density 1.225 kg m-3, dynamic viscosity 1.7894e-5 Pa s\", \"PREREQUISITES\": [{\"SLOT\": \"VELOCITY\", \"KIND\": \"DOF\", \"DIMENSION\": \"L1 T-1\", \"MIN\": 1, \"MAX\": 3, \"LABEL\": \"the velocity components of the body, one per axis\"}], \"PARAMETERS\": [{\"NAME\": \"rho_air\", \"DIMENSION\": \"L-3 M1\", \"SUPPLY\": \"DECLARED\", \"VALUE\": \"1.225\", \"UNIT\": \"kg m-3\", \"OVERRIDABLE\": \"NO\", \"LABEL\": \"the density of air at sea level\"}, {\"NAME\": \"mu_air\", \"DIMENSION\": \"L-1 M1 T-1\", \"SUPPLY\": \"DECLARED\", \"VALUE\": \"1.7894e-5\", \"UNIT\": \"Pa s\", \"OVERRIDABLE\": \"NO\", \"LABEL\": \"the dynamic viscosity of air at sea level\"}, {\"NAME\": \"C_d\", \"DIMENSION\": \"1\", \"SUPPLY\": \"AUTHOR\", \"LABEL\": \"the drag coefficient of the body\"}, {\"NAME\": \"A_ref\", \"DIMENSION\": \"L2\", \"SUPPLY\": \"AUTHOR\", \"LABEL\": \"the reference area of the drag coefficient\"}, {\"NAME\": \"L_ref\", \"DIMENSION\": \"L1\", \"SUPPLY\": \"AUTHOR\", \"LABEL\": \"the reference length of the Reynolds number\"}], \"SUMS\": [{\"NAME\": \"SPEED2\", \"OVER\": \"VELOCITY\", \"EACH\": \"VELOCITY^2\"}], \"TERMS\": [{\"TARGET\": \"VELOCITY\", \"SIGN\": \"-\", \"EXPR\": \"0.5*rho_air*C_d*A_ref*sqrt(SPEED2)*VELOCITY\", \"LABEL\": \"the quadratic drag\"}], \"ASSUMPTIONS\": [{\"NAME\": \"air_still\", \"PROPOSITION\": \"the air is at rest in the frame of the body's velocity\", \"REFS\": [\"VELOCITY\"]}, {\"NAME\": \"air_uniform\", \"PROPOSITION\": \"the air density is uniform over the region of motion\", \"REFS\": [\"rho_air\"]}, {\"NAME\": \"drag_cd_constant\", \"PROPOSITION\": \"the drag coefficient C_d is constant over the motion\", \"REFS\": [\"C_d\"]}, {\"NAME\": \"drag_no_lift\", \"PROPOSITION\": \"the body experiences no lift force\", \"REFS\": [\"VELOCITY\"]}, {\"NAME\": \"drag_no_magnus\", \"PROPOSITION\": \"the body experiences no Magnus force\", \"REFS\": [\"VELOCITY\"]}], \"BOUNDARIES\": [{\"NAME\": \"drag_quadratic_regime\", \"PREDICATE\": \"1e3 < rho_air |v| L_ref / mu_air < 2e5: the Reynolds window of the quadratic law\", \"CONDITION\": \"mu_air != 0 and SPEED2 >= 0 and rho_air*sqrt(SPEED2)*L_ref/mu_air > 1000 and rho_air*sqrt(SPEED2)*L_ref/mu_air < 200000\"}], \"NOT_CHOSEN\": \"No quadratic air resistance.\", \"NOT_INCLUDED\": [\"No wind: the air is at rest.\", \"No change of air density or viscosity with altitude or temperature.\", \"No lift, Magnus or added-mass force.\", \"No drag outside the Reynolds window of the quadratic law.\"], \"EXCLUDES\": [\"AIR-LINEAR\"], \"INTERACTS_WITH\": [], \"TEST_BINDINGS\": [{\"NAME\": \"PROJECTILE_2D\", \"TPK\": {\"DOF\": [{\"NAME\": \"t\", \"DIMENSION\": \"T1\"}, {\"NAME\": \"x\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"z\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"v_x\", \"DIMENSION\": \"L1 T-1\"}, {\"NAME\": \"v_z\", \"DIMENSION\": \"L1 T-1\"}], \"CONSTANT\": [{\"NAME\": \"m\", \"DIMENSION\": \"M1\"}], \"LAW\": [{\"NAME\": \"KIN_X\", \"STATEMENT\": \"dx/dt = v_x\", \"REFS\": [\"t\", \"v_x\", \"x\"], \"ROLE\": \"EOM(x)\", \"EQUATION\": \"D(x,t)=v_x\"}, {\"NAME\": \"KIN_Z\", \"STATEMENT\": \"dz/dt = v_z\", \"REFS\": [\"t\", \"v_z\", \"z\"], \"ROLE\": \"EOM(z)\", \"EQUATION\": \"D(z,t)=v_z\"}, {\"NAME\": \"EOM_X\", \"STATEMENT\": \"m dv_x/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_x\"], \"ROLE\": \"EOM(v_x)\", \"EQUATION\": \"m*D(v_x,t)=0\"}, {\"NAME\": \"EOM_Z\", \"STATEMENT\": \"m dv_z/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_z\"], \"ROLE\": \"EOM(v_z)\", \"EQUATION\": \"m*D(v_z,t)=0\"}], \"ASSUMPTION\": [{\"NAME\": \"point_mass\", \"PROPOSITION\": \"the body is treated as a point mass\", \"REFS\": [\"m\"]}]}, \"BIND\": {\"VELOCITY\": [\"v_x\", \"v_z\"]}, \"VALUES\": {\"A_ref\": {}, \"C_d\": {}, \"L_ref\": {}}, \"ANSWERS\": {}}]}",
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it acts in this kernel only where one of your own laws states it.\", \"NO_LINE\": \"No buoyancy: the air's upthrust on the body is not included.\"}], \"TEST_BINDINGS\": [{\"NAME\": \"PROJECTILE_2D\", \"TPK\": {\"DOF\": [{\"NAME\": \"t\", \"DIMENSION\": \"T1\"}, {\"NAME\": \"x\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"z\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"v_x\", \"DIMENSION\": \"L1 T-1\"}, {\"NAME\": \"v_z\", \"DIMENSION\": \"L1 T-1\"}], \"CONSTANT\": [{\"NAME\": \"m\", \"DIMENSION\": \"M1\"}], \"LAW\": [{\"NAME\": \"KIN_X\", \"STATEMENT\": \"dx/dt = v_x\", \"REFS\": [\"t\", \"v_x\", \"x\"], \"ROLE\": \"EOM(x)\", \"EQUATION\": \"D(x,t)=v_x\"}, {\"NAME\": \"KIN_Z\", \"STATEMENT\": \"dz/dt = v_z\", \"REFS\": [\"t\", \"v_z\", \"z\"], \"ROLE\": \"EOM(z)\", \"EQUATION\": \"D(z,t)=v_z\"}, {\"NAME\": \"EOM_X\", \"STATEMENT\": \"m dv_x/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_x\"], \"ROLE\": \"EOM(v_x)\", \"EQUATION\": \"m*D(v_x,t)=0\"}, {\"NAME\": \"EOM_Z\", \"STATEMENT\": \"m dv_z/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_z\"], \"ROLE\": \"EOM(v_z)\", \"EQUATION\": \"m*D(v_z,t)=0\"}], \"ASSUMPTION\": [{\"NAME\": \"point_mass\", \"PROPOSITION\": \"the body is treated as a point mass\", \"REFS\": [\"m\"]}]}, \"BIND\": {\"HEIGHT\": [\"z\"], \"MASS\": [\"m\"], \"UP_VELOCITY\": [\"v_z\"]}, \"VALUES\": {\"h_max\": {\"VALUE\": \"100\", \"UNIT\": \"m\"}}, \"ANSWERS\": {}}, {\"NAME\": \"TABLE\", \"TPK\": {\"DOF\": [{\"NAME\": \"t\", \"DIMENSION\": \"T1\"}, {\"NAME\": \"x\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"z\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"v_x\", \"DIMENSION\": \"L1 T-1\"}, {\"NAME\": \"v_z\", \"DIMENSION\": \"L1 T-1\"}], \"CONSTANT\": [{\"NAME\": \"m\", \"DIMENSION\": \"M1\"}], \"LAW\": [{\"NAME\": \"KIN_X\", \"STATEMENT\": \"dx/dt = v_x\", \"REFS\": [\"t\", \"v_x\", \"x\"], \"ROLE\": \"EOM(x)\", \"EQUATION\": \"D(x,t)=v_x\"}, {\"NAME\": \"KIN_Z\", \"STATEMENT\": \"dz/dt = v_z\", \"REFS\": [\"t\", \"v_z\", \"z\"], \"ROLE\": \"CONSTRAINT\", \"EQUATION\": \"D(z,t)=v_z\"}, {\"NAME\": \"EOM_X\", \"STATEMENT\": \"m dv_x/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_x\"], \"ROLE\": \"EOM(v_x)\", \"EQUATION\": \"m*D(v_x,t)=0\"}], \"CONSTRAINT\": [{\"NAME\": \"C_Z\", \"TARGET\": \"z\", \"ACTION\": \"FIX\", \"VALUE\": \"0\", \"UNIT\": \"m\", \"STATEMENT\": \"the puck stays on the table top, z = 0\"}, {\"NAME\": \"C_VZ\", \"TARGET\": \"v_z\", \"ACTION\": \"FIX\", \"VALUE\": \"0\", \"UNIT\": \"m s-1\", \"STATEMENT\": \"the puck has no vertical velocity\"}]}, \"BIND\": {\"HEIGHT\": [\"z\"], \"MASS\": [\"m\"], \"UP_VELOCITY\": [\"v_z\"]}, \"VALUES\": {\"h_max\": {\"VALUE\": \"1\", \"UNIT\": \"m\"}}, \"ANSWERS\": {\"FIXED:v_z\": \"YES\"}}]}",
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},
{
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{
"ACT": "MODULE ADD",
"DATE": "2026-10-01",
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"{\"ID\": \"AIR-LINEAR\", \"VERSION\": \"1.0.0\", \"TITLE\": \"Air resistance at sea level, linear in the speed (Stokes drag on a sphere)\", \"SOURCE\": \"ISO 2533:1975, Standard Atmosphere, sea-level values: density 1.225 kg m-3, dynamic viscosity 1.7894e-5 Pa s\", \"PREREQUISITES\": [{\"SLOT\": \"VELOCITY\", \"KIND\": \"DOF\", \"DIMENSION\": \"L1 T-1\", \"MIN\": 1, \"MAX\": 3, \"LABEL\": \"the velocity components of the body, one per axis\"}], \"PARAMETERS\": [{\"NAME\": \"rho_air\", \"DIMENSION\": \"L-3 M1\", \"SUPPLY\": \"DECLARED\", \"VALUE\": \"1.225\", \"UNIT\": \"kg m-3\", \"OVERRIDABLE\": \"NO\", \"LABEL\": \"the density of air at sea level\"}, {\"NAME\": \"mu_air\", \"DIMENSION\": \"L-1 M1 T-1\", \"SUPPLY\": \"DECLARED\", \"VALUE\": \"1.7894e-5\", \"UNIT\": \"Pa s\", \"OVERRIDABLE\": \"NO\", \"LABEL\": \"the dynamic viscosity of air at sea level\"}, {\"NAME\": \"pi_c\", \"DIMENSION\": \"1\", \"SUPPLY\": \"DECLARED\", \"VALUE\": \"3.141592653589793\", \"UNIT\": \"1\", \"OVERRIDABLE\": \"NO\", \"LABEL\": \"pi, to 16 significant digits\"}, {\"NAME\": \"R_s\", \"DIMENSION\": \"L1\", \"SUPPLY\": \"AUTHOR\", \"LABEL\": \"the radius of the sphere\"}], \"SUMS\": [{\"NAME\": \"SPEED2\", \"OVER\": \"VELOCITY\", \"EACH\": \"VELOCITY^2\"}], \"TERMS\": [{\"TARGET\": \"VELOCITY\", \"SIGN\": \"-\", \"EXPR\": \"6*pi_c*mu_air*R_s*VELOCITY\", \"LABEL\": \"the linear (Stokes) drag\"}], \"ASSUMPTIONS\": [{\"NAME\": \"air_still\", \"PROPOSITION\": \"the air is at rest in the frame of the body's velocity\", \"REFS\": [\"VELOCITY\"]}, {\"NAME\": \"air_uniform\", \"PROPOSITION\": \"the air density is uniform over the region of motion\", \"REFS\": [\"rho_air\"]}, {\"NAME\": \"drag_sphere\", \"PROPOSITION\": \"the body is a rigid sphere of radius R_s\", \"REFS\": [\"R_s\"]}], \"BOUNDARIES\": [{\"NAME\": \"drag_linear_regime\", \"PREDICATE\": \"2 rho_air |v| R_s / mu_air < 1: the regime of the linear law\", \"CONDITION\": \"mu_air != 0 and SPEED2 >= 0 and 2*rho_air*sqrt(SPEED2)*R_s/mu_air < 1\"}], \"NOT_CHOSEN\": \"No linear (Stokes) air resistance.\", \"NOT_INCLUDED\": [\"No wind: the air is at rest.\", \"No change of air density or viscosity with altitude or temperature.\", \"No drag outside the regime of the linear law.\"], \"EXCLUDES\": [], \"INTERACTS_WITH\": [], \"TEST_BINDINGS\": [{\"NAME\": \"PROJECTILE_2D\", \"TPK\": {\"DOF\": [{\"NAME\": \"t\", \"DIMENSION\": \"T1\"}, {\"NAME\": \"x\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"z\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"v_x\", \"DIMENSION\": \"L1 T-1\"}, {\"NAME\": \"v_z\", \"DIMENSION\": \"L1 T-1\"}], \"CONSTANT\": [{\"NAME\": \"m\", \"DIMENSION\": \"M1\"}], \"LAW\": [{\"NAME\": \"KIN_X\", \"STATEMENT\": \"dx/dt = v_x\", \"REFS\": [\"t\", \"v_x\", \"x\"], \"ROLE\": \"EOM(x)\", \"EQUATION\": \"D(x,t)=v_x\"}, {\"NAME\": \"KIN_Z\", \"STATEMENT\": \"dz/dt = v_z\", \"REFS\": [\"t\", \"v_z\", \"z\"], \"ROLE\": \"EOM(z)\", \"EQUATION\": \"D(z,t)=v_z\"}, {\"NAME\": \"EOM_X\", \"STATEMENT\": \"m dv_x/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_x\"], \"ROLE\": \"EOM(v_x)\", \"EQUATION\": \"m*D(v_x,t)=0\"}, {\"NAME\": \"EOM_Z\", \"STATEMENT\": \"m dv_z/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_z\"], \"ROLE\": \"EOM(v_z)\", \"EQUATION\": \"m*D(v_z,t)=0\"}], \"ASSUMPTION\": [{\"NAME\": \"point_mass\", \"PROPOSITION\": \"the body is treated as a point mass\", \"REFS\": [\"m\"]}]}, \"BIND\": {\"VELOCITY\": [\"v_x\", \"v_z\"]}, \"VALUES\": {\"R_s\": {}}, \"ANSWERS\": {}}]}",
"{\"ID\": \"AIR-QUADRATIC\", \"VERSION\": \"1.0.0\", \"TITLE\": \"Air resistance at sea level, quadratic in the speed\", \"SOURCE\": \"ISO 2533:1975, Standard Atmosphere, sea-level values: density 1.225 kg m-3, dynamic viscosity 1.7894e-5 Pa s\", \"PREREQUISITES\": [{\"SLOT\": \"VELOCITY\", \"KIND\": \"DOF\", \"DIMENSION\": \"L1 T-1\", \"MIN\": 1, \"MAX\": 3, \"LABEL\": \"the velocity components of the body, one per axis\"}], \"PARAMETERS\": [{\"NAME\": \"rho_air\", \"DIMENSION\": \"L-3 M1\", \"SUPPLY\": \"DECLARED\", \"VALUE\": \"1.225\", \"UNIT\": \"kg m-3\", \"OVERRIDABLE\": \"NO\", \"LABEL\": \"the density of air at sea level\"}, {\"NAME\": \"mu_air\", \"DIMENSION\": \"L-1 M1 T-1\", \"SUPPLY\": \"DECLARED\", \"VALUE\": \"1.7894e-5\", \"UNIT\": \"Pa s\", \"OVERRIDABLE\": \"NO\", \"LABEL\": \"the dynamic viscosity of air at sea level\"}, {\"NAME\": \"C_d\", \"DIMENSION\": \"1\", \"SUPPLY\": \"AUTHOR\", \"LABEL\": \"the drag coefficient of the body\"}, {\"NAME\": \"A_ref\", \"DIMENSION\": \"L2\", \"SUPPLY\": \"AUTHOR\", \"LABEL\": \"the reference area of the drag coefficient\"}, {\"NAME\": \"L_ref\", \"DIMENSION\": \"L1\", \"SUPPLY\": \"AUTHOR\", \"LABEL\": \"the reference length of the Reynolds number\"}], \"SUMS\": [{\"NAME\": \"SPEED2\", \"OVER\": \"VELOCITY\", \"EACH\": \"VELOCITY^2\"}], \"TERMS\": [{\"TARGET\": \"VELOCITY\", \"SIGN\": \"-\", \"EXPR\": \"0.5*rho_air*C_d*A_ref*sqrt(SPEED2)*VELOCITY\", \"LABEL\": \"the quadratic drag\"}], \"ASSUMPTIONS\": [{\"NAME\": \"air_still\", \"PROPOSITION\": \"the air is at rest in the frame of the body's velocity\", \"REFS\": [\"VELOCITY\"]}, {\"NAME\": \"air_uniform\", \"PROPOSITION\": \"the air density is uniform over the region of motion\", \"REFS\": [\"rho_air\"]}, {\"NAME\": \"drag_cd_constant\", \"PROPOSITION\": \"the drag coefficient C_d is constant over the motion\", \"REFS\": [\"C_d\"]}, {\"NAME\": \"drag_no_lift\", \"PROPOSITION\": \"the body experiences no lift force\", \"REFS\": [\"VELOCITY\"]}, {\"NAME\": \"drag_no_magnus\", \"PROPOSITION\": \"the body experiences no Magnus force\", \"REFS\": [\"VELOCITY\"]}], \"BOUNDARIES\": [{\"NAME\": \"drag_quadratic_regime\", \"PREDICATE\": \"1e3 < rho_air |v| L_ref / mu_air < 2e5: the Reynolds window of the quadratic law\", \"CONDITION\": \"mu_air != 0 and SPEED2 >= 0 and rho_air*sqrt(SPEED2)*L_ref/mu_air > 1000 and rho_air*sqrt(SPEED2)*L_ref/mu_air < 200000\"}], \"NOT_CHOSEN\": \"No quadratic air resistance.\", \"NOT_INCLUDED\": [\"No wind: the air is at rest.\", \"No change of air density or viscosity with altitude or temperature.\", \"No lift, Magnus or added-mass force.\", \"No drag outside the Reynolds window of the quadratic law.\"], \"EXCLUDES\": [\"AIR-LINEAR\"], \"INTERACTS_WITH\": [], \"TEST_BINDINGS\": [{\"NAME\": \"PROJECTILE_2D\", \"TPK\": {\"DOF\": [{\"NAME\": \"t\", \"DIMENSION\": \"T1\"}, {\"NAME\": \"x\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"z\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"v_x\", \"DIMENSION\": \"L1 T-1\"}, {\"NAME\": \"v_z\", \"DIMENSION\": \"L1 T-1\"}], \"CONSTANT\": [{\"NAME\": \"m\", \"DIMENSION\": \"M1\"}], \"LAW\": [{\"NAME\": \"KIN_X\", \"STATEMENT\": \"dx/dt = v_x\", \"REFS\": [\"t\", \"v_x\", \"x\"], \"ROLE\": \"EOM(x)\", \"EQUATION\": \"D(x,t)=v_x\"}, {\"NAME\": \"KIN_Z\", \"STATEMENT\": \"dz/dt = v_z\", \"REFS\": [\"t\", \"v_z\", \"z\"], \"ROLE\": \"EOM(z)\", \"EQUATION\": \"D(z,t)=v_z\"}, {\"NAME\": \"EOM_X\", \"STATEMENT\": \"m dv_x/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_x\"], \"ROLE\": \"EOM(v_x)\", \"EQUATION\": \"m*D(v_x,t)=0\"}, {\"NAME\": \"EOM_Z\", \"STATEMENT\": \"m dv_z/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_z\"], \"ROLE\": \"EOM(v_z)\", \"EQUATION\": \"m*D(v_z,t)=0\"}], \"ASSUMPTION\": [{\"NAME\": \"point_mass\", \"PROPOSITION\": \"the body is treated as a point mass\", \"REFS\": [\"m\"]}]}, \"BIND\": {\"VELOCITY\": [\"v_x\", \"v_z\"]}, \"VALUES\": {\"A_ref\": {}, \"C_d\": {}, \"L_ref\": {}}, \"ANSWERS\": {}}]}",
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it acts in this kernel only where one of your own laws states it.\", \"NO_LINE\": \"No buoyancy: the air's upthrust on the body is not included.\"}], \"TEST_BINDINGS\": [{\"NAME\": \"PROJECTILE_2D\", \"TPK\": {\"DOF\": [{\"NAME\": \"t\", \"DIMENSION\": \"T1\"}, {\"NAME\": \"x\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"z\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"v_x\", \"DIMENSION\": \"L1 T-1\"}, {\"NAME\": \"v_z\", \"DIMENSION\": \"L1 T-1\"}], \"CONSTANT\": [{\"NAME\": \"m\", \"DIMENSION\": \"M1\"}], \"LAW\": [{\"NAME\": \"KIN_X\", \"STATEMENT\": \"dx/dt = v_x\", \"REFS\": [\"t\", \"v_x\", \"x\"], \"ROLE\": \"EOM(x)\", \"EQUATION\": \"D(x,t)=v_x\"}, {\"NAME\": \"KIN_Z\", \"STATEMENT\": \"dz/dt = v_z\", \"REFS\": [\"t\", \"v_z\", \"z\"], \"ROLE\": \"EOM(z)\", \"EQUATION\": \"D(z,t)=v_z\"}, {\"NAME\": \"EOM_X\", \"STATEMENT\": \"m dv_x/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_x\"], \"ROLE\": \"EOM(v_x)\", \"EQUATION\": \"m*D(v_x,t)=0\"}, {\"NAME\": \"EOM_Z\", \"STATEMENT\": \"m dv_z/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_z\"], \"ROLE\": \"EOM(v_z)\", \"EQUATION\": \"m*D(v_z,t)=0\"}], \"ASSUMPTION\": [{\"NAME\": \"point_mass\", \"PROPOSITION\": \"the body is treated as a point mass\", \"REFS\": [\"m\"]}]}, \"BIND\": {\"HEIGHT\": [\"z\"], \"MASS\": [\"m\"], \"UP_VELOCITY\": [\"v_z\"]}, \"VALUES\": {\"h_max\": {\"VALUE\": \"100\", \"UNIT\": \"m\"}}, \"ANSWERS\": {}}, {\"NAME\": \"TABLE\", \"TPK\": {\"DOF\": [{\"NAME\": \"t\", \"DIMENSION\": \"T1\"}, {\"NAME\": \"x\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"z\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"v_x\", \"DIMENSION\": \"L1 T-1\"}, {\"NAME\": \"v_z\", \"DIMENSION\": \"L1 T-1\"}], \"CONSTANT\": [{\"NAME\": \"m\", \"DIMENSION\": \"M1\"}], \"LAW\": [{\"NAME\": \"KIN_X\", \"STATEMENT\": \"dx/dt = v_x\", \"REFS\": [\"t\", \"v_x\", \"x\"], \"ROLE\": \"EOM(x)\", \"EQUATION\": \"D(x,t)=v_x\"}, {\"NAME\": \"KIN_Z\", \"STATEMENT\": \"dz/dt = v_z\", \"REFS\": [\"t\", \"v_z\", \"z\"], \"ROLE\": \"CONSTRAINT\", \"EQUATION\": \"D(z,t)=v_z\"}, {\"NAME\": \"EOM_X\", \"STATEMENT\": \"m dv_x/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_x\"], \"ROLE\": \"EOM(v_x)\", \"EQUATION\": \"m*D(v_x,t)=0\"}], \"CONSTRAINT\": [{\"NAME\": \"C_Z\", \"TARGET\": \"z\", \"ACTION\": \"FIX\", \"VALUE\": \"0\", \"UNIT\": \"m\", \"STATEMENT\": \"the puck stays on the table top, z = 0\"}, {\"NAME\": \"C_VZ\", \"TARGET\": \"v_z\", \"ACTION\": \"FIX\", \"VALUE\": \"0\", \"UNIT\": \"m s-1\", \"STATEMENT\": \"the puck has no vertical velocity\"}]}, \"BIND\": {\"HEIGHT\": [\"z\"], \"MASS\": [\"m\"], \"UP_VELOCITY\": [\"v_z\"]}, \"VALUES\": {\"h_max\": {\"VALUE\": \"1\", \"UNIT\": \"m\"}}, \"ANSWERS\": {\"FIXED:v_z\": \"YES\"}}]}",
"{\"ID\": \"MATH\", \"VERSION\": \"1.0.0\", \"TITLE\": \"The mathematical constant pi, as the CONSTANT pi_c\", \"SOURCE\": \"pi to 16 significant digits, 3.141592653589793, the nearest IEEE 754 binary64 value\", \"PREREQUISITES\": [], \"PARAMETERS\": [{\"NAME\": \"pi_c\", \"DIMENSION\": \"1\", \"SUPPLY\": \"DECLARED\", \"VALUE\": \"3.141592653589793\", \"UNIT\": \"1\", \"OVERRIDABLE\": \"NO\", \"LABEL\": \"pi, to 16 significant digits\"}], \"SUMS\": [], \"TERMS\": [], \"ASSUMPTIONS\": [], \"BOUNDARIES\": [], \"NOT_CHOSEN\": \"No mathematical constant: pi exists only if you declare it.\", \"NOT_INCLUDED\": [\"pi_c is pi rounded to 16 significant digits; no other mathematical constant is declared.\"], \"EXCLUDES\": [], \"INTERACTS_WITH\": [], \"TEST_BINDINGS\": [{\"NAME\": \"PROJECTILE_2D\", \"TPK\": {\"DOF\": [{\"NAME\": \"t\", \"DIMENSION\": \"T1\"}, {\"NAME\": \"x\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"z\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"v_x\", \"DIMENSION\": \"L1 T-1\"}, {\"NAME\": \"v_z\", \"DIMENSION\": \"L1 T-1\"}], \"CONSTANT\": [{\"NAME\": \"m\", \"DIMENSION\": \"M1\"}], \"LAW\": [{\"NAME\": \"KIN_X\", \"STATEMENT\": \"dx/dt = v_x\", \"REFS\": [\"t\", \"v_x\", \"x\"], \"ROLE\": \"EOM(x)\", \"EQUATION\": \"D(x,t)=v_x\"}, {\"NAME\": \"KIN_Z\", \"STATEMENT\": \"dz/dt = v_z\", \"REFS\": [\"t\", \"v_z\", \"z\"], \"ROLE\": \"EOM(z)\", \"EQUATION\": \"D(z,t)=v_z\"}, {\"NAME\": \"EOM_X\", \"STATEMENT\": \"m dv_x/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_x\"], \"ROLE\": \"EOM(v_x)\", \"EQUATION\": \"m*D(v_x,t)=0\"}, {\"NAME\": \"EOM_Z\", \"STATEMENT\": \"m dv_z/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_z\"], \"ROLE\": \"EOM(v_z)\", \"EQUATION\": \"m*D(v_z,t)=0\"}], \"ASSUMPTION\": [{\"NAME\": \"point_mass\", \"PROPOSITION\": \"the body is treated as a point mass\", \"REFS\": [\"m\"]}]}, \"BIND\": {}, \"VALUES\": {}, \"ANSWERS\": {}}]}"
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"fn": "interview_check",
"hand_checked": true,
"name": "I27 a claim DIGEST not the declared one"
},
{
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{
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{
"ACT": "MODULE ADD",
"DATE": "2026-10-01",
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"{\"ID\": \"AIR-LINEAR\", \"VERSION\": \"1.0.0\", \"TITLE\": \"Air resistance at sea level, linear in the speed (Stokes drag on a sphere)\", \"SOURCE\": \"ISO 2533:1975, Standard Atmosphere, sea-level values: density 1.225 kg m-3, dynamic viscosity 1.7894e-5 Pa s\", \"PREREQUISITES\": [{\"SLOT\": \"VELOCITY\", \"KIND\": \"DOF\", \"DIMENSION\": \"L1 T-1\", \"MIN\": 1, \"MAX\": 3, \"LABEL\": \"the velocity components of the body, one per axis\"}], \"PARAMETERS\": [{\"NAME\": \"rho_air\", \"DIMENSION\": \"L-3 M1\", \"SUPPLY\": \"DECLARED\", \"VALUE\": \"1.225\", \"UNIT\": \"kg m-3\", \"OVERRIDABLE\": \"NO\", \"LABEL\": \"the density of air at sea level\"}, {\"NAME\": \"mu_air\", \"DIMENSION\": \"L-1 M1 T-1\", \"SUPPLY\": \"DECLARED\", \"VALUE\": \"1.7894e-5\", \"UNIT\": \"Pa s\", \"OVERRIDABLE\": \"NO\", \"LABEL\": \"the dynamic viscosity of air at sea level\"}, {\"NAME\": \"pi_c\", \"DIMENSION\": \"1\", \"SUPPLY\": \"DECLARED\", \"VALUE\": \"3.141592653589793\", \"UNIT\": \"1\", \"OVERRIDABLE\": \"NO\", \"LABEL\": \"pi, to 16 significant digits\"}, {\"NAME\": \"R_s\", \"DIMENSION\": \"L1\", \"SUPPLY\": \"AUTHOR\", \"LABEL\": \"the radius of the sphere\"}], \"SUMS\": [{\"NAME\": \"SPEED2\", \"OVER\": \"VELOCITY\", \"EACH\": \"VELOCITY^2\"}], \"TERMS\": [{\"TARGET\": \"VELOCITY\", \"SIGN\": \"-\", \"EXPR\": \"6*pi_c*mu_air*R_s*VELOCITY\", \"LABEL\": \"the linear (Stokes) drag\"}], \"ASSUMPTIONS\": [{\"NAME\": \"air_still\", \"PROPOSITION\": \"the air is at rest in the frame of the body's velocity\", \"REFS\": [\"VELOCITY\"]}, {\"NAME\": \"air_uniform\", \"PROPOSITION\": \"the air density is uniform over the region of motion\", \"REFS\": [\"rho_air\"]}, {\"NAME\": \"drag_sphere\", \"PROPOSITION\": \"the body is a rigid sphere of radius R_s\", \"REFS\": [\"R_s\"]}], \"BOUNDARIES\": [{\"NAME\": \"drag_linear_regime\", \"PREDICATE\": \"2 rho_air |v| R_s / mu_air < 1: the regime of the linear law\", \"CONDITION\": \"mu_air != 0 and SPEED2 >= 0 and 2*rho_air*sqrt(SPEED2)*R_s/mu_air < 1\"}], \"NOT_CHOSEN\": \"No linear (Stokes) air resistance.\", \"NOT_INCLUDED\": [\"No wind: the air is at rest.\", \"No change of air density or viscosity with altitude or temperature.\", \"No drag outside the regime of the linear law.\"], \"EXCLUDES\": [], \"INTERACTS_WITH\": [], \"TEST_BINDINGS\": [{\"NAME\": \"PROJECTILE_2D\", \"TPK\": {\"DOF\": [{\"NAME\": \"t\", \"DIMENSION\": \"T1\"}, {\"NAME\": \"x\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"z\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"v_x\", \"DIMENSION\": \"L1 T-1\"}, {\"NAME\": \"v_z\", \"DIMENSION\": \"L1 T-1\"}], \"CONSTANT\": [{\"NAME\": \"m\", \"DIMENSION\": \"M1\"}], \"LAW\": [{\"NAME\": \"KIN_X\", \"STATEMENT\": \"dx/dt = v_x\", \"REFS\": [\"t\", \"v_x\", \"x\"], \"ROLE\": \"EOM(x)\", \"EQUATION\": \"D(x,t)=v_x\"}, {\"NAME\": \"KIN_Z\", \"STATEMENT\": \"dz/dt = v_z\", \"REFS\": [\"t\", \"v_z\", \"z\"], \"ROLE\": \"EOM(z)\", \"EQUATION\": \"D(z,t)=v_z\"}, {\"NAME\": \"EOM_X\", \"STATEMENT\": \"m dv_x/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_x\"], \"ROLE\": \"EOM(v_x)\", \"EQUATION\": \"m*D(v_x,t)=0\"}, {\"NAME\": \"EOM_Z\", \"STATEMENT\": \"m dv_z/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_z\"], \"ROLE\": \"EOM(v_z)\", \"EQUATION\": \"m*D(v_z,t)=0\"}], \"ASSUMPTION\": [{\"NAME\": \"point_mass\", \"PROPOSITION\": \"the body is treated as a point mass\", \"REFS\": [\"m\"]}]}, \"BIND\": {\"VELOCITY\": [\"v_x\", \"v_z\"]}, \"VALUES\": {\"R_s\": {}}, \"ANSWERS\": {}}]}",
"{\"ID\": \"AIR-QUADRATIC\", \"VERSION\": \"1.0.0\", \"TITLE\": \"Air resistance at sea level, quadratic in the speed\", \"SOURCE\": \"ISO 2533:1975, Standard Atmosphere, sea-level values: density 1.225 kg m-3, dynamic viscosity 1.7894e-5 Pa s\", \"PREREQUISITES\": [{\"SLOT\": \"VELOCITY\", \"KIND\": \"DOF\", \"DIMENSION\": \"L1 T-1\", \"MIN\": 1, \"MAX\": 3, \"LABEL\": \"the velocity components of the body, one per axis\"}], \"PARAMETERS\": [{\"NAME\": \"rho_air\", \"DIMENSION\": \"L-3 M1\", \"SUPPLY\": \"DECLARED\", \"VALUE\": \"1.225\", \"UNIT\": \"kg m-3\", \"OVERRIDABLE\": \"NO\", \"LABEL\": \"the density of air at sea level\"}, {\"NAME\": \"mu_air\", \"DIMENSION\": \"L-1 M1 T-1\", \"SUPPLY\": \"DECLARED\", \"VALUE\": \"1.7894e-5\", \"UNIT\": \"Pa s\", \"OVERRIDABLE\": \"NO\", \"LABEL\": \"the dynamic viscosity of air at sea level\"}, {\"NAME\": \"C_d\", \"DIMENSION\": \"1\", \"SUPPLY\": \"AUTHOR\", \"LABEL\": \"the drag coefficient of the body\"}, {\"NAME\": \"A_ref\", \"DIMENSION\": \"L2\", \"SUPPLY\": \"AUTHOR\", \"LABEL\": \"the reference area of the drag coefficient\"}, {\"NAME\": \"L_ref\", \"DIMENSION\": \"L1\", \"SUPPLY\": \"AUTHOR\", \"LABEL\": \"the reference length of the Reynolds number\"}], \"SUMS\": [{\"NAME\": \"SPEED2\", \"OVER\": \"VELOCITY\", \"EACH\": \"VELOCITY^2\"}], \"TERMS\": [{\"TARGET\": \"VELOCITY\", \"SIGN\": \"-\", \"EXPR\": \"0.5*rho_air*C_d*A_ref*sqrt(SPEED2)*VELOCITY\", \"LABEL\": \"the quadratic drag\"}], \"ASSUMPTIONS\": [{\"NAME\": \"air_still\", \"PROPOSITION\": \"the air is at rest in the frame of the body's velocity\", \"REFS\": [\"VELOCITY\"]}, {\"NAME\": \"air_uniform\", \"PROPOSITION\": \"the air density is uniform over the region of motion\", \"REFS\": [\"rho_air\"]}, {\"NAME\": \"drag_cd_constant\", \"PROPOSITION\": \"the drag coefficient C_d is constant over the motion\", \"REFS\": [\"C_d\"]}, {\"NAME\": \"drag_no_lift\", \"PROPOSITION\": \"the body experiences no lift force\", \"REFS\": [\"VELOCITY\"]}, {\"NAME\": \"drag_no_magnus\", \"PROPOSITION\": \"the body experiences no Magnus force\", \"REFS\": [\"VELOCITY\"]}], \"BOUNDARIES\": [{\"NAME\": \"drag_quadratic_regime\", \"PREDICATE\": \"1e3 < rho_air |v| L_ref / mu_air < 2e5: the Reynolds window of the quadratic law\", \"CONDITION\": \"mu_air != 0 and SPEED2 >= 0 and rho_air*sqrt(SPEED2)*L_ref/mu_air > 1000 and rho_air*sqrt(SPEED2)*L_ref/mu_air < 200000\"}], \"NOT_CHOSEN\": \"No quadratic air resistance.\", \"NOT_INCLUDED\": [\"No wind: the air is at rest.\", \"No change of air density or viscosity with altitude or temperature.\", \"No lift, Magnus or added-mass force.\", \"No drag outside the Reynolds window of the quadratic law.\"], \"EXCLUDES\": [\"AIR-LINEAR\"], \"INTERACTS_WITH\": [], \"TEST_BINDINGS\": [{\"NAME\": \"PROJECTILE_2D\", \"TPK\": {\"DOF\": [{\"NAME\": \"t\", \"DIMENSION\": \"T1\"}, {\"NAME\": \"x\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"z\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"v_x\", \"DIMENSION\": \"L1 T-1\"}, {\"NAME\": \"v_z\", \"DIMENSION\": \"L1 T-1\"}], \"CONSTANT\": [{\"NAME\": \"m\", \"DIMENSION\": \"M1\"}], \"LAW\": [{\"NAME\": \"KIN_X\", \"STATEMENT\": \"dx/dt = v_x\", \"REFS\": [\"t\", \"v_x\", \"x\"], \"ROLE\": \"EOM(x)\", \"EQUATION\": \"D(x,t)=v_x\"}, {\"NAME\": \"KIN_Z\", \"STATEMENT\": \"dz/dt = v_z\", \"REFS\": [\"t\", \"v_z\", \"z\"], \"ROLE\": \"EOM(z)\", \"EQUATION\": \"D(z,t)=v_z\"}, {\"NAME\": \"EOM_X\", \"STATEMENT\": \"m dv_x/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_x\"], \"ROLE\": \"EOM(v_x)\", \"EQUATION\": \"m*D(v_x,t)=0\"}, {\"NAME\": \"EOM_Z\", \"STATEMENT\": \"m dv_z/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_z\"], \"ROLE\": \"EOM(v_z)\", \"EQUATION\": \"m*D(v_z,t)=0\"}], \"ASSUMPTION\": [{\"NAME\": \"point_mass\", \"PROPOSITION\": \"the body is treated as a point mass\", \"REFS\": [\"m\"]}]}, \"BIND\": {\"VELOCITY\": [\"v_x\", \"v_z\"]}, \"VALUES\": {\"A_ref\": {}, \"C_d\": {}, \"L_ref\": {}}, \"ANSWERS\": {}}]}",
"{\"ID\": \"GRAV-UNIFORM\", \"VERSION\": \"1.0.0\", \"TITLE\": \"Uniform gravity at the standard value g_n\", \"SOURCE\": \"g_n = 9.80665 m s-2, exact by definition: 3rd CGPM (1901), declaration on the unit of mass and on the definition of weight\", \"PREREQUISITES\": [{\"SLOT\": \"MASS\", \"KIND\": \"CONSTANT\", \"DIMENSION\": \"M1\", \"MIN\": 1, \"MAX\": 1, \"LABEL\": \"the mass of the body\"}, {\"SLOT\": \"UP_VELOCITY\", \"KIND\": \"DOF\", \"DIMENSION\": \"L1 T-1\", \"MIN\": 1, \"MAX\": 1, \"LABEL\": \"the velocity component pointing up; its equation of motion receives the weight\"}, {\"SLOT\": \"HEIGHT\", \"KIND\": \"DOF\", \"DIMENSION\": \"L1\", \"MIN\": 1, \"MAX\": 1, \"LABEL\": \"the position along the same upward axis\"}], \"PARAMETERS\": [{\"NAME\": \"g_n\", \"DIMENSION\": \"L1 T-2\", \"SUPPLY\": \"DECLARED\", \"VALUE\": \"9.80665\", \"UNIT\": \"m s-2\", \"OVERRIDABLE\": \"NO\", \"LABEL\": \"the standard acceleration of gravity\"}, {\"NAME\": \"h_max\", \"DIMENSION\": \"L1\", \"SUPPLY\": \"AUTHOR\", \"LABEL\": \"the largest height, above or below the origin, over which the field is taken as uniform\"}], \"SUMS\": [], \"TERMS\": [{\"TARGET\": \"UP_VELOCITY\", \"SIGN\": \"-\", \"EXPR\": \"MASS*g_n\", \"LABEL\": \"the weight\"}], \"ASSUMPTIONS\": [{\"NAME\": \"gravity_uniform\", \"PROPOSITION\": \"the gravitational field is uniform over the region abs({HEIGHT}) < h_max\", \"REFS\": [\"HEIGHT\", \"h_max\"]}, {\"NAME\": \"gravity_standard\", \"PROPOSITION\": \"the local gravitational acceleration equals the conventional standard value g_n\", \"REFS\": [\"g_n\"]}, {\"NAME\": \"frame_inertial\", \"PROPOSITION\": \"the frame in which {HEIGHT} is measured is treated as inertial\", \"REFS\": [\"HEIGHT\"]}], \"BOUNDARIES\": [{\"NAME\": \"gravity_region\", \"PREDICATE\": \"abs({HEIGHT}) < h_max\", \"CONDITION\": \"abs(HEIGHT) < h_max\"}], \"NOT_CHOSEN\": \"No gravity: no weight acts on any DOF.\", \"NOT_INCLUDED\": [\"No variation of gravity with height or latitude beyond what g_n contains.\", \"No Earth rotation (Coriolis or centrifugal force) beyond what g_n contains.\", \"No gravity of bodies other than the Earth.\"], \"EXCLUDES\": [], \"INTERACTS_WITH\": [{\"WITH\": \"AIR-*\", \"QUESTION_ID\": \"BUOYANCY\", \"QUESTION\": \"Does the air's buoyancy (upthrust) act on the body in the system you mean?\", \"YES_LINE\": \"Buoyancy acts (your answer): no module adds it; it acts in this kernel only where one of your own laws states it.\", \"NO_LINE\": \"No buoyancy: the air's upthrust on the body is not included.\"}], \"TEST_BINDINGS\": [{\"NAME\": \"PROJECTILE_2D\", \"TPK\": {\"DOF\": [{\"NAME\": \"t\", \"DIMENSION\": \"T1\"}, {\"NAME\": \"x\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"z\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"v_x\", \"DIMENSION\": \"L1 T-1\"}, {\"NAME\": \"v_z\", \"DIMENSION\": \"L1 T-1\"}], \"CONSTANT\": [{\"NAME\": \"m\", \"DIMENSION\": \"M1\"}], \"LAW\": [{\"NAME\": \"KIN_X\", \"STATEMENT\": \"dx/dt = v_x\", \"REFS\": [\"t\", \"v_x\", \"x\"], \"ROLE\": \"EOM(x)\", \"EQUATION\": \"D(x,t)=v_x\"}, {\"NAME\": \"KIN_Z\", \"STATEMENT\": \"dz/dt = v_z\", \"REFS\": [\"t\", \"v_z\", \"z\"], \"ROLE\": \"EOM(z)\", \"EQUATION\": \"D(z,t)=v_z\"}, {\"NAME\": \"EOM_X\", \"STATEMENT\": \"m dv_x/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_x\"], \"ROLE\": \"EOM(v_x)\", \"EQUATION\": \"m*D(v_x,t)=0\"}, {\"NAME\": \"EOM_Z\", \"STATEMENT\": \"m dv_z/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_z\"], \"ROLE\": \"EOM(v_z)\", \"EQUATION\": \"m*D(v_z,t)=0\"}], \"ASSUMPTION\": [{\"NAME\": \"point_mass\", \"PROPOSITION\": \"the body is treated as a point mass\", \"REFS\": [\"m\"]}]}, \"BIND\": {\"HEIGHT\": [\"z\"], \"MASS\": [\"m\"], \"UP_VELOCITY\": [\"v_z\"]}, \"VALUES\": {\"h_max\": {\"VALUE\": \"100\", \"UNIT\": \"m\"}}, \"ANSWERS\": {}}, {\"NAME\": \"TABLE\", \"TPK\": {\"DOF\": [{\"NAME\": \"t\", \"DIMENSION\": \"T1\"}, {\"NAME\": \"x\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"z\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"v_x\", \"DIMENSION\": \"L1 T-1\"}, {\"NAME\": \"v_z\", \"DIMENSION\": \"L1 T-1\"}], \"CONSTANT\": [{\"NAME\": \"m\", \"DIMENSION\": \"M1\"}], \"LAW\": [{\"NAME\": \"KIN_X\", \"STATEMENT\": \"dx/dt = v_x\", \"REFS\": [\"t\", \"v_x\", \"x\"], \"ROLE\": \"EOM(x)\", \"EQUATION\": \"D(x,t)=v_x\"}, {\"NAME\": \"KIN_Z\", \"STATEMENT\": \"dz/dt = v_z\", \"REFS\": [\"t\", \"v_z\", \"z\"], \"ROLE\": \"CONSTRAINT\", \"EQUATION\": \"D(z,t)=v_z\"}, {\"NAME\": \"EOM_X\", \"STATEMENT\": \"m dv_x/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_x\"], \"ROLE\": \"EOM(v_x)\", \"EQUATION\": \"m*D(v_x,t)=0\"}], \"CONSTRAINT\": [{\"NAME\": \"C_Z\", \"TARGET\": \"z\", \"ACTION\": \"FIX\", \"VALUE\": \"0\", \"UNIT\": \"m\", \"STATEMENT\": \"the puck stays on the table top, z = 0\"}, {\"NAME\": \"C_VZ\", \"TARGET\": \"v_z\", \"ACTION\": \"FIX\", \"VALUE\": \"0\", \"UNIT\": \"m s-1\", \"STATEMENT\": \"the puck has no vertical velocity\"}]}, \"BIND\": {\"HEIGHT\": [\"z\"], \"MASS\": [\"m\"], \"UP_VELOCITY\": [\"v_z\"]}, \"VALUES\": {\"h_max\": {\"VALUE\": \"1\", \"UNIT\": \"m\"}}, \"ANSWERS\": {\"FIXED:v_z\": \"YES\"}}]}",
"{\"ID\": \"MATH\", \"VERSION\": \"1.0.0\", \"TITLE\": \"The mathematical constant pi, as the CONSTANT pi_c\", \"SOURCE\": \"pi to 16 significant digits, 3.141592653589793, the nearest IEEE 754 binary64 value\", \"PREREQUISITES\": [], \"PARAMETERS\": [{\"NAME\": \"pi_c\", \"DIMENSION\": \"1\", \"SUPPLY\": \"DECLARED\", \"VALUE\": \"3.141592653589793\", \"UNIT\": \"1\", \"OVERRIDABLE\": \"NO\", \"LABEL\": \"pi, to 16 significant digits\"}], \"SUMS\": [], \"TERMS\": [], \"ASSUMPTIONS\": [], \"BOUNDARIES\": [], \"NOT_CHOSEN\": \"No mathematical constant: pi exists only if you declare it.\", \"NOT_INCLUDED\": [\"pi_c is pi rounded to 16 significant digits; no other mathematical constant is declared.\"], \"EXCLUDES\": [], \"INTERACTS_WITH\": [], \"TEST_BINDINGS\": [{\"NAME\": \"PROJECTILE_2D\", \"TPK\": {\"DOF\": [{\"NAME\": \"t\", \"DIMENSION\": \"T1\"}, {\"NAME\": \"x\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"z\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"v_x\", \"DIMENSION\": \"L1 T-1\"}, {\"NAME\": \"v_z\", \"DIMENSION\": \"L1 T-1\"}], \"CONSTANT\": [{\"NAME\": \"m\", \"DIMENSION\": \"M1\"}], \"LAW\": [{\"NAME\": \"KIN_X\", \"STATEMENT\": \"dx/dt = v_x\", \"REFS\": [\"t\", \"v_x\", \"x\"], \"ROLE\": \"EOM(x)\", \"EQUATION\": \"D(x,t)=v_x\"}, {\"NAME\": \"KIN_Z\", \"STATEMENT\": \"dz/dt = v_z\", \"REFS\": [\"t\", \"v_z\", \"z\"], \"ROLE\": \"EOM(z)\", \"EQUATION\": \"D(z,t)=v_z\"}, {\"NAME\": \"EOM_X\", \"STATEMENT\": \"m dv_x/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_x\"], \"ROLE\": \"EOM(v_x)\", \"EQUATION\": \"m*D(v_x,t)=0\"}, {\"NAME\": \"EOM_Z\", \"STATEMENT\": \"m dv_z/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_z\"], \"ROLE\": \"EOM(v_z)\", \"EQUATION\": \"m*D(v_z,t)=0\"}], \"ASSUMPTION\": [{\"NAME\": \"point_mass\", \"PROPOSITION\": \"the body is treated as a point mass\", \"REFS\": [\"m\"]}]}, \"BIND\": {}, \"VALUES\": {}, \"ANSWERS\": {}}]}"
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"name": "I28 carried not a list of triples"
},
{
"args": {
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{
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{
"ACT": "MODULE ADD",
"DATE": "2026-10-01",
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"{\"ID\": \"AIR-LINEAR\", \"VERSION\": \"1.0.0\", \"TITLE\": \"Air resistance at sea level, linear in the speed (Stokes drag on a sphere)\", \"SOURCE\": \"ISO 2533:1975, Standard Atmosphere, sea-level values: density 1.225 kg m-3, dynamic viscosity 1.7894e-5 Pa s\", \"PREREQUISITES\": [{\"SLOT\": \"VELOCITY\", \"KIND\": \"DOF\", \"DIMENSION\": \"L1 T-1\", \"MIN\": 1, \"MAX\": 3, \"LABEL\": \"the velocity components of the body, one per axis\"}], \"PARAMETERS\": [{\"NAME\": \"rho_air\", \"DIMENSION\": \"L-3 M1\", \"SUPPLY\": \"DECLARED\", \"VALUE\": \"1.225\", \"UNIT\": \"kg m-3\", \"OVERRIDABLE\": \"NO\", \"LABEL\": \"the density of air at sea level\"}, {\"NAME\": \"mu_air\", \"DIMENSION\": \"L-1 M1 T-1\", \"SUPPLY\": \"DECLARED\", \"VALUE\": \"1.7894e-5\", \"UNIT\": \"Pa s\", \"OVERRIDABLE\": \"NO\", \"LABEL\": \"the dynamic viscosity of air at sea level\"}, {\"NAME\": \"pi_c\", \"DIMENSION\": \"1\", \"SUPPLY\": \"DECLARED\", \"VALUE\": \"3.141592653589793\", \"UNIT\": \"1\", \"OVERRIDABLE\": \"NO\", \"LABEL\": \"pi, to 16 significant digits\"}, {\"NAME\": \"R_s\", \"DIMENSION\": \"L1\", \"SUPPLY\": \"AUTHOR\", \"LABEL\": \"the radius of the sphere\"}], \"SUMS\": [{\"NAME\": \"SPEED2\", \"OVER\": \"VELOCITY\", \"EACH\": \"VELOCITY^2\"}], \"TERMS\": [{\"TARGET\": \"VELOCITY\", \"SIGN\": \"-\", \"EXPR\": \"6*pi_c*mu_air*R_s*VELOCITY\", \"LABEL\": \"the linear (Stokes) drag\"}], \"ASSUMPTIONS\": [{\"NAME\": \"air_still\", \"PROPOSITION\": \"the air is at rest in the frame of the body's velocity\", \"REFS\": [\"VELOCITY\"]}, {\"NAME\": \"air_uniform\", \"PROPOSITION\": \"the air density is uniform over the region of motion\", \"REFS\": [\"rho_air\"]}, {\"NAME\": \"drag_sphere\", \"PROPOSITION\": \"the body is a rigid sphere of radius R_s\", \"REFS\": [\"R_s\"]}], \"BOUNDARIES\": [{\"NAME\": \"drag_linear_regime\", \"PREDICATE\": \"2 rho_air |v| R_s / mu_air < 1: the regime of the linear law\", \"CONDITION\": \"mu_air != 0 and SPEED2 >= 0 and 2*rho_air*sqrt(SPEED2)*R_s/mu_air < 1\"}], \"NOT_CHOSEN\": \"No linear (Stokes) air resistance.\", \"NOT_INCLUDED\": [\"No wind: the air is at rest.\", \"No change of air density or viscosity with altitude or temperature.\", \"No drag outside the regime of the linear law.\"], \"EXCLUDES\": [], \"INTERACTS_WITH\": [], \"TEST_BINDINGS\": [{\"NAME\": \"PROJECTILE_2D\", \"TPK\": {\"DOF\": [{\"NAME\": \"t\", \"DIMENSION\": \"T1\"}, {\"NAME\": \"x\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"z\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"v_x\", \"DIMENSION\": \"L1 T-1\"}, {\"NAME\": \"v_z\", \"DIMENSION\": \"L1 T-1\"}], \"CONSTANT\": [{\"NAME\": \"m\", \"DIMENSION\": \"M1\"}], \"LAW\": [{\"NAME\": \"KIN_X\", \"STATEMENT\": \"dx/dt = v_x\", \"REFS\": [\"t\", \"v_x\", \"x\"], \"ROLE\": \"EOM(x)\", \"EQUATION\": \"D(x,t)=v_x\"}, {\"NAME\": \"KIN_Z\", \"STATEMENT\": \"dz/dt = v_z\", \"REFS\": [\"t\", \"v_z\", \"z\"], \"ROLE\": \"EOM(z)\", \"EQUATION\": \"D(z,t)=v_z\"}, {\"NAME\": \"EOM_X\", \"STATEMENT\": \"m dv_x/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_x\"], \"ROLE\": \"EOM(v_x)\", \"EQUATION\": \"m*D(v_x,t)=0\"}, {\"NAME\": \"EOM_Z\", \"STATEMENT\": \"m dv_z/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_z\"], \"ROLE\": \"EOM(v_z)\", \"EQUATION\": \"m*D(v_z,t)=0\"}], \"ASSUMPTION\": [{\"NAME\": \"point_mass\", \"PROPOSITION\": \"the body is treated as a point mass\", \"REFS\": [\"m\"]}]}, \"BIND\": {\"VELOCITY\": [\"v_x\", \"v_z\"]}, \"VALUES\": {\"R_s\": {}}, \"ANSWERS\": {}}]}",
"{\"ID\": \"AIR-QUADRATIC\", \"VERSION\": \"1.0.0\", \"TITLE\": \"Air resistance at sea level, quadratic in the speed\", \"SOURCE\": \"ISO 2533:1975, Standard Atmosphere, sea-level values: density 1.225 kg m-3, dynamic viscosity 1.7894e-5 Pa s\", \"PREREQUISITES\": [{\"SLOT\": \"VELOCITY\", \"KIND\": \"DOF\", \"DIMENSION\": \"L1 T-1\", \"MIN\": 1, \"MAX\": 3, \"LABEL\": \"the velocity components of the body, one per axis\"}], \"PARAMETERS\": [{\"NAME\": \"rho_air\", \"DIMENSION\": \"L-3 M1\", \"SUPPLY\": \"DECLARED\", \"VALUE\": \"1.225\", \"UNIT\": \"kg m-3\", \"OVERRIDABLE\": \"NO\", \"LABEL\": \"the density of air at sea level\"}, {\"NAME\": \"mu_air\", \"DIMENSION\": \"L-1 M1 T-1\", \"SUPPLY\": \"DECLARED\", \"VALUE\": \"1.7894e-5\", \"UNIT\": \"Pa s\", \"OVERRIDABLE\": \"NO\", \"LABEL\": \"the dynamic viscosity of air at sea level\"}, {\"NAME\": \"C_d\", \"DIMENSION\": \"1\", \"SUPPLY\": \"AUTHOR\", \"LABEL\": \"the drag coefficient of the body\"}, {\"NAME\": \"A_ref\", \"DIMENSION\": \"L2\", \"SUPPLY\": \"AUTHOR\", \"LABEL\": \"the reference area of the drag coefficient\"}, {\"NAME\": \"L_ref\", \"DIMENSION\": \"L1\", \"SUPPLY\": \"AUTHOR\", \"LABEL\": \"the reference length of the Reynolds number\"}], \"SUMS\": [{\"NAME\": \"SPEED2\", \"OVER\": \"VELOCITY\", \"EACH\": \"VELOCITY^2\"}], \"TERMS\": [{\"TARGET\": \"VELOCITY\", \"SIGN\": \"-\", \"EXPR\": \"0.5*rho_air*C_d*A_ref*sqrt(SPEED2)*VELOCITY\", \"LABEL\": \"the quadratic drag\"}], \"ASSUMPTIONS\": [{\"NAME\": \"air_still\", \"PROPOSITION\": \"the air is at rest in the frame of the body's velocity\", \"REFS\": [\"VELOCITY\"]}, {\"NAME\": \"air_uniform\", \"PROPOSITION\": \"the air density is uniform over the region of motion\", \"REFS\": [\"rho_air\"]}, {\"NAME\": \"drag_cd_constant\", \"PROPOSITION\": \"the drag coefficient C_d is constant over the motion\", \"REFS\": [\"C_d\"]}, {\"NAME\": \"drag_no_lift\", \"PROPOSITION\": \"the body experiences no lift force\", \"REFS\": [\"VELOCITY\"]}, {\"NAME\": \"drag_no_magnus\", \"PROPOSITION\": \"the body experiences no Magnus force\", \"REFS\": [\"VELOCITY\"]}], \"BOUNDARIES\": [{\"NAME\": \"drag_quadratic_regime\", \"PREDICATE\": \"1e3 < rho_air |v| L_ref / mu_air < 2e5: the Reynolds window of the quadratic law\", \"CONDITION\": \"mu_air != 0 and SPEED2 >= 0 and rho_air*sqrt(SPEED2)*L_ref/mu_air > 1000 and rho_air*sqrt(SPEED2)*L_ref/mu_air < 200000\"}], \"NOT_CHOSEN\": \"No quadratic air resistance.\", \"NOT_INCLUDED\": [\"No wind: the air is at rest.\", \"No change of air density or viscosity with altitude or temperature.\", \"No lift, Magnus or added-mass force.\", \"No drag outside the Reynolds window of the quadratic law.\"], \"EXCLUDES\": [\"AIR-LINEAR\"], \"INTERACTS_WITH\": [], \"TEST_BINDINGS\": [{\"NAME\": \"PROJECTILE_2D\", \"TPK\": {\"DOF\": [{\"NAME\": \"t\", \"DIMENSION\": \"T1\"}, {\"NAME\": \"x\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"z\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"v_x\", \"DIMENSION\": \"L1 T-1\"}, {\"NAME\": \"v_z\", \"DIMENSION\": \"L1 T-1\"}], \"CONSTANT\": [{\"NAME\": \"m\", \"DIMENSION\": \"M1\"}], \"LAW\": [{\"NAME\": \"KIN_X\", \"STATEMENT\": \"dx/dt = v_x\", \"REFS\": [\"t\", \"v_x\", \"x\"], \"ROLE\": \"EOM(x)\", \"EQUATION\": \"D(x,t)=v_x\"}, {\"NAME\": \"KIN_Z\", \"STATEMENT\": \"dz/dt = v_z\", \"REFS\": [\"t\", \"v_z\", \"z\"], \"ROLE\": \"EOM(z)\", \"EQUATION\": \"D(z,t)=v_z\"}, {\"NAME\": \"EOM_X\", \"STATEMENT\": \"m dv_x/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_x\"], \"ROLE\": \"EOM(v_x)\", \"EQUATION\": \"m*D(v_x,t)=0\"}, {\"NAME\": \"EOM_Z\", \"STATEMENT\": \"m dv_z/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_z\"], \"ROLE\": \"EOM(v_z)\", \"EQUATION\": \"m*D(v_z,t)=0\"}], \"ASSUMPTION\": [{\"NAME\": \"point_mass\", \"PROPOSITION\": \"the body is treated as a point mass\", \"REFS\": [\"m\"]}]}, \"BIND\": {\"VELOCITY\": [\"v_x\", \"v_z\"]}, \"VALUES\": {\"A_ref\": {}, \"C_d\": {}, \"L_ref\": {}}, \"ANSWERS\": {}}]}",
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it acts in this kernel only where one of your own laws states it.\", \"NO_LINE\": \"No buoyancy: the air's upthrust on the body is not included.\"}], \"TEST_BINDINGS\": [{\"NAME\": \"PROJECTILE_2D\", \"TPK\": {\"DOF\": [{\"NAME\": \"t\", \"DIMENSION\": \"T1\"}, {\"NAME\": \"x\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"z\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"v_x\", \"DIMENSION\": \"L1 T-1\"}, {\"NAME\": \"v_z\", \"DIMENSION\": \"L1 T-1\"}], \"CONSTANT\": [{\"NAME\": \"m\", \"DIMENSION\": \"M1\"}], \"LAW\": [{\"NAME\": \"KIN_X\", \"STATEMENT\": \"dx/dt = v_x\", \"REFS\": [\"t\", \"v_x\", \"x\"], \"ROLE\": \"EOM(x)\", \"EQUATION\": \"D(x,t)=v_x\"}, {\"NAME\": \"KIN_Z\", \"STATEMENT\": \"dz/dt = v_z\", \"REFS\": [\"t\", \"v_z\", \"z\"], \"ROLE\": \"EOM(z)\", \"EQUATION\": \"D(z,t)=v_z\"}, {\"NAME\": \"EOM_X\", \"STATEMENT\": \"m dv_x/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_x\"], \"ROLE\": \"EOM(v_x)\", \"EQUATION\": \"m*D(v_x,t)=0\"}, {\"NAME\": \"EOM_Z\", \"STATEMENT\": \"m dv_z/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_z\"], \"ROLE\": \"EOM(v_z)\", \"EQUATION\": \"m*D(v_z,t)=0\"}], \"ASSUMPTION\": [{\"NAME\": \"point_mass\", \"PROPOSITION\": \"the body is treated as a point mass\", \"REFS\": [\"m\"]}]}, \"BIND\": {\"HEIGHT\": [\"z\"], \"MASS\": [\"m\"], \"UP_VELOCITY\": [\"v_z\"]}, \"VALUES\": {\"h_max\": {\"VALUE\": \"100\", \"UNIT\": \"m\"}}, \"ANSWERS\": {}}, {\"NAME\": \"TABLE\", \"TPK\": {\"DOF\": [{\"NAME\": \"t\", \"DIMENSION\": \"T1\"}, {\"NAME\": \"x\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"z\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"v_x\", \"DIMENSION\": \"L1 T-1\"}, {\"NAME\": \"v_z\", \"DIMENSION\": \"L1 T-1\"}], \"CONSTANT\": [{\"NAME\": \"m\", \"DIMENSION\": \"M1\"}], \"LAW\": [{\"NAME\": \"KIN_X\", \"STATEMENT\": \"dx/dt = v_x\", \"REFS\": [\"t\", \"v_x\", \"x\"], \"ROLE\": \"EOM(x)\", \"EQUATION\": \"D(x,t)=v_x\"}, {\"NAME\": \"KIN_Z\", \"STATEMENT\": \"dz/dt = v_z\", \"REFS\": [\"t\", \"v_z\", \"z\"], \"ROLE\": \"CONSTRAINT\", \"EQUATION\": \"D(z,t)=v_z\"}, {\"NAME\": \"EOM_X\", \"STATEMENT\": \"m dv_x/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_x\"], \"ROLE\": \"EOM(v_x)\", \"EQUATION\": \"m*D(v_x,t)=0\"}], \"CONSTRAINT\": [{\"NAME\": \"C_Z\", \"TARGET\": \"z\", \"ACTION\": \"FIX\", \"VALUE\": \"0\", \"UNIT\": \"m\", \"STATEMENT\": \"the puck stays on the table top, z = 0\"}, {\"NAME\": \"C_VZ\", \"TARGET\": \"v_z\", \"ACTION\": \"FIX\", \"VALUE\": \"0\", \"UNIT\": \"m s-1\", \"STATEMENT\": \"the puck has no vertical velocity\"}]}, \"BIND\": {\"HEIGHT\": [\"z\"], \"MASS\": [\"m\"], \"UP_VELOCITY\": [\"v_z\"]}, \"VALUES\": {\"h_max\": {\"VALUE\": \"1\", \"UNIT\": \"m\"}}, \"ANSWERS\": {\"FIXED:v_z\": \"YES\"}}]}",
"{\"ID\": \"MATH\", \"VERSION\": \"1.0.0\", \"TITLE\": \"The mathematical constant pi, as the CONSTANT pi_c\", \"SOURCE\": \"pi to 16 significant digits, 3.141592653589793, the nearest IEEE 754 binary64 value\", \"PREREQUISITES\": [], \"PARAMETERS\": [{\"NAME\": \"pi_c\", \"DIMENSION\": \"1\", \"SUPPLY\": \"DECLARED\", \"VALUE\": \"3.141592653589793\", \"UNIT\": \"1\", \"OVERRIDABLE\": \"NO\", \"LABEL\": \"pi, to 16 significant digits\"}], \"SUMS\": [], \"TERMS\": [], \"ASSUMPTIONS\": [], \"BOUNDARIES\": [], \"NOT_CHOSEN\": \"No mathematical constant: pi exists only if you declare it.\", \"NOT_INCLUDED\": [\"pi_c is pi rounded to 16 significant digits; no other mathematical constant is declared.\"], \"EXCLUDES\": [], \"INTERACTS_WITH\": [], \"TEST_BINDINGS\": [{\"NAME\": \"PROJECTILE_2D\", \"TPK\": {\"DOF\": [{\"NAME\": \"t\", \"DIMENSION\": \"T1\"}, {\"NAME\": \"x\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"z\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"v_x\", \"DIMENSION\": \"L1 T-1\"}, {\"NAME\": \"v_z\", \"DIMENSION\": \"L1 T-1\"}], \"CONSTANT\": [{\"NAME\": \"m\", \"DIMENSION\": \"M1\"}], \"LAW\": [{\"NAME\": \"KIN_X\", \"STATEMENT\": \"dx/dt = v_x\", \"REFS\": [\"t\", \"v_x\", \"x\"], \"ROLE\": \"EOM(x)\", \"EQUATION\": \"D(x,t)=v_x\"}, {\"NAME\": \"KIN_Z\", \"STATEMENT\": \"dz/dt = v_z\", \"REFS\": [\"t\", \"v_z\", \"z\"], \"ROLE\": \"EOM(z)\", \"EQUATION\": \"D(z,t)=v_z\"}, {\"NAME\": \"EOM_X\", \"STATEMENT\": \"m dv_x/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_x\"], \"ROLE\": \"EOM(v_x)\", \"EQUATION\": \"m*D(v_x,t)=0\"}, {\"NAME\": \"EOM_Z\", \"STATEMENT\": \"m dv_z/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_z\"], \"ROLE\": \"EOM(v_z)\", \"EQUATION\": \"m*D(v_z,t)=0\"}], \"ASSUMPTION\": [{\"NAME\": \"point_mass\", \"PROPOSITION\": \"the body is treated as a point mass\", \"REFS\": [\"m\"]}]}, \"BIND\": {}, \"VALUES\": {}, \"ANSWERS\": {}}]}"
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{
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"ACT": "MODULE ADD",
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"{\"ID\": \"AIR-LINEAR\", \"VERSION\": \"1.0.0\", \"TITLE\": \"Air resistance at sea level, linear in the speed (Stokes drag on a sphere)\", \"SOURCE\": \"ISO 2533:1975, Standard Atmosphere, sea-level values: density 1.225 kg m-3, dynamic viscosity 1.7894e-5 Pa s\", \"PREREQUISITES\": [{\"SLOT\": \"VELOCITY\", \"KIND\": \"DOF\", \"DIMENSION\": \"L1 T-1\", \"MIN\": 1, \"MAX\": 3, \"LABEL\": \"the velocity components of the body, one per axis\"}], \"PARAMETERS\": [{\"NAME\": \"rho_air\", \"DIMENSION\": \"L-3 M1\", \"SUPPLY\": \"DECLARED\", \"VALUE\": \"1.225\", \"UNIT\": \"kg m-3\", \"OVERRIDABLE\": \"NO\", \"LABEL\": \"the density of air at sea level\"}, {\"NAME\": \"mu_air\", \"DIMENSION\": \"L-1 M1 T-1\", \"SUPPLY\": \"DECLARED\", \"VALUE\": \"1.7894e-5\", \"UNIT\": \"Pa s\", \"OVERRIDABLE\": \"NO\", \"LABEL\": \"the dynamic viscosity of air at sea level\"}, {\"NAME\": \"pi_c\", \"DIMENSION\": \"1\", \"SUPPLY\": \"DECLARED\", \"VALUE\": \"3.141592653589793\", \"UNIT\": \"1\", \"OVERRIDABLE\": \"NO\", \"LABEL\": \"pi, to 16 significant digits\"}, {\"NAME\": \"R_s\", \"DIMENSION\": \"L1\", \"SUPPLY\": \"AUTHOR\", \"LABEL\": \"the radius of the sphere\"}], \"SUMS\": [{\"NAME\": \"SPEED2\", \"OVER\": \"VELOCITY\", \"EACH\": \"VELOCITY^2\"}], \"TERMS\": [{\"TARGET\": \"VELOCITY\", \"SIGN\": \"-\", \"EXPR\": \"6*pi_c*mu_air*R_s*VELOCITY\", \"LABEL\": \"the linear (Stokes) drag\"}], \"ASSUMPTIONS\": [{\"NAME\": \"air_still\", \"PROPOSITION\": \"the air is at rest in the frame of the body's velocity\", \"REFS\": [\"VELOCITY\"]}, {\"NAME\": \"air_uniform\", \"PROPOSITION\": \"the air density is uniform over the region of motion\", \"REFS\": [\"rho_air\"]}, {\"NAME\": \"drag_sphere\", \"PROPOSITION\": \"the body is a rigid sphere of radius R_s\", \"REFS\": [\"R_s\"]}], \"BOUNDARIES\": [{\"NAME\": \"drag_linear_regime\", \"PREDICATE\": \"2 rho_air |v| R_s / mu_air < 1: the regime of the linear law\", \"CONDITION\": \"mu_air != 0 and SPEED2 >= 0 and 2*rho_air*sqrt(SPEED2)*R_s/mu_air < 1\"}], \"NOT_CHOSEN\": \"No linear (Stokes) air resistance.\", \"NOT_INCLUDED\": [\"No wind: the air is at rest.\", \"No change of air density or viscosity with altitude or temperature.\", \"No drag outside the regime of the linear law.\"], \"EXCLUDES\": [], \"INTERACTS_WITH\": [], \"TEST_BINDINGS\": [{\"NAME\": \"PROJECTILE_2D\", \"TPK\": {\"DOF\": [{\"NAME\": \"t\", \"DIMENSION\": \"T1\"}, {\"NAME\": \"x\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"z\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"v_x\", \"DIMENSION\": \"L1 T-1\"}, {\"NAME\": \"v_z\", \"DIMENSION\": \"L1 T-1\"}], \"CONSTANT\": [{\"NAME\": \"m\", \"DIMENSION\": \"M1\"}], \"LAW\": [{\"NAME\": \"KIN_X\", \"STATEMENT\": \"dx/dt = v_x\", \"REFS\": [\"t\", \"v_x\", \"x\"], \"ROLE\": \"EOM(x)\", \"EQUATION\": \"D(x,t)=v_x\"}, {\"NAME\": \"KIN_Z\", \"STATEMENT\": \"dz/dt = v_z\", \"REFS\": [\"t\", \"v_z\", \"z\"], \"ROLE\": \"EOM(z)\", \"EQUATION\": \"D(z,t)=v_z\"}, {\"NAME\": \"EOM_X\", \"STATEMENT\": \"m dv_x/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_x\"], \"ROLE\": \"EOM(v_x)\", \"EQUATION\": \"m*D(v_x,t)=0\"}, {\"NAME\": \"EOM_Z\", \"STATEMENT\": \"m dv_z/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_z\"], \"ROLE\": \"EOM(v_z)\", \"EQUATION\": \"m*D(v_z,t)=0\"}], \"ASSUMPTION\": [{\"NAME\": \"point_mass\", \"PROPOSITION\": \"the body is treated as a point mass\", \"REFS\": [\"m\"]}]}, \"BIND\": {\"VELOCITY\": [\"v_x\", \"v_z\"]}, \"VALUES\": {\"R_s\": {}}, \"ANSWERS\": {}}]}",
"{\"ID\": \"AIR-QUADRATIC\", \"VERSION\": \"1.0.0\", \"TITLE\": \"Air resistance at sea level, quadratic in the speed\", \"SOURCE\": \"ISO 2533:1975, Standard Atmosphere, sea-level values: density 1.225 kg m-3, dynamic viscosity 1.7894e-5 Pa s\", \"PREREQUISITES\": [{\"SLOT\": \"VELOCITY\", \"KIND\": \"DOF\", \"DIMENSION\": \"L1 T-1\", \"MIN\": 1, \"MAX\": 3, \"LABEL\": \"the velocity components of the body, one per axis\"}], \"PARAMETERS\": [{\"NAME\": \"rho_air\", \"DIMENSION\": \"L-3 M1\", \"SUPPLY\": \"DECLARED\", \"VALUE\": \"1.225\", \"UNIT\": \"kg m-3\", \"OVERRIDABLE\": \"NO\", \"LABEL\": \"the density of air at sea level\"}, {\"NAME\": \"mu_air\", \"DIMENSION\": \"L-1 M1 T-1\", \"SUPPLY\": \"DECLARED\", \"VALUE\": \"1.7894e-5\", \"UNIT\": \"Pa s\", \"OVERRIDABLE\": \"NO\", \"LABEL\": \"the dynamic viscosity of air at sea level\"}, {\"NAME\": \"C_d\", \"DIMENSION\": \"1\", \"SUPPLY\": \"AUTHOR\", \"LABEL\": \"the drag coefficient of the body\"}, {\"NAME\": \"A_ref\", \"DIMENSION\": \"L2\", \"SUPPLY\": \"AUTHOR\", \"LABEL\": \"the reference area of the drag coefficient\"}, {\"NAME\": \"L_ref\", \"DIMENSION\": \"L1\", \"SUPPLY\": \"AUTHOR\", \"LABEL\": \"the reference length of the Reynolds number\"}], \"SUMS\": [{\"NAME\": \"SPEED2\", \"OVER\": \"VELOCITY\", \"EACH\": \"VELOCITY^2\"}], \"TERMS\": [{\"TARGET\": \"VELOCITY\", \"SIGN\": \"-\", \"EXPR\": \"0.5*rho_air*C_d*A_ref*sqrt(SPEED2)*VELOCITY\", \"LABEL\": \"the quadratic drag\"}], \"ASSUMPTIONS\": [{\"NAME\": \"air_still\", \"PROPOSITION\": \"the air is at rest in the frame of the body's velocity\", \"REFS\": [\"VELOCITY\"]}, {\"NAME\": \"air_uniform\", \"PROPOSITION\": \"the air density is uniform over the region of motion\", \"REFS\": [\"rho_air\"]}, {\"NAME\": \"drag_cd_constant\", \"PROPOSITION\": \"the drag coefficient C_d is constant over the motion\", \"REFS\": [\"C_d\"]}, {\"NAME\": \"drag_no_lift\", \"PROPOSITION\": \"the body experiences no lift force\", \"REFS\": [\"VELOCITY\"]}, {\"NAME\": \"drag_no_magnus\", \"PROPOSITION\": \"the body experiences no Magnus force\", \"REFS\": [\"VELOCITY\"]}], \"BOUNDARIES\": [{\"NAME\": \"drag_quadratic_regime\", \"PREDICATE\": \"1e3 < rho_air |v| L_ref / mu_air < 2e5: the Reynolds window of the quadratic law\", \"CONDITION\": \"mu_air != 0 and SPEED2 >= 0 and rho_air*sqrt(SPEED2)*L_ref/mu_air > 1000 and rho_air*sqrt(SPEED2)*L_ref/mu_air < 200000\"}], \"NOT_CHOSEN\": \"No quadratic air resistance.\", \"NOT_INCLUDED\": [\"No wind: the air is at rest.\", \"No change of air density or viscosity with altitude or temperature.\", \"No lift, Magnus or added-mass force.\", \"No drag outside the Reynolds window of the quadratic law.\"], \"EXCLUDES\": [\"AIR-LINEAR\"], \"INTERACTS_WITH\": [], \"TEST_BINDINGS\": [{\"NAME\": \"PROJECTILE_2D\", \"TPK\": {\"DOF\": [{\"NAME\": \"t\", \"DIMENSION\": \"T1\"}, {\"NAME\": \"x\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"z\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"v_x\", \"DIMENSION\": \"L1 T-1\"}, {\"NAME\": \"v_z\", \"DIMENSION\": \"L1 T-1\"}], \"CONSTANT\": [{\"NAME\": \"m\", \"DIMENSION\": \"M1\"}], \"LAW\": [{\"NAME\": \"KIN_X\", \"STATEMENT\": \"dx/dt = v_x\", \"REFS\": [\"t\", \"v_x\", \"x\"], \"ROLE\": \"EOM(x)\", \"EQUATION\": \"D(x,t)=v_x\"}, {\"NAME\": \"KIN_Z\", \"STATEMENT\": \"dz/dt = v_z\", \"REFS\": [\"t\", \"v_z\", \"z\"], \"ROLE\": \"EOM(z)\", \"EQUATION\": \"D(z,t)=v_z\"}, {\"NAME\": \"EOM_X\", \"STATEMENT\": \"m dv_x/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_x\"], \"ROLE\": \"EOM(v_x)\", \"EQUATION\": \"m*D(v_x,t)=0\"}, {\"NAME\": \"EOM_Z\", \"STATEMENT\": \"m dv_z/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_z\"], \"ROLE\": \"EOM(v_z)\", \"EQUATION\": \"m*D(v_z,t)=0\"}], \"ASSUMPTION\": [{\"NAME\": \"point_mass\", \"PROPOSITION\": \"the body is treated as a point mass\", \"REFS\": [\"m\"]}]}, \"BIND\": {\"VELOCITY\": [\"v_x\", \"v_z\"]}, \"VALUES\": {\"A_ref\": {}, \"C_d\": {}, \"L_ref\": {}}, \"ANSWERS\": {}}]}",
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it acts in this kernel only where one of your own laws states it.\", \"NO_LINE\": \"No buoyancy: the air's upthrust on the body is not included.\"}], \"TEST_BINDINGS\": [{\"NAME\": \"PROJECTILE_2D\", \"TPK\": {\"DOF\": [{\"NAME\": \"t\", \"DIMENSION\": \"T1\"}, {\"NAME\": \"x\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"z\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"v_x\", \"DIMENSION\": \"L1 T-1\"}, {\"NAME\": \"v_z\", \"DIMENSION\": \"L1 T-1\"}], \"CONSTANT\": [{\"NAME\": \"m\", \"DIMENSION\": \"M1\"}], \"LAW\": [{\"NAME\": \"KIN_X\", \"STATEMENT\": \"dx/dt = v_x\", \"REFS\": [\"t\", \"v_x\", \"x\"], \"ROLE\": \"EOM(x)\", \"EQUATION\": \"D(x,t)=v_x\"}, {\"NAME\": \"KIN_Z\", \"STATEMENT\": \"dz/dt = v_z\", \"REFS\": [\"t\", \"v_z\", \"z\"], \"ROLE\": \"EOM(z)\", \"EQUATION\": \"D(z,t)=v_z\"}, {\"NAME\": \"EOM_X\", \"STATEMENT\": \"m dv_x/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_x\"], \"ROLE\": \"EOM(v_x)\", \"EQUATION\": \"m*D(v_x,t)=0\"}, {\"NAME\": \"EOM_Z\", \"STATEMENT\": \"m dv_z/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_z\"], \"ROLE\": \"EOM(v_z)\", \"EQUATION\": \"m*D(v_z,t)=0\"}], \"ASSUMPTION\": [{\"NAME\": \"point_mass\", \"PROPOSITION\": \"the body is treated as a point mass\", \"REFS\": [\"m\"]}]}, \"BIND\": {\"HEIGHT\": [\"z\"], \"MASS\": [\"m\"], \"UP_VELOCITY\": [\"v_z\"]}, \"VALUES\": {\"h_max\": {\"VALUE\": \"100\", \"UNIT\": \"m\"}}, \"ANSWERS\": {}}, {\"NAME\": \"TABLE\", \"TPK\": {\"DOF\": [{\"NAME\": \"t\", \"DIMENSION\": \"T1\"}, {\"NAME\": \"x\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"z\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"v_x\", \"DIMENSION\": \"L1 T-1\"}, {\"NAME\": \"v_z\", \"DIMENSION\": \"L1 T-1\"}], \"CONSTANT\": [{\"NAME\": \"m\", \"DIMENSION\": \"M1\"}], \"LAW\": [{\"NAME\": \"KIN_X\", \"STATEMENT\": \"dx/dt = v_x\", \"REFS\": [\"t\", \"v_x\", \"x\"], \"ROLE\": \"EOM(x)\", \"EQUATION\": \"D(x,t)=v_x\"}, {\"NAME\": \"KIN_Z\", \"STATEMENT\": \"dz/dt = v_z\", \"REFS\": [\"t\", \"v_z\", \"z\"], \"ROLE\": \"CONSTRAINT\", \"EQUATION\": \"D(z,t)=v_z\"}, {\"NAME\": \"EOM_X\", \"STATEMENT\": \"m dv_x/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_x\"], \"ROLE\": \"EOM(v_x)\", \"EQUATION\": \"m*D(v_x,t)=0\"}], \"CONSTRAINT\": [{\"NAME\": \"C_Z\", \"TARGET\": \"z\", \"ACTION\": \"FIX\", \"VALUE\": \"0\", \"UNIT\": \"m\", \"STATEMENT\": \"the puck stays on the table top, z = 0\"}, {\"NAME\": \"C_VZ\", \"TARGET\": \"v_z\", \"ACTION\": \"FIX\", \"VALUE\": \"0\", \"UNIT\": \"m s-1\", \"STATEMENT\": \"the puck has no vertical velocity\"}]}, \"BIND\": {\"HEIGHT\": [\"z\"], \"MASS\": [\"m\"], \"UP_VELOCITY\": [\"v_z\"]}, \"VALUES\": {\"h_max\": {\"VALUE\": \"1\", \"UNIT\": \"m\"}}, \"ANSWERS\": {\"FIXED:v_z\": \"YES\"}}]}",
"{\"ID\": \"MATH\", \"VERSION\": \"1.0.0\", \"TITLE\": \"The mathematical constant pi, as the CONSTANT pi_c\", \"SOURCE\": \"pi to 16 significant digits, 3.141592653589793, the nearest IEEE 754 binary64 value\", \"PREREQUISITES\": [], \"PARAMETERS\": [{\"NAME\": \"pi_c\", \"DIMENSION\": \"1\", \"SUPPLY\": \"DECLARED\", \"VALUE\": \"3.141592653589793\", \"UNIT\": \"1\", \"OVERRIDABLE\": \"NO\", \"LABEL\": \"pi, to 16 significant digits\"}], \"SUMS\": [], \"TERMS\": [], \"ASSUMPTIONS\": [], \"BOUNDARIES\": [], \"NOT_CHOSEN\": \"No mathematical constant: pi exists only if you declare it.\", \"NOT_INCLUDED\": [\"pi_c is pi rounded to 16 significant digits; no other mathematical constant is declared.\"], \"EXCLUDES\": [], \"INTERACTS_WITH\": [], \"TEST_BINDINGS\": [{\"NAME\": \"PROJECTILE_2D\", \"TPK\": {\"DOF\": [{\"NAME\": \"t\", \"DIMENSION\": \"T1\"}, {\"NAME\": \"x\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"z\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"v_x\", \"DIMENSION\": \"L1 T-1\"}, {\"NAME\": \"v_z\", \"DIMENSION\": \"L1 T-1\"}], \"CONSTANT\": [{\"NAME\": \"m\", \"DIMENSION\": \"M1\"}], \"LAW\": [{\"NAME\": \"KIN_X\", \"STATEMENT\": \"dx/dt = v_x\", \"REFS\": [\"t\", \"v_x\", \"x\"], \"ROLE\": \"EOM(x)\", \"EQUATION\": \"D(x,t)=v_x\"}, {\"NAME\": \"KIN_Z\", \"STATEMENT\": \"dz/dt = v_z\", \"REFS\": [\"t\", \"v_z\", \"z\"], \"ROLE\": \"EOM(z)\", \"EQUATION\": \"D(z,t)=v_z\"}, {\"NAME\": \"EOM_X\", \"STATEMENT\": \"m dv_x/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_x\"], \"ROLE\": \"EOM(v_x)\", \"EQUATION\": \"m*D(v_x,t)=0\"}, {\"NAME\": \"EOM_Z\", \"STATEMENT\": \"m dv_z/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_z\"], \"ROLE\": \"EOM(v_z)\", \"EQUATION\": \"m*D(v_z,t)=0\"}], \"ASSUMPTION\": [{\"NAME\": \"point_mass\", \"PROPOSITION\": \"the body is treated as a point mass\", \"REFS\": [\"m\"]}]}, \"BIND\": {}, \"VALUES\": {}, \"ANSWERS\": {}}]}"
]
},
"expected": "[\"REFUSED\",\"ANSWER ROUND 1: COVERED is not the offer the round was given over\"]",
"fn": "interview_check",
"hand_checked": true,
"name": "I30 COVERED in another order"
},
{
"args": {
"answer": [
{
"AT": 0,
"CHOSEN": "NONE",
"COVERED": []
}
],
"carried": [],
"claims": [],
"lines": [],
"modified": [],
"modules": []
},
"expected": "[\"OK\",[\"ASK\",[]],[\"CLAIMS\",[]]]",
"fn": "interview_check",
"hand_checked": true,
"name": "I31 an empty catalogue answered NONE at AT 0"
},
{
"args": {
"answer": [
{
"AT": 0,
"CHOSEN": "NONE",
"COVERED": []
}
],
"carried": [],
"claims": [],
"lines": [
{
"ACT": "MODULE ADD",
"DATE": "2026-10-01",
"DIGEST": "5f3fe27b42378bce0830b0d0959f892f4a8e73b12b540ae877e39e6439d08b4d",
"ID": "AIR-LINEAR",
"VERSION": "1.0.0"
},
{
"ACT": "MODULE ADD",
"DATE": "2026-10-01",
"DIGEST": "6fb53c3a6546151eead2bd6e72e9cf8334f3a2040ad0ee2f5b988ec96d6fc852",
"ID": "AIR-QUADRATIC",
"VERSION": "1.0.0"
},
{
"ACT": "MODULE ADD",
"DATE": "2026-10-01",
"DIGEST": "24877ccb5c8ec300d29ed82ce6650592f35cf8899a3d878ccce9c08d4c72c025",
"ID": "GRAV-UNIFORM",
"VERSION": "1.0.0"
},
{
"ACT": "MODULE ADD",
"DATE": "2026-10-01",
"DIGEST": "8f39a356f35527b901fcee012764590f0819c8ffdeccad4bc05195ce3d2e0bcf",
"ID": "MATH",
"VERSION": "1.0.0"
}
],
"modified": [],
"modules": [
"{\"ID\": \"AIR-LINEAR\", \"VERSION\": \"1.0.0\", \"TITLE\": \"Air resistance at sea level, linear in the speed (Stokes drag on a sphere)\", \"SOURCE\": \"ISO 2533:1975, Standard Atmosphere, sea-level values: density 1.225 kg m-3, dynamic viscosity 1.7894e-5 Pa s\", \"PREREQUISITES\": [{\"SLOT\": \"VELOCITY\", \"KIND\": \"DOF\", \"DIMENSION\": \"L1 T-1\", \"MIN\": 1, \"MAX\": 3, \"LABEL\": \"the velocity components of the body, one per axis\"}], \"PARAMETERS\": [{\"NAME\": \"rho_air\", \"DIMENSION\": \"L-3 M1\", \"SUPPLY\": \"DECLARED\", \"VALUE\": \"1.225\", \"UNIT\": \"kg m-3\", \"OVERRIDABLE\": \"NO\", \"LABEL\": \"the density of air at sea level\"}, {\"NAME\": \"mu_air\", \"DIMENSION\": \"L-1 M1 T-1\", \"SUPPLY\": \"DECLARED\", \"VALUE\": \"1.7894e-5\", \"UNIT\": \"Pa s\", \"OVERRIDABLE\": \"NO\", \"LABEL\": \"the dynamic viscosity of air at sea level\"}, {\"NAME\": \"pi_c\", \"DIMENSION\": \"1\", \"SUPPLY\": \"DECLARED\", \"VALUE\": \"3.141592653589793\", \"UNIT\": \"1\", \"OVERRIDABLE\": \"NO\", \"LABEL\": \"pi, to 16 significant digits\"}, {\"NAME\": \"R_s\", \"DIMENSION\": \"L1\", \"SUPPLY\": \"AUTHOR\", \"LABEL\": \"the radius of the sphere\"}], \"SUMS\": [{\"NAME\": \"SPEED2\", \"OVER\": \"VELOCITY\", \"EACH\": \"VELOCITY^2\"}], \"TERMS\": [{\"TARGET\": \"VELOCITY\", \"SIGN\": \"-\", \"EXPR\": \"6*pi_c*mu_air*R_s*VELOCITY\", \"LABEL\": \"the linear (Stokes) drag\"}], \"ASSUMPTIONS\": [{\"NAME\": \"air_still\", \"PROPOSITION\": \"the air is at rest in the frame of the body's velocity\", \"REFS\": [\"VELOCITY\"]}, {\"NAME\": \"air_uniform\", \"PROPOSITION\": \"the air density is uniform over the region of motion\", \"REFS\": [\"rho_air\"]}, {\"NAME\": \"drag_sphere\", \"PROPOSITION\": \"the body is a rigid sphere of radius R_s\", \"REFS\": [\"R_s\"]}], \"BOUNDARIES\": [{\"NAME\": \"drag_linear_regime\", \"PREDICATE\": \"2 rho_air |v| R_s / mu_air < 1: the regime of the linear law\", \"CONDITION\": \"mu_air != 0 and SPEED2 >= 0 and 2*rho_air*sqrt(SPEED2)*R_s/mu_air < 1\"}], \"NOT_CHOSEN\": \"No linear (Stokes) air resistance.\", \"NOT_INCLUDED\": [\"No wind: the air is at rest.\", \"No change of air density or viscosity with altitude or temperature.\", \"No drag outside the regime of the linear law.\"], \"EXCLUDES\": [], \"INTERACTS_WITH\": [], \"TEST_BINDINGS\": [{\"NAME\": \"PROJECTILE_2D\", \"TPK\": {\"DOF\": [{\"NAME\": \"t\", \"DIMENSION\": \"T1\"}, {\"NAME\": \"x\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"z\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"v_x\", \"DIMENSION\": \"L1 T-1\"}, {\"NAME\": \"v_z\", \"DIMENSION\": \"L1 T-1\"}], \"CONSTANT\": [{\"NAME\": \"m\", \"DIMENSION\": \"M1\"}], \"LAW\": [{\"NAME\": \"KIN_X\", \"STATEMENT\": \"dx/dt = v_x\", \"REFS\": [\"t\", \"v_x\", \"x\"], \"ROLE\": \"EOM(x)\", \"EQUATION\": \"D(x,t)=v_x\"}, {\"NAME\": \"KIN_Z\", \"STATEMENT\": \"dz/dt = v_z\", \"REFS\": [\"t\", \"v_z\", \"z\"], \"ROLE\": \"EOM(z)\", \"EQUATION\": \"D(z,t)=v_z\"}, {\"NAME\": \"EOM_X\", \"STATEMENT\": \"m dv_x/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_x\"], \"ROLE\": \"EOM(v_x)\", \"EQUATION\": \"m*D(v_x,t)=0\"}, {\"NAME\": \"EOM_Z\", \"STATEMENT\": \"m dv_z/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_z\"], \"ROLE\": \"EOM(v_z)\", \"EQUATION\": \"m*D(v_z,t)=0\"}], \"ASSUMPTION\": [{\"NAME\": \"point_mass\", \"PROPOSITION\": \"the body is treated as a point mass\", \"REFS\": [\"m\"]}]}, \"BIND\": {\"VELOCITY\": [\"v_x\", \"v_z\"]}, \"VALUES\": {\"R_s\": {}}, \"ANSWERS\": {}}]}",
"{\"ID\": \"AIR-QUADRATIC\", \"VERSION\": \"1.0.0\", \"TITLE\": \"Air resistance at sea level, quadratic in the speed\", \"SOURCE\": \"ISO 2533:1975, Standard Atmosphere, sea-level values: density 1.225 kg m-3, dynamic viscosity 1.7894e-5 Pa s\", \"PREREQUISITES\": [{\"SLOT\": \"VELOCITY\", \"KIND\": \"DOF\", \"DIMENSION\": \"L1 T-1\", \"MIN\": 1, \"MAX\": 3, \"LABEL\": \"the velocity components of the body, one per axis\"}], \"PARAMETERS\": [{\"NAME\": \"rho_air\", \"DIMENSION\": \"L-3 M1\", \"SUPPLY\": \"DECLARED\", \"VALUE\": \"1.225\", \"UNIT\": \"kg m-3\", \"OVERRIDABLE\": \"NO\", \"LABEL\": \"the density of air at sea level\"}, {\"NAME\": \"mu_air\", \"DIMENSION\": \"L-1 M1 T-1\", \"SUPPLY\": \"DECLARED\", \"VALUE\": \"1.7894e-5\", \"UNIT\": \"Pa s\", \"OVERRIDABLE\": \"NO\", \"LABEL\": \"the dynamic viscosity of air at sea level\"}, {\"NAME\": \"C_d\", \"DIMENSION\": \"1\", \"SUPPLY\": \"AUTHOR\", \"LABEL\": \"the drag coefficient of the body\"}, {\"NAME\": \"A_ref\", \"DIMENSION\": \"L2\", \"SUPPLY\": \"AUTHOR\", \"LABEL\": \"the reference area of the drag coefficient\"}, {\"NAME\": \"L_ref\", \"DIMENSION\": \"L1\", \"SUPPLY\": \"AUTHOR\", \"LABEL\": \"the reference length of the Reynolds number\"}], \"SUMS\": [{\"NAME\": \"SPEED2\", \"OVER\": \"VELOCITY\", \"EACH\": \"VELOCITY^2\"}], \"TERMS\": [{\"TARGET\": \"VELOCITY\", \"SIGN\": \"-\", \"EXPR\": \"0.5*rho_air*C_d*A_ref*sqrt(SPEED2)*VELOCITY\", \"LABEL\": \"the quadratic drag\"}], \"ASSUMPTIONS\": [{\"NAME\": \"air_still\", \"PROPOSITION\": \"the air is at rest in the frame of the body's velocity\", \"REFS\": [\"VELOCITY\"]}, {\"NAME\": \"air_uniform\", \"PROPOSITION\": \"the air density is uniform over the region of motion\", \"REFS\": [\"rho_air\"]}, {\"NAME\": \"drag_cd_constant\", \"PROPOSITION\": \"the drag coefficient C_d is constant over the motion\", \"REFS\": [\"C_d\"]}, {\"NAME\": \"drag_no_lift\", \"PROPOSITION\": \"the body experiences no lift force\", \"REFS\": [\"VELOCITY\"]}, {\"NAME\": \"drag_no_magnus\", \"PROPOSITION\": \"the body experiences no Magnus force\", \"REFS\": [\"VELOCITY\"]}], \"BOUNDARIES\": [{\"NAME\": \"drag_quadratic_regime\", \"PREDICATE\": \"1e3 < rho_air |v| L_ref / mu_air < 2e5: the Reynolds window of the quadratic law\", \"CONDITION\": \"mu_air != 0 and SPEED2 >= 0 and rho_air*sqrt(SPEED2)*L_ref/mu_air > 1000 and rho_air*sqrt(SPEED2)*L_ref/mu_air < 200000\"}], \"NOT_CHOSEN\": \"No quadratic air resistance.\", \"NOT_INCLUDED\": [\"No wind: the air is at rest.\", \"No change of air density or viscosity with altitude or temperature.\", \"No lift, Magnus or added-mass force.\", \"No drag outside the Reynolds window of the quadratic law.\"], \"EXCLUDES\": [\"AIR-LINEAR\"], \"INTERACTS_WITH\": [], \"TEST_BINDINGS\": [{\"NAME\": \"PROJECTILE_2D\", \"TPK\": {\"DOF\": [{\"NAME\": \"t\", \"DIMENSION\": \"T1\"}, {\"NAME\": \"x\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"z\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"v_x\", \"DIMENSION\": \"L1 T-1\"}, {\"NAME\": \"v_z\", \"DIMENSION\": \"L1 T-1\"}], \"CONSTANT\": [{\"NAME\": \"m\", \"DIMENSION\": \"M1\"}], \"LAW\": [{\"NAME\": \"KIN_X\", \"STATEMENT\": \"dx/dt = v_x\", \"REFS\": [\"t\", \"v_x\", \"x\"], \"ROLE\": \"EOM(x)\", \"EQUATION\": \"D(x,t)=v_x\"}, {\"NAME\": \"KIN_Z\", \"STATEMENT\": \"dz/dt = v_z\", \"REFS\": [\"t\", \"v_z\", \"z\"], \"ROLE\": \"EOM(z)\", \"EQUATION\": \"D(z,t)=v_z\"}, {\"NAME\": \"EOM_X\", \"STATEMENT\": \"m dv_x/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_x\"], \"ROLE\": \"EOM(v_x)\", \"EQUATION\": \"m*D(v_x,t)=0\"}, {\"NAME\": \"EOM_Z\", \"STATEMENT\": \"m dv_z/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_z\"], \"ROLE\": \"EOM(v_z)\", \"EQUATION\": \"m*D(v_z,t)=0\"}], \"ASSUMPTION\": [{\"NAME\": \"point_mass\", \"PROPOSITION\": \"the body is treated as a point mass\", \"REFS\": [\"m\"]}]}, \"BIND\": {\"VELOCITY\": [\"v_x\", \"v_z\"]}, \"VALUES\": {\"A_ref\": {}, \"C_d\": {}, \"L_ref\": {}}, \"ANSWERS\": {}}]}",
"{\"ID\": \"GRAV-UNIFORM\", \"VERSION\": \"1.0.0\", \"TITLE\": \"Uniform gravity at the standard value g_n\", \"SOURCE\": \"g_n = 9.80665 m s-2, exact by definition: 3rd CGPM (1901), declaration on the unit of mass and on the definition of weight\", \"PREREQUISITES\": [{\"SLOT\": \"MASS\", \"KIND\": \"CONSTANT\", \"DIMENSION\": \"M1\", \"MIN\": 1, \"MAX\": 1, \"LABEL\": \"the mass of the body\"}, {\"SLOT\": \"UP_VELOCITY\", \"KIND\": \"DOF\", \"DIMENSION\": \"L1 T-1\", \"MIN\": 1, \"MAX\": 1, \"LABEL\": \"the velocity component pointing up; its equation of motion receives the weight\"}, {\"SLOT\": \"HEIGHT\", \"KIND\": \"DOF\", \"DIMENSION\": \"L1\", \"MIN\": 1, \"MAX\": 1, \"LABEL\": \"the position along the same upward axis\"}], \"PARAMETERS\": [{\"NAME\": \"g_n\", \"DIMENSION\": \"L1 T-2\", \"SUPPLY\": \"DECLARED\", \"VALUE\": \"9.80665\", \"UNIT\": \"m s-2\", \"OVERRIDABLE\": \"NO\", \"LABEL\": \"the standard acceleration of gravity\"}, {\"NAME\": \"h_max\", \"DIMENSION\": \"L1\", \"SUPPLY\": \"AUTHOR\", \"LABEL\": \"the largest height, above or below the origin, over which the field is taken as uniform\"}], \"SUMS\": [], \"TERMS\": [{\"TARGET\": \"UP_VELOCITY\", \"SIGN\": \"-\", \"EXPR\": \"MASS*g_n\", \"LABEL\": \"the weight\"}], \"ASSUMPTIONS\": [{\"NAME\": \"gravity_uniform\", \"PROPOSITION\": \"the gravitational field is uniform over the region abs({HEIGHT}) < h_max\", \"REFS\": [\"HEIGHT\", \"h_max\"]}, {\"NAME\": \"gravity_standard\", \"PROPOSITION\": \"the local gravitational acceleration equals the conventional standard value g_n\", \"REFS\": [\"g_n\"]}, {\"NAME\": \"frame_inertial\", \"PROPOSITION\": \"the frame in which {HEIGHT} is measured is treated as inertial\", \"REFS\": [\"HEIGHT\"]}], \"BOUNDARIES\": [{\"NAME\": \"gravity_region\", \"PREDICATE\": \"abs({HEIGHT}) < h_max\", \"CONDITION\": \"abs(HEIGHT) < h_max\"}], \"NOT_CHOSEN\": \"No gravity: no weight acts on any DOF.\", \"NOT_INCLUDED\": [\"No variation of gravity with height or latitude beyond what g_n contains.\", \"No Earth rotation (Coriolis or centrifugal force) beyond what g_n contains.\", \"No gravity of bodies other than the Earth.\"], \"EXCLUDES\": [], \"INTERACTS_WITH\": [{\"WITH\": \"AIR-*\", \"QUESTION_ID\": \"BUOYANCY\", \"QUESTION\": \"Does the air's buoyancy (upthrust) act on the body in the system you mean?\", \"YES_LINE\": \"Buoyancy acts (your answer): no module adds it; it acts in this kernel only where one of your own laws states it.\", \"NO_LINE\": \"No buoyancy: the air's upthrust on the body is not included.\"}], \"TEST_BINDINGS\": [{\"NAME\": \"PROJECTILE_2D\", \"TPK\": {\"DOF\": [{\"NAME\": \"t\", \"DIMENSION\": \"T1\"}, {\"NAME\": \"x\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"z\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"v_x\", \"DIMENSION\": \"L1 T-1\"}, {\"NAME\": \"v_z\", \"DIMENSION\": \"L1 T-1\"}], \"CONSTANT\": [{\"NAME\": \"m\", \"DIMENSION\": \"M1\"}], \"LAW\": [{\"NAME\": \"KIN_X\", \"STATEMENT\": \"dx/dt = v_x\", \"REFS\": [\"t\", \"v_x\", \"x\"], \"ROLE\": \"EOM(x)\", \"EQUATION\": \"D(x,t)=v_x\"}, {\"NAME\": \"KIN_Z\", \"STATEMENT\": \"dz/dt = v_z\", \"REFS\": [\"t\", \"v_z\", \"z\"], \"ROLE\": \"EOM(z)\", \"EQUATION\": \"D(z,t)=v_z\"}, {\"NAME\": \"EOM_X\", \"STATEMENT\": \"m dv_x/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_x\"], \"ROLE\": \"EOM(v_x)\", \"EQUATION\": \"m*D(v_x,t)=0\"}, {\"NAME\": \"EOM_Z\", \"STATEMENT\": \"m dv_z/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_z\"], \"ROLE\": \"EOM(v_z)\", \"EQUATION\": \"m*D(v_z,t)=0\"}], \"ASSUMPTION\": [{\"NAME\": \"point_mass\", \"PROPOSITION\": \"the body is treated as a point mass\", \"REFS\": [\"m\"]}]}, \"BIND\": {\"HEIGHT\": [\"z\"], \"MASS\": [\"m\"], \"UP_VELOCITY\": [\"v_z\"]}, \"VALUES\": {\"h_max\": {\"VALUE\": \"100\", \"UNIT\": \"m\"}}, \"ANSWERS\": {}}, {\"NAME\": \"TABLE\", \"TPK\": {\"DOF\": [{\"NAME\": \"t\", \"DIMENSION\": \"T1\"}, {\"NAME\": \"x\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"z\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"v_x\", \"DIMENSION\": \"L1 T-1\"}, {\"NAME\": \"v_z\", \"DIMENSION\": \"L1 T-1\"}], \"CONSTANT\": [{\"NAME\": \"m\", \"DIMENSION\": \"M1\"}], \"LAW\": [{\"NAME\": \"KIN_X\", \"STATEMENT\": \"dx/dt = v_x\", \"REFS\": [\"t\", \"v_x\", \"x\"], \"ROLE\": \"EOM(x)\", \"EQUATION\": \"D(x,t)=v_x\"}, {\"NAME\": \"KIN_Z\", \"STATEMENT\": \"dz/dt = v_z\", \"REFS\": [\"t\", \"v_z\", \"z\"], \"ROLE\": \"CONSTRAINT\", \"EQUATION\": \"D(z,t)=v_z\"}, {\"NAME\": \"EOM_X\", \"STATEMENT\": \"m dv_x/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_x\"], \"ROLE\": \"EOM(v_x)\", \"EQUATION\": \"m*D(v_x,t)=0\"}], \"CONSTRAINT\": [{\"NAME\": \"C_Z\", \"TARGET\": \"z\", \"ACTION\": \"FIX\", \"VALUE\": \"0\", \"UNIT\": \"m\", \"STATEMENT\": \"the puck stays on the table top, z = 0\"}, {\"NAME\": \"C_VZ\", \"TARGET\": \"v_z\", \"ACTION\": \"FIX\", \"VALUE\": \"0\", \"UNIT\": \"m s-1\", \"STATEMENT\": \"the puck has no vertical velocity\"}]}, \"BIND\": {\"HEIGHT\": [\"z\"], \"MASS\": [\"m\"], \"UP_VELOCITY\": [\"v_z\"]}, \"VALUES\": {\"h_max\": {\"VALUE\": \"1\", \"UNIT\": \"m\"}}, \"ANSWERS\": {\"FIXED:v_z\": \"YES\"}}]}",
"{\"ID\": \"MATH\", \"VERSION\": \"1.0.0\", \"TITLE\": \"The mathematical constant pi, as the CONSTANT pi_c\", \"SOURCE\": \"pi to 16 significant digits, 3.141592653589793, the nearest IEEE 754 binary64 value\", \"PREREQUISITES\": [], \"PARAMETERS\": [{\"NAME\": \"pi_c\", \"DIMENSION\": \"1\", \"SUPPLY\": \"DECLARED\", \"VALUE\": \"3.141592653589793\", \"UNIT\": \"1\", \"OVERRIDABLE\": \"NO\", \"LABEL\": \"pi, to 16 significant digits\"}], \"SUMS\": [], \"TERMS\": [], \"ASSUMPTIONS\": [], \"BOUNDARIES\": [], \"NOT_CHOSEN\": \"No mathematical constant: pi exists only if you declare it.\", \"NOT_INCLUDED\": [\"pi_c is pi rounded to 16 significant digits; no other mathematical constant is declared.\"], \"EXCLUDES\": [], \"INTERACTS_WITH\": [], \"TEST_BINDINGS\": [{\"NAME\": \"PROJECTILE_2D\", \"TPK\": {\"DOF\": [{\"NAME\": \"t\", \"DIMENSION\": \"T1\"}, {\"NAME\": \"x\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"z\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"v_x\", \"DIMENSION\": \"L1 T-1\"}, {\"NAME\": \"v_z\", \"DIMENSION\": \"L1 T-1\"}], \"CONSTANT\": [{\"NAME\": \"m\", \"DIMENSION\": \"M1\"}], \"LAW\": [{\"NAME\": \"KIN_X\", \"STATEMENT\": \"dx/dt = v_x\", \"REFS\": [\"t\", \"v_x\", \"x\"], \"ROLE\": \"EOM(x)\", \"EQUATION\": \"D(x,t)=v_x\"}, {\"NAME\": \"KIN_Z\", \"STATEMENT\": \"dz/dt = v_z\", \"REFS\": [\"t\", \"v_z\", \"z\"], \"ROLE\": \"EOM(z)\", \"EQUATION\": \"D(z,t)=v_z\"}, {\"NAME\": \"EOM_X\", \"STATEMENT\": \"m dv_x/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_x\"], \"ROLE\": \"EOM(v_x)\", \"EQUATION\": \"m*D(v_x,t)=0\"}, {\"NAME\": \"EOM_Z\", \"STATEMENT\": \"m dv_z/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_z\"], \"ROLE\": \"EOM(v_z)\", \"EQUATION\": \"m*D(v_z,t)=0\"}], \"ASSUMPTION\": [{\"NAME\": \"point_mass\", \"PROPOSITION\": \"the body is treated as a point mass\", \"REFS\": [\"m\"]}]}, \"BIND\": {}, \"VALUES\": {}, \"ANSWERS\": {}}]}"
]
},
"computed": "digests by existing TPC-PY functions over literal data",
"expected": "[\"OK\",[\"ASK\",[[\"AIR-LINEAR\",\"1.0.0\",\"5f3fe27b42378bce0830b0d0959f892f4a8e73b12b540ae877e39e6439d08b4d\"],[\"AIR-QUADRATIC\",\"1.0.0\",\"6fb53c3a6546151eead2bd6e72e9cf8334f3a2040ad0ee2f5b988ec96d6fc852\"],[\"GRAV-UNIFORM\",\"1.0.0\",\"24877ccb5c8ec300d29ed82ce6650592f35cf8899a3d878ccce9c08d4c72c025\"],[\"MATH\",\"1.0.0\",\"8f39a356f35527b901fcee012764590f0819c8ffdeccad4bc05195ce3d2e0bcf\"]]],[\"CLAIMS\",[]]]",
"fn": "interview_check",
"hand_checked": false,
"name": "I32 answered before any module: every module asked"
},
{
"args": {
"answer": [
{
"AT": 4,
"CHOSEN": [
"GRAV-UNIFORM"
],
"COVERED": [
[
"AIR-LINEAR",
"1.0.0",
"5f3fe27b42378bce0830b0d0959f892f4a8e73b12b540ae877e39e6439d08b4d"
],
[
"AIR-QUADRATIC",
"1.0.0",
"6fb53c3a6546151eead2bd6e72e9cf8334f3a2040ad0ee2f5b988ec96d6fc852"
],
[
"GRAV-UNIFORM",
"1.0.0",
"24877ccb5c8ec300d29ed82ce6650592f35cf8899a3d878ccce9c08d4c72c025"
],
[
"MATH",
"1.0.0",
"8f39a356f35527b901fcee012764590f0819c8ffdeccad4bc05195ce3d2e0bcf"
]
]
}
],
"carried": [],
"claims": [
{
"ANSWERS": {},
"BIND": {
"HEIGHT": [
"z"
],
"MASS": [
"m"
],
"UP_VELOCITY": [
"v_z"
]
},
"DIGEST": "24877ccb5c8ec300d29ed82ce6650592f35cf8899a3d878ccce9c08d4c72c025",
"ID": "GRAV-UNIFORM",
"VALUES": {
"h_max": {
"UNIT": "m",
"VALUE": "100"
}
},
"VERSION": "1.0.0"
}
],
"lines": [
{
"ACT": "MODULE ADD",
"DATE": "2026-10-01",
"DIGEST": "5f3fe27b42378bce0830b0d0959f892f4a8e73b12b540ae877e39e6439d08b4d",
"ID": "AIR-LINEAR",
"VERSION": "1.0.0"
},
{
"ACT": "MODULE ADD",
"DATE": "2026-10-01",
"DIGEST": "6fb53c3a6546151eead2bd6e72e9cf8334f3a2040ad0ee2f5b988ec96d6fc852",
"ID": "AIR-QUADRATIC",
"VERSION": "1.0.0"
},
{
"ACT": "MODULE ADD",
"DATE": "2026-10-01",
"DIGEST": "24877ccb5c8ec300d29ed82ce6650592f35cf8899a3d878ccce9c08d4c72c025",
"ID": "GRAV-UNIFORM",
"VERSION": "1.0.0"
},
{
"ACT": "MODULE ADD",
"DATE": "2026-10-01",
"DIGEST": "8f39a356f35527b901fcee012764590f0819c8ffdeccad4bc05195ce3d2e0bcf",
"ID": "MATH",
"VERSION": "1.0.0"
},
{
"ACT": "MODULE WITHDRAW",
"DATE": "2026-10-02",
"ID": "GRAV-UNIFORM",
"REASON": "the weight's sign was reversed in the binding page's preview",
"VERSION": "1.0.0"
}
],
"modified": [],
"modules": [
"{\"ID\": \"AIR-LINEAR\", \"VERSION\": \"1.0.0\", \"TITLE\": \"Air resistance at sea level, linear in the speed (Stokes drag on a sphere)\", \"SOURCE\": \"ISO 2533:1975, Standard Atmosphere, sea-level values: density 1.225 kg m-3, dynamic viscosity 1.7894e-5 Pa s\", \"PREREQUISITES\": [{\"SLOT\": \"VELOCITY\", \"KIND\": \"DOF\", \"DIMENSION\": \"L1 T-1\", \"MIN\": 1, \"MAX\": 3, \"LABEL\": \"the velocity components of the body, one per axis\"}], \"PARAMETERS\": [{\"NAME\": \"rho_air\", \"DIMENSION\": \"L-3 M1\", \"SUPPLY\": \"DECLARED\", \"VALUE\": \"1.225\", \"UNIT\": \"kg m-3\", \"OVERRIDABLE\": \"NO\", \"LABEL\": \"the density of air at sea level\"}, {\"NAME\": \"mu_air\", \"DIMENSION\": \"L-1 M1 T-1\", \"SUPPLY\": \"DECLARED\", \"VALUE\": \"1.7894e-5\", \"UNIT\": \"Pa s\", \"OVERRIDABLE\": \"NO\", \"LABEL\": \"the dynamic viscosity of air at sea level\"}, {\"NAME\": \"pi_c\", \"DIMENSION\": \"1\", \"SUPPLY\": \"DECLARED\", \"VALUE\": \"3.141592653589793\", \"UNIT\": \"1\", \"OVERRIDABLE\": \"NO\", \"LABEL\": \"pi, to 16 significant digits\"}, {\"NAME\": \"R_s\", \"DIMENSION\": \"L1\", \"SUPPLY\": \"AUTHOR\", \"LABEL\": \"the radius of the sphere\"}], \"SUMS\": [{\"NAME\": \"SPEED2\", \"OVER\": \"VELOCITY\", \"EACH\": \"VELOCITY^2\"}], \"TERMS\": [{\"TARGET\": \"VELOCITY\", \"SIGN\": \"-\", \"EXPR\": \"6*pi_c*mu_air*R_s*VELOCITY\", \"LABEL\": \"the linear (Stokes) drag\"}], \"ASSUMPTIONS\": [{\"NAME\": \"air_still\", \"PROPOSITION\": \"the air is at rest in the frame of the body's velocity\", \"REFS\": [\"VELOCITY\"]}, {\"NAME\": \"air_uniform\", \"PROPOSITION\": \"the air density is uniform over the region of motion\", \"REFS\": [\"rho_air\"]}, {\"NAME\": \"drag_sphere\", \"PROPOSITION\": \"the body is a rigid sphere of radius R_s\", \"REFS\": [\"R_s\"]}], \"BOUNDARIES\": [{\"NAME\": \"drag_linear_regime\", \"PREDICATE\": \"2 rho_air |v| R_s / mu_air < 1: the regime of the linear law\", \"CONDITION\": \"mu_air != 0 and SPEED2 >= 0 and 2*rho_air*sqrt(SPEED2)*R_s/mu_air < 1\"}], \"NOT_CHOSEN\": \"No linear (Stokes) air resistance.\", \"NOT_INCLUDED\": [\"No wind: the air is at rest.\", \"No change of air density or viscosity with altitude or temperature.\", \"No drag outside the regime of the linear law.\"], \"EXCLUDES\": [], \"INTERACTS_WITH\": [], \"TEST_BINDINGS\": [{\"NAME\": \"PROJECTILE_2D\", \"TPK\": {\"DOF\": [{\"NAME\": \"t\", \"DIMENSION\": \"T1\"}, {\"NAME\": \"x\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"z\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"v_x\", \"DIMENSION\": \"L1 T-1\"}, {\"NAME\": \"v_z\", \"DIMENSION\": \"L1 T-1\"}], \"CONSTANT\": [{\"NAME\": \"m\", \"DIMENSION\": \"M1\"}], \"LAW\": [{\"NAME\": \"KIN_X\", \"STATEMENT\": \"dx/dt = v_x\", \"REFS\": [\"t\", \"v_x\", \"x\"], \"ROLE\": \"EOM(x)\", \"EQUATION\": \"D(x,t)=v_x\"}, {\"NAME\": \"KIN_Z\", \"STATEMENT\": \"dz/dt = v_z\", \"REFS\": [\"t\", \"v_z\", \"z\"], \"ROLE\": \"EOM(z)\", \"EQUATION\": \"D(z,t)=v_z\"}, {\"NAME\": \"EOM_X\", \"STATEMENT\": \"m dv_x/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_x\"], \"ROLE\": \"EOM(v_x)\", \"EQUATION\": \"m*D(v_x,t)=0\"}, {\"NAME\": \"EOM_Z\", \"STATEMENT\": \"m dv_z/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_z\"], \"ROLE\": \"EOM(v_z)\", \"EQUATION\": \"m*D(v_z,t)=0\"}], \"ASSUMPTION\": [{\"NAME\": \"point_mass\", \"PROPOSITION\": \"the body is treated as a point mass\", \"REFS\": [\"m\"]}]}, \"BIND\": {\"VELOCITY\": [\"v_x\", \"v_z\"]}, \"VALUES\": {\"R_s\": {}}, \"ANSWERS\": {}}]}",
"{\"ID\": \"AIR-QUADRATIC\", \"VERSION\": \"1.0.0\", \"TITLE\": \"Air resistance at sea level, quadratic in the speed\", \"SOURCE\": \"ISO 2533:1975, Standard Atmosphere, sea-level values: density 1.225 kg m-3, dynamic viscosity 1.7894e-5 Pa s\", \"PREREQUISITES\": [{\"SLOT\": \"VELOCITY\", \"KIND\": \"DOF\", \"DIMENSION\": \"L1 T-1\", \"MIN\": 1, \"MAX\": 3, \"LABEL\": \"the velocity components of the body, one per axis\"}], \"PARAMETERS\": [{\"NAME\": \"rho_air\", \"DIMENSION\": \"L-3 M1\", \"SUPPLY\": \"DECLARED\", \"VALUE\": \"1.225\", \"UNIT\": \"kg m-3\", \"OVERRIDABLE\": \"NO\", \"LABEL\": \"the density of air at sea level\"}, {\"NAME\": \"mu_air\", \"DIMENSION\": \"L-1 M1 T-1\", \"SUPPLY\": \"DECLARED\", \"VALUE\": \"1.7894e-5\", \"UNIT\": \"Pa s\", \"OVERRIDABLE\": \"NO\", \"LABEL\": \"the dynamic viscosity of air at sea level\"}, {\"NAME\": \"C_d\", \"DIMENSION\": \"1\", \"SUPPLY\": \"AUTHOR\", \"LABEL\": \"the drag coefficient of the body\"}, {\"NAME\": \"A_ref\", \"DIMENSION\": \"L2\", \"SUPPLY\": \"AUTHOR\", \"LABEL\": \"the reference area of the drag coefficient\"}, {\"NAME\": \"L_ref\", \"DIMENSION\": \"L1\", \"SUPPLY\": \"AUTHOR\", \"LABEL\": \"the reference length of the Reynolds number\"}], \"SUMS\": [{\"NAME\": \"SPEED2\", \"OVER\": \"VELOCITY\", \"EACH\": \"VELOCITY^2\"}], \"TERMS\": [{\"TARGET\": \"VELOCITY\", \"SIGN\": \"-\", \"EXPR\": \"0.5*rho_air*C_d*A_ref*sqrt(SPEED2)*VELOCITY\", \"LABEL\": \"the quadratic drag\"}], \"ASSUMPTIONS\": [{\"NAME\": \"air_still\", \"PROPOSITION\": \"the air is at rest in the frame of the body's velocity\", \"REFS\": [\"VELOCITY\"]}, {\"NAME\": \"air_uniform\", \"PROPOSITION\": \"the air density is uniform over the region of motion\", \"REFS\": [\"rho_air\"]}, {\"NAME\": \"drag_cd_constant\", \"PROPOSITION\": \"the drag coefficient C_d is constant over the motion\", \"REFS\": [\"C_d\"]}, {\"NAME\": \"drag_no_lift\", \"PROPOSITION\": \"the body experiences no lift force\", \"REFS\": [\"VELOCITY\"]}, {\"NAME\": \"drag_no_magnus\", \"PROPOSITION\": \"the body experiences no Magnus force\", \"REFS\": [\"VELOCITY\"]}], \"BOUNDARIES\": [{\"NAME\": \"drag_quadratic_regime\", \"PREDICATE\": \"1e3 < rho_air |v| L_ref / mu_air < 2e5: the Reynolds window of the quadratic law\", \"CONDITION\": \"mu_air != 0 and SPEED2 >= 0 and rho_air*sqrt(SPEED2)*L_ref/mu_air > 1000 and rho_air*sqrt(SPEED2)*L_ref/mu_air < 200000\"}], \"NOT_CHOSEN\": \"No quadratic air resistance.\", \"NOT_INCLUDED\": [\"No wind: the air is at rest.\", \"No change of air density or viscosity with altitude or temperature.\", \"No lift, Magnus or added-mass force.\", \"No drag outside the Reynolds window of the quadratic law.\"], \"EXCLUDES\": [\"AIR-LINEAR\"], \"INTERACTS_WITH\": [], \"TEST_BINDINGS\": [{\"NAME\": \"PROJECTILE_2D\", \"TPK\": {\"DOF\": [{\"NAME\": \"t\", \"DIMENSION\": \"T1\"}, {\"NAME\": \"x\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"z\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"v_x\", \"DIMENSION\": \"L1 T-1\"}, {\"NAME\": \"v_z\", \"DIMENSION\": \"L1 T-1\"}], \"CONSTANT\": [{\"NAME\": \"m\", \"DIMENSION\": \"M1\"}], \"LAW\": [{\"NAME\": \"KIN_X\", \"STATEMENT\": \"dx/dt = v_x\", \"REFS\": [\"t\", \"v_x\", \"x\"], \"ROLE\": \"EOM(x)\", \"EQUATION\": \"D(x,t)=v_x\"}, {\"NAME\": \"KIN_Z\", \"STATEMENT\": \"dz/dt = v_z\", \"REFS\": [\"t\", \"v_z\", \"z\"], \"ROLE\": \"EOM(z)\", \"EQUATION\": \"D(z,t)=v_z\"}, {\"NAME\": \"EOM_X\", \"STATEMENT\": \"m dv_x/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_x\"], \"ROLE\": \"EOM(v_x)\", \"EQUATION\": \"m*D(v_x,t)=0\"}, {\"NAME\": \"EOM_Z\", \"STATEMENT\": \"m dv_z/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_z\"], \"ROLE\": \"EOM(v_z)\", \"EQUATION\": \"m*D(v_z,t)=0\"}], \"ASSUMPTION\": [{\"NAME\": \"point_mass\", \"PROPOSITION\": \"the body is treated as a point mass\", \"REFS\": [\"m\"]}]}, \"BIND\": {\"VELOCITY\": [\"v_x\", \"v_z\"]}, \"VALUES\": {\"A_ref\": {}, \"C_d\": {}, \"L_ref\": {}}, \"ANSWERS\": {}}]}",
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it acts in this kernel only where one of your own laws states it.\", \"NO_LINE\": \"No buoyancy: the air's upthrust on the body is not included.\"}], \"TEST_BINDINGS\": [{\"NAME\": \"PROJECTILE_2D\", \"TPK\": {\"DOF\": [{\"NAME\": \"t\", \"DIMENSION\": \"T1\"}, {\"NAME\": \"x\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"z\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"v_x\", \"DIMENSION\": \"L1 T-1\"}, {\"NAME\": \"v_z\", \"DIMENSION\": \"L1 T-1\"}], \"CONSTANT\": [{\"NAME\": \"m\", \"DIMENSION\": \"M1\"}], \"LAW\": [{\"NAME\": \"KIN_X\", \"STATEMENT\": \"dx/dt = v_x\", \"REFS\": [\"t\", \"v_x\", \"x\"], \"ROLE\": \"EOM(x)\", \"EQUATION\": \"D(x,t)=v_x\"}, {\"NAME\": \"KIN_Z\", \"STATEMENT\": \"dz/dt = v_z\", \"REFS\": [\"t\", \"v_z\", \"z\"], \"ROLE\": \"EOM(z)\", \"EQUATION\": \"D(z,t)=v_z\"}, {\"NAME\": \"EOM_X\", \"STATEMENT\": \"m dv_x/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_x\"], \"ROLE\": \"EOM(v_x)\", \"EQUATION\": \"m*D(v_x,t)=0\"}, {\"NAME\": \"EOM_Z\", \"STATEMENT\": \"m dv_z/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_z\"], \"ROLE\": \"EOM(v_z)\", \"EQUATION\": \"m*D(v_z,t)=0\"}], \"ASSUMPTION\": [{\"NAME\": \"point_mass\", \"PROPOSITION\": \"the body is treated as a point mass\", \"REFS\": [\"m\"]}]}, \"BIND\": {\"HEIGHT\": [\"z\"], \"MASS\": [\"m\"], \"UP_VELOCITY\": [\"v_z\"]}, \"VALUES\": {\"h_max\": {\"VALUE\": \"100\", \"UNIT\": \"m\"}}, \"ANSWERS\": {}}, {\"NAME\": \"TABLE\", \"TPK\": {\"DOF\": [{\"NAME\": \"t\", \"DIMENSION\": \"T1\"}, {\"NAME\": \"x\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"z\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"v_x\", \"DIMENSION\": \"L1 T-1\"}, {\"NAME\": \"v_z\", \"DIMENSION\": \"L1 T-1\"}], \"CONSTANT\": [{\"NAME\": \"m\", \"DIMENSION\": \"M1\"}], \"LAW\": [{\"NAME\": \"KIN_X\", \"STATEMENT\": \"dx/dt = v_x\", \"REFS\": [\"t\", \"v_x\", \"x\"], \"ROLE\": \"EOM(x)\", \"EQUATION\": \"D(x,t)=v_x\"}, {\"NAME\": \"KIN_Z\", \"STATEMENT\": \"dz/dt = v_z\", \"REFS\": [\"t\", \"v_z\", \"z\"], \"ROLE\": \"CONSTRAINT\", \"EQUATION\": \"D(z,t)=v_z\"}, {\"NAME\": \"EOM_X\", \"STATEMENT\": \"m dv_x/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_x\"], \"ROLE\": \"EOM(v_x)\", \"EQUATION\": \"m*D(v_x,t)=0\"}], \"CONSTRAINT\": [{\"NAME\": \"C_Z\", \"TARGET\": \"z\", \"ACTION\": \"FIX\", \"VALUE\": \"0\", \"UNIT\": \"m\", \"STATEMENT\": \"the puck stays on the table top, z = 0\"}, {\"NAME\": \"C_VZ\", \"TARGET\": \"v_z\", \"ACTION\": \"FIX\", \"VALUE\": \"0\", \"UNIT\": \"m s-1\", \"STATEMENT\": \"the puck has no vertical velocity\"}]}, \"BIND\": {\"HEIGHT\": [\"z\"], \"MASS\": [\"m\"], \"UP_VELOCITY\": [\"v_z\"]}, \"VALUES\": {\"h_max\": {\"VALUE\": \"1\", \"UNIT\": \"m\"}}, \"ANSWERS\": {\"FIXED:v_z\": \"YES\"}}]}",
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"fn": "interview_check",
"hand_checked": true,
"name": "I33 a pinned claim whose version was WITHDRAWN after the answer: kept"
},
{
"args": {
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{
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"lines": [
{
"ACT": "MODULE ADD",
"DATE": "2026-10-01",
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"{\"ID\": \"AIR-LINEAR\", \"VERSION\": \"1.0.0\", \"TITLE\": \"Air resistance at sea level, linear in the speed (Stokes drag on a sphere)\", \"SOURCE\": \"ISO 2533:1975, Standard Atmosphere, sea-level values: density 1.225 kg m-3, dynamic viscosity 1.7894e-5 Pa s\", \"PREREQUISITES\": [{\"SLOT\": \"VELOCITY\", \"KIND\": \"DOF\", \"DIMENSION\": \"L1 T-1\", \"MIN\": 1, \"MAX\": 3, \"LABEL\": \"the velocity components of the body, one per axis\"}], \"PARAMETERS\": [{\"NAME\": \"rho_air\", \"DIMENSION\": \"L-3 M1\", \"SUPPLY\": \"DECLARED\", \"VALUE\": \"1.225\", \"UNIT\": \"kg m-3\", \"OVERRIDABLE\": \"NO\", \"LABEL\": \"the density of air at sea level\"}, {\"NAME\": \"mu_air\", \"DIMENSION\": \"L-1 M1 T-1\", \"SUPPLY\": \"DECLARED\", \"VALUE\": \"1.7894e-5\", \"UNIT\": \"Pa s\", \"OVERRIDABLE\": \"NO\", \"LABEL\": \"the dynamic viscosity of air at sea level\"}, {\"NAME\": \"pi_c\", \"DIMENSION\": \"1\", \"SUPPLY\": \"DECLARED\", \"VALUE\": \"3.141592653589793\", \"UNIT\": \"1\", \"OVERRIDABLE\": \"NO\", \"LABEL\": \"pi, to 16 significant digits\"}, {\"NAME\": \"R_s\", \"DIMENSION\": \"L1\", \"SUPPLY\": \"AUTHOR\", \"LABEL\": \"the radius of the sphere\"}], \"SUMS\": [{\"NAME\": \"SPEED2\", \"OVER\": \"VELOCITY\", \"EACH\": \"VELOCITY^2\"}], \"TERMS\": [{\"TARGET\": \"VELOCITY\", \"SIGN\": \"-\", \"EXPR\": \"6*pi_c*mu_air*R_s*VELOCITY\", \"LABEL\": \"the linear (Stokes) drag\"}], \"ASSUMPTIONS\": [{\"NAME\": \"air_still\", \"PROPOSITION\": \"the air is at rest in the frame of the body's velocity\", \"REFS\": [\"VELOCITY\"]}, {\"NAME\": \"air_uniform\", \"PROPOSITION\": \"the air density is uniform over the region of motion\", \"REFS\": [\"rho_air\"]}, {\"NAME\": \"drag_sphere\", \"PROPOSITION\": \"the body is a rigid sphere of radius R_s\", \"REFS\": [\"R_s\"]}], \"BOUNDARIES\": [{\"NAME\": \"drag_linear_regime\", \"PREDICATE\": \"2 rho_air |v| R_s / mu_air < 1: the regime of the linear law\", \"CONDITION\": \"mu_air != 0 and SPEED2 >= 0 and 2*rho_air*sqrt(SPEED2)*R_s/mu_air < 1\"}], \"NOT_CHOSEN\": \"No linear (Stokes) air resistance.\", \"NOT_INCLUDED\": [\"No wind: the air is at rest.\", \"No change of air density or viscosity with altitude or temperature.\", \"No drag outside the regime of the linear law.\"], \"EXCLUDES\": [], \"INTERACTS_WITH\": [], \"TEST_BINDINGS\": [{\"NAME\": \"PROJECTILE_2D\", \"TPK\": {\"DOF\": [{\"NAME\": \"t\", \"DIMENSION\": \"T1\"}, {\"NAME\": \"x\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"z\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"v_x\", \"DIMENSION\": \"L1 T-1\"}, {\"NAME\": \"v_z\", \"DIMENSION\": \"L1 T-1\"}], \"CONSTANT\": [{\"NAME\": \"m\", \"DIMENSION\": \"M1\"}], \"LAW\": [{\"NAME\": \"KIN_X\", \"STATEMENT\": \"dx/dt = v_x\", \"REFS\": [\"t\", \"v_x\", \"x\"], \"ROLE\": \"EOM(x)\", \"EQUATION\": \"D(x,t)=v_x\"}, {\"NAME\": \"KIN_Z\", \"STATEMENT\": \"dz/dt = v_z\", \"REFS\": [\"t\", \"v_z\", \"z\"], \"ROLE\": \"EOM(z)\", \"EQUATION\": \"D(z,t)=v_z\"}, {\"NAME\": \"EOM_X\", \"STATEMENT\": \"m dv_x/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_x\"], \"ROLE\": \"EOM(v_x)\", \"EQUATION\": \"m*D(v_x,t)=0\"}, {\"NAME\": \"EOM_Z\", \"STATEMENT\": \"m dv_z/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_z\"], \"ROLE\": \"EOM(v_z)\", \"EQUATION\": \"m*D(v_z,t)=0\"}], \"ASSUMPTION\": [{\"NAME\": \"point_mass\", \"PROPOSITION\": \"the body is treated as a point mass\", \"REFS\": [\"m\"]}]}, \"BIND\": {\"VELOCITY\": [\"v_x\", \"v_z\"]}, \"VALUES\": {\"R_s\": {}}, \"ANSWERS\": {}}]}",
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"{\"ID\": \"AIR-LINEAR\", \"VERSION\": \"1.0.0\", \"TITLE\": \"Air resistance at sea level, linear in the speed (Stokes drag on a sphere)\", \"SOURCE\": \"ISO 2533:1975, Standard Atmosphere, sea-level values: density 1.225 kg m-3, dynamic viscosity 1.7894e-5 Pa s\", \"PREREQUISITES\": [{\"SLOT\": \"VELOCITY\", \"KIND\": \"DOF\", \"DIMENSION\": \"L1 T-1\", \"MIN\": 1, \"MAX\": 3, \"LABEL\": \"the velocity components of the body, one per axis\"}], \"PARAMETERS\": [{\"NAME\": \"rho_air\", \"DIMENSION\": \"L-3 M1\", \"SUPPLY\": \"DECLARED\", \"VALUE\": \"1.225\", \"UNIT\": \"kg m-3\", \"OVERRIDABLE\": \"NO\", \"LABEL\": \"the density of air at sea level\"}, {\"NAME\": \"mu_air\", \"DIMENSION\": \"L-1 M1 T-1\", \"SUPPLY\": \"DECLARED\", \"VALUE\": \"1.7894e-5\", \"UNIT\": \"Pa s\", \"OVERRIDABLE\": \"NO\", \"LABEL\": \"the dynamic viscosity of air at sea level\"}, {\"NAME\": \"pi_c\", \"DIMENSION\": \"1\", \"SUPPLY\": \"DECLARED\", \"VALUE\": \"3.141592653589793\", \"UNIT\": \"1\", \"OVERRIDABLE\": \"NO\", \"LABEL\": \"pi, to 16 significant digits\"}, {\"NAME\": \"R_s\", \"DIMENSION\": \"L1\", \"SUPPLY\": \"AUTHOR\", \"LABEL\": \"the radius of the sphere\"}], \"SUMS\": [{\"NAME\": \"SPEED2\", \"OVER\": \"VELOCITY\", \"EACH\": \"VELOCITY^2\"}], \"TERMS\": [{\"TARGET\": \"VELOCITY\", \"SIGN\": \"-\", \"EXPR\": \"6*pi_c*mu_air*R_s*VELOCITY\", \"LABEL\": \"the linear (Stokes) drag\"}], \"ASSUMPTIONS\": [{\"NAME\": \"air_still\", \"PROPOSITION\": \"the air is at rest in the frame of the body's velocity\", \"REFS\": [\"VELOCITY\"]}, {\"NAME\": \"air_uniform\", \"PROPOSITION\": \"the air density is uniform over the region of motion\", \"REFS\": [\"rho_air\"]}, {\"NAME\": \"drag_sphere\", \"PROPOSITION\": \"the body is a rigid sphere of radius R_s\", \"REFS\": [\"R_s\"]}], \"BOUNDARIES\": [{\"NAME\": \"drag_linear_regime\", \"PREDICATE\": \"2 rho_air |v| R_s / mu_air < 1: the regime of the linear law\", \"CONDITION\": \"mu_air != 0 and SPEED2 >= 0 and 2*rho_air*sqrt(SPEED2)*R_s/mu_air < 1\"}], \"NOT_CHOSEN\": \"No linear (Stokes) air resistance.\", \"NOT_INCLUDED\": [\"No wind: the air is at rest.\", \"No change of air density or viscosity with altitude or temperature.\", \"No drag outside the regime of the linear law.\"], \"EXCLUDES\": [], \"INTERACTS_WITH\": [], \"TEST_BINDINGS\": [{\"NAME\": \"PROJECTILE_2D\", \"TPK\": {\"DOF\": [{\"NAME\": \"t\", \"DIMENSION\": \"T1\"}, {\"NAME\": \"x\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"z\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"v_x\", \"DIMENSION\": \"L1 T-1\"}, {\"NAME\": \"v_z\", \"DIMENSION\": \"L1 T-1\"}], \"CONSTANT\": [{\"NAME\": \"m\", \"DIMENSION\": \"M1\"}], \"LAW\": [{\"NAME\": \"KIN_X\", \"STATEMENT\": \"dx/dt = v_x\", \"REFS\": [\"t\", \"v_x\", \"x\"], \"ROLE\": \"EOM(x)\", \"EQUATION\": \"D(x,t)=v_x\"}, {\"NAME\": \"KIN_Z\", \"STATEMENT\": \"dz/dt = v_z\", \"REFS\": [\"t\", \"v_z\", \"z\"], \"ROLE\": \"EOM(z)\", \"EQUATION\": \"D(z,t)=v_z\"}, {\"NAME\": \"EOM_X\", \"STATEMENT\": \"m dv_x/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_x\"], \"ROLE\": \"EOM(v_x)\", \"EQUATION\": \"m*D(v_x,t)=0\"}, {\"NAME\": \"EOM_Z\", \"STATEMENT\": \"m dv_z/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_z\"], \"ROLE\": \"EOM(v_z)\", \"EQUATION\": \"m*D(v_z,t)=0\"}], \"ASSUMPTION\": [{\"NAME\": \"point_mass\", \"PROPOSITION\": \"the body is treated as a point mass\", \"REFS\": [\"m\"]}]}, \"BIND\": {\"VELOCITY\": [\"v_x\", \"v_z\"]}, \"VALUES\": {\"R_s\": {}}, \"ANSWERS\": {}}]}",
"{\"ID\": \"AIR-QUADRATIC\", \"VERSION\": \"1.0.0\", \"TITLE\": \"Air resistance at sea level, quadratic in the speed\", \"SOURCE\": \"ISO 2533:1975, Standard Atmosphere, sea-level values: density 1.225 kg m-3, dynamic viscosity 1.7894e-5 Pa s\", \"PREREQUISITES\": [{\"SLOT\": \"VELOCITY\", \"KIND\": \"DOF\", \"DIMENSION\": \"L1 T-1\", \"MIN\": 1, \"MAX\": 3, \"LABEL\": \"the velocity components of the body, one per axis\"}], \"PARAMETERS\": [{\"NAME\": \"rho_air\", \"DIMENSION\": \"L-3 M1\", \"SUPPLY\": \"DECLARED\", \"VALUE\": \"1.225\", \"UNIT\": \"kg m-3\", \"OVERRIDABLE\": \"NO\", \"LABEL\": \"the density of air at sea level\"}, {\"NAME\": \"mu_air\", \"DIMENSION\": \"L-1 M1 T-1\", \"SUPPLY\": \"DECLARED\", \"VALUE\": \"1.7894e-5\", \"UNIT\": \"Pa s\", \"OVERRIDABLE\": \"NO\", \"LABEL\": \"the dynamic viscosity of air at sea level\"}, {\"NAME\": \"C_d\", \"DIMENSION\": \"1\", \"SUPPLY\": \"AUTHOR\", \"LABEL\": \"the drag coefficient of the body\"}, {\"NAME\": \"A_ref\", \"DIMENSION\": \"L2\", \"SUPPLY\": \"AUTHOR\", \"LABEL\": \"the reference area of the drag coefficient\"}, {\"NAME\": \"L_ref\", \"DIMENSION\": \"L1\", \"SUPPLY\": \"AUTHOR\", \"LABEL\": \"the reference length of the Reynolds number\"}], \"SUMS\": [{\"NAME\": \"SPEED2\", \"OVER\": \"VELOCITY\", \"EACH\": \"VELOCITY^2\"}], \"TERMS\": [{\"TARGET\": \"VELOCITY\", \"SIGN\": \"-\", \"EXPR\": \"0.5*rho_air*C_d*A_ref*sqrt(SPEED2)*VELOCITY\", \"LABEL\": \"the quadratic drag\"}], \"ASSUMPTIONS\": [{\"NAME\": \"air_still\", \"PROPOSITION\": \"the air is at rest in the frame of the body's velocity\", \"REFS\": [\"VELOCITY\"]}, {\"NAME\": \"air_uniform\", \"PROPOSITION\": \"the air density is uniform over the region of motion\", \"REFS\": [\"rho_air\"]}, {\"NAME\": \"drag_cd_constant\", \"PROPOSITION\": \"the drag coefficient C_d is constant over the motion\", \"REFS\": [\"C_d\"]}, {\"NAME\": \"drag_no_lift\", \"PROPOSITION\": \"the body experiences no lift force\", \"REFS\": [\"VELOCITY\"]}, {\"NAME\": \"drag_no_magnus\", \"PROPOSITION\": \"the body experiences no Magnus force\", \"REFS\": [\"VELOCITY\"]}], \"BOUNDARIES\": [{\"NAME\": \"drag_quadratic_regime\", \"PREDICATE\": \"1e3 < rho_air |v| L_ref / mu_air < 2e5: the Reynolds window of the quadratic law\", \"CONDITION\": \"mu_air != 0 and SPEED2 >= 0 and rho_air*sqrt(SPEED2)*L_ref/mu_air > 1000 and rho_air*sqrt(SPEED2)*L_ref/mu_air < 200000\"}], \"NOT_CHOSEN\": \"No quadratic air resistance.\", \"NOT_INCLUDED\": [\"No wind: the air is at rest.\", \"No change of air density or viscosity with altitude or temperature.\", \"No lift, Magnus or added-mass force.\", \"No drag outside the Reynolds window of the quadratic law.\"], \"EXCLUDES\": [\"AIR-LINEAR\"], \"INTERACTS_WITH\": [], \"TEST_BINDINGS\": [{\"NAME\": \"PROJECTILE_2D\", \"TPK\": {\"DOF\": [{\"NAME\": \"t\", \"DIMENSION\": \"T1\"}, {\"NAME\": \"x\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"z\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"v_x\", \"DIMENSION\": \"L1 T-1\"}, {\"NAME\": \"v_z\", \"DIMENSION\": \"L1 T-1\"}], \"CONSTANT\": [{\"NAME\": \"m\", \"DIMENSION\": \"M1\"}], \"LAW\": [{\"NAME\": \"KIN_X\", \"STATEMENT\": \"dx/dt = v_x\", \"REFS\": [\"t\", \"v_x\", \"x\"], \"ROLE\": \"EOM(x)\", \"EQUATION\": \"D(x,t)=v_x\"}, {\"NAME\": \"KIN_Z\", \"STATEMENT\": \"dz/dt = v_z\", \"REFS\": [\"t\", \"v_z\", \"z\"], \"ROLE\": \"EOM(z)\", \"EQUATION\": \"D(z,t)=v_z\"}, {\"NAME\": \"EOM_X\", \"STATEMENT\": \"m dv_x/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_x\"], \"ROLE\": \"EOM(v_x)\", \"EQUATION\": \"m*D(v_x,t)=0\"}, {\"NAME\": \"EOM_Z\", \"STATEMENT\": \"m dv_z/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_z\"], \"ROLE\": \"EOM(v_z)\", \"EQUATION\": \"m*D(v_z,t)=0\"}], \"ASSUMPTION\": [{\"NAME\": \"point_mass\", \"PROPOSITION\": \"the body is treated as a point mass\", \"REFS\": [\"m\"]}]}, \"BIND\": {\"VELOCITY\": [\"v_x\", \"v_z\"]}, \"VALUES\": {\"A_ref\": {}, \"C_d\": {}, \"L_ref\": {}}, \"ANSWERS\": {}}]}",
"{\"ID\": \"GRAV-UNIFORM\", \"VERSION\": \"1.0.0\", \"TITLE\": \"Uniform gravity at the standard value g_n\", \"SOURCE\": \"g_n = 9.80665 m s-2, exact by definition: 3rd CGPM (1901), declaration on the unit of mass and on the definition of weight\", \"PREREQUISITES\": [{\"SLOT\": \"MASS\", \"KIND\": \"CONSTANT\", \"DIMENSION\": \"M1\", \"MIN\": 1, \"MAX\": 1, \"LABEL\": \"the mass of the body\"}, {\"SLOT\": \"UP_VELOCITY\", \"KIND\": \"DOF\", \"DIMENSION\": \"L1 T-1\", \"MIN\": 1, \"MAX\": 1, \"LABEL\": \"the velocity component pointing up; its equation of motion receives the weight\"}, {\"SLOT\": \"HEIGHT\", \"KIND\": \"DOF\", \"DIMENSION\": \"L1\", \"MIN\": 1, \"MAX\": 1, \"LABEL\": \"the position along the same upward axis\"}], \"PARAMETERS\": [{\"NAME\": \"g_n\", \"DIMENSION\": \"L1 T-2\", \"SUPPLY\": \"DECLARED\", \"VALUE\": \"9.80665\", \"UNIT\": \"m s-2\", \"OVERRIDABLE\": \"NO\", \"LABEL\": \"the standard acceleration of gravity\"}, {\"NAME\": \"h_max\", \"DIMENSION\": \"L1\", \"SUPPLY\": \"AUTHOR\", \"LABEL\": \"the largest height, above or below the origin, over which the field is taken as uniform\"}], \"SUMS\": [], \"TERMS\": [{\"TARGET\": \"UP_VELOCITY\", \"SIGN\": \"-\", \"EXPR\": \"MASS*g_n\", \"LABEL\": \"the weight\"}], \"ASSUMPTIONS\": [{\"NAME\": \"gravity_uniform\", \"PROPOSITION\": \"the gravitational field is uniform over the region abs({HEIGHT}) < h_max\", \"REFS\": [\"HEIGHT\", \"h_max\"]}, {\"NAME\": \"gravity_standard\", \"PROPOSITION\": \"the local gravitational acceleration equals the conventional standard value g_n\", \"REFS\": [\"g_n\"]}, {\"NAME\": \"frame_inertial\", \"PROPOSITION\": \"the frame in which {HEIGHT} is measured is treated as inertial\", \"REFS\": [\"HEIGHT\"]}], \"BOUNDARIES\": [{\"NAME\": \"gravity_region\", \"PREDICATE\": \"abs({HEIGHT}) < h_max\", \"CONDITION\": \"abs(HEIGHT) < h_max\"}], \"NOT_CHOSEN\": \"No gravity: no weight acts on any DOF.\", \"NOT_INCLUDED\": [\"No variation of gravity with height or latitude beyond what g_n contains.\", \"No Earth rotation (Coriolis or centrifugal force) beyond what g_n contains.\", \"No gravity of bodies other than the Earth.\"], \"EXCLUDES\": [], \"INTERACTS_WITH\": [{\"WITH\": \"AIR-*\", \"QUESTION_ID\": \"BUOYANCY\", \"QUESTION\": \"Does the air's buoyancy (upthrust) act on the body in the system you mean?\", \"YES_LINE\": \"Buoyancy acts (your answer): no module adds it; it acts in this kernel only where one of your own laws states it.\", \"NO_LINE\": \"No buoyancy: the air's upthrust on the body is not included.\"}], \"TEST_BINDINGS\": [{\"NAME\": \"PROJECTILE_2D\", \"TPK\": {\"DOF\": [{\"NAME\": \"t\", \"DIMENSION\": \"T1\"}, {\"NAME\": \"x\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"z\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"v_x\", \"DIMENSION\": \"L1 T-1\"}, {\"NAME\": \"v_z\", \"DIMENSION\": \"L1 T-1\"}], \"CONSTANT\": [{\"NAME\": \"m\", \"DIMENSION\": \"M1\"}], \"LAW\": [{\"NAME\": \"KIN_X\", \"STATEMENT\": \"dx/dt = v_x\", \"REFS\": [\"t\", \"v_x\", \"x\"], \"ROLE\": \"EOM(x)\", \"EQUATION\": \"D(x,t)=v_x\"}, {\"NAME\": \"KIN_Z\", \"STATEMENT\": \"dz/dt = v_z\", \"REFS\": [\"t\", \"v_z\", \"z\"], \"ROLE\": \"EOM(z)\", \"EQUATION\": \"D(z,t)=v_z\"}, {\"NAME\": \"EOM_X\", \"STATEMENT\": \"m dv_x/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_x\"], \"ROLE\": \"EOM(v_x)\", \"EQUATION\": \"m*D(v_x,t)=0\"}, {\"NAME\": \"EOM_Z\", \"STATEMENT\": \"m dv_z/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_z\"], \"ROLE\": \"EOM(v_z)\", \"EQUATION\": \"m*D(v_z,t)=0\"}], \"ASSUMPTION\": [{\"NAME\": \"point_mass\", \"PROPOSITION\": \"the body is treated as a point mass\", \"REFS\": [\"m\"]}]}, \"BIND\": {\"HEIGHT\": [\"z\"], \"MASS\": [\"m\"], \"UP_VELOCITY\": [\"v_z\"]}, \"VALUES\": {\"h_max\": {\"VALUE\": \"100\", \"UNIT\": \"m\"}}, \"ANSWERS\": {}}, {\"NAME\": \"TABLE\", \"TPK\": {\"DOF\": [{\"NAME\": \"t\", \"DIMENSION\": \"T1\"}, {\"NAME\": \"x\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"z\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"v_x\", \"DIMENSION\": \"L1 T-1\"}, {\"NAME\": \"v_z\", \"DIMENSION\": \"L1 T-1\"}], \"CONSTANT\": [{\"NAME\": \"m\", \"DIMENSION\": \"M1\"}], \"LAW\": [{\"NAME\": \"KIN_X\", \"STATEMENT\": \"dx/dt = v_x\", \"REFS\": [\"t\", \"v_x\", \"x\"], \"ROLE\": \"EOM(x)\", \"EQUATION\": \"D(x,t)=v_x\"}, {\"NAME\": \"KIN_Z\", \"STATEMENT\": \"dz/dt = v_z\", \"REFS\": [\"t\", \"v_z\", \"z\"], \"ROLE\": \"CONSTRAINT\", \"EQUATION\": \"D(z,t)=v_z\"}, {\"NAME\": \"EOM_X\", \"STATEMENT\": \"m dv_x/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_x\"], \"ROLE\": \"EOM(v_x)\", \"EQUATION\": \"m*D(v_x,t)=0\"}], \"CONSTRAINT\": [{\"NAME\": \"C_Z\", \"TARGET\": \"z\", \"ACTION\": \"FIX\", \"VALUE\": \"0\", \"UNIT\": \"m\", \"STATEMENT\": \"the puck stays on the table top, z = 0\"}, {\"NAME\": \"C_VZ\", \"TARGET\": \"v_z\", \"ACTION\": \"FIX\", \"VALUE\": \"0\", \"UNIT\": \"m s-1\", \"STATEMENT\": \"the puck has no vertical velocity\"}]}, \"BIND\": {\"HEIGHT\": [\"z\"], \"MASS\": [\"m\"], \"UP_VELOCITY\": [\"v_z\"]}, \"VALUES\": {\"h_max\": {\"VALUE\": \"1\", \"UNIT\": \"m\"}}, \"ANSWERS\": {\"FIXED:v_z\": \"YES\"}}]}",
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"name": "I35 a text of a version not declared"
},
{
"args": {
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{
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"{\"ID\": \"AIR-LINEAR\", \"VERSION\": \"1.0.0\", \"TITLE\": \"Air resistance at sea level, linear in the speed (Stokes drag on a sphere)\", \"SOURCE\": \"ISO 2533:1975, Standard Atmosphere, sea-level values: density 1.225 kg m-3, dynamic viscosity 1.7894e-5 Pa s\", \"PREREQUISITES\": [{\"SLOT\": \"VELOCITY\", \"KIND\": \"DOF\", \"DIMENSION\": \"L1 T-1\", \"MIN\": 1, \"MAX\": 3, \"LABEL\": \"the velocity components of the body, one per axis\"}], \"PARAMETERS\": [{\"NAME\": \"rho_air\", \"DIMENSION\": \"L-3 M1\", \"SUPPLY\": \"DECLARED\", \"VALUE\": \"1.225\", \"UNIT\": \"kg m-3\", \"OVERRIDABLE\": \"NO\", \"LABEL\": \"the density of air at sea level\"}, {\"NAME\": \"mu_air\", \"DIMENSION\": \"L-1 M1 T-1\", \"SUPPLY\": \"DECLARED\", \"VALUE\": \"1.7894e-5\", \"UNIT\": \"Pa s\", \"OVERRIDABLE\": \"NO\", \"LABEL\": \"the dynamic viscosity of air at sea level\"}, {\"NAME\": \"pi_c\", \"DIMENSION\": \"1\", \"SUPPLY\": \"DECLARED\", \"VALUE\": \"3.141592653589793\", \"UNIT\": \"1\", \"OVERRIDABLE\": \"NO\", \"LABEL\": \"pi, to 16 significant digits\"}, {\"NAME\": \"R_s\", \"DIMENSION\": \"L1\", \"SUPPLY\": \"AUTHOR\", \"LABEL\": \"the radius of the sphere\"}], \"SUMS\": [{\"NAME\": \"SPEED2\", \"OVER\": \"VELOCITY\", \"EACH\": \"VELOCITY^2\"}], \"TERMS\": [{\"TARGET\": \"VELOCITY\", \"SIGN\": \"-\", \"EXPR\": \"6*pi_c*mu_air*R_s*VELOCITY\", \"LABEL\": \"the linear (Stokes) drag\"}], \"ASSUMPTIONS\": [{\"NAME\": \"air_still\", \"PROPOSITION\": \"the air is at rest in the frame of the body's velocity\", \"REFS\": [\"VELOCITY\"]}, {\"NAME\": \"air_uniform\", \"PROPOSITION\": \"the air density is uniform over the region of motion\", \"REFS\": [\"rho_air\"]}, {\"NAME\": \"drag_sphere\", \"PROPOSITION\": \"the body is a rigid sphere of radius R_s\", \"REFS\": [\"R_s\"]}], \"BOUNDARIES\": [{\"NAME\": \"drag_linear_regime\", \"PREDICATE\": \"2 rho_air |v| R_s / mu_air < 1: the regime of the linear law\", \"CONDITION\": \"mu_air != 0 and SPEED2 >= 0 and 2*rho_air*sqrt(SPEED2)*R_s/mu_air < 1\"}], \"NOT_CHOSEN\": \"No linear (Stokes) air resistance.\", \"NOT_INCLUDED\": [\"No wind: the air is at rest.\", \"No change of air density or viscosity with altitude or temperature.\", \"No drag outside the regime of the linear law.\"], \"EXCLUDES\": [], \"INTERACTS_WITH\": [], \"TEST_BINDINGS\": [{\"NAME\": \"PROJECTILE_2D\", \"TPK\": {\"DOF\": [{\"NAME\": \"t\", \"DIMENSION\": \"T1\"}, {\"NAME\": \"x\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"z\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"v_x\", \"DIMENSION\": \"L1 T-1\"}, {\"NAME\": \"v_z\", \"DIMENSION\": \"L1 T-1\"}], \"CONSTANT\": [{\"NAME\": \"m\", \"DIMENSION\": \"M1\"}], \"LAW\": [{\"NAME\": \"KIN_X\", \"STATEMENT\": \"dx/dt = v_x\", \"REFS\": [\"t\", \"v_x\", \"x\"], \"ROLE\": \"EOM(x)\", \"EQUATION\": \"D(x,t)=v_x\"}, {\"NAME\": \"KIN_Z\", \"STATEMENT\": \"dz/dt = v_z\", \"REFS\": [\"t\", \"v_z\", \"z\"], \"ROLE\": \"EOM(z)\", \"EQUATION\": \"D(z,t)=v_z\"}, {\"NAME\": \"EOM_X\", \"STATEMENT\": \"m dv_x/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_x\"], \"ROLE\": \"EOM(v_x)\", \"EQUATION\": \"m*D(v_x,t)=0\"}, {\"NAME\": \"EOM_Z\", \"STATEMENT\": \"m dv_z/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_z\"], \"ROLE\": \"EOM(v_z)\", \"EQUATION\": \"m*D(v_z,t)=0\"}], \"ASSUMPTION\": [{\"NAME\": \"point_mass\", \"PROPOSITION\": \"the body is treated as a point mass\", \"REFS\": [\"m\"]}]}, \"BIND\": {\"VELOCITY\": [\"v_x\", \"v_z\"]}, \"VALUES\": {\"R_s\": {}}, \"ANSWERS\": {}}]}",
"{\"ID\": \"AIR-QUADRATIC\", \"VERSION\": \"1.0.0\", \"TITLE\": \"Air resistance at sea level, quadratic in the speed\", \"SOURCE\": \"ISO 2533:1975, Standard Atmosphere, sea-level values: density 1.225 kg m-3, dynamic viscosity 1.7894e-5 Pa s\", \"PREREQUISITES\": [{\"SLOT\": \"VELOCITY\", \"KIND\": \"DOF\", \"DIMENSION\": \"L1 T-1\", \"MIN\": 1, \"MAX\": 3, \"LABEL\": \"the velocity components of the body, one per axis\"}], \"PARAMETERS\": [{\"NAME\": \"rho_air\", \"DIMENSION\": \"L-3 M1\", \"SUPPLY\": \"DECLARED\", \"VALUE\": \"1.225\", \"UNIT\": \"kg m-3\", \"OVERRIDABLE\": \"NO\", \"LABEL\": \"the density of air at sea level\"}, {\"NAME\": \"mu_air\", \"DIMENSION\": \"L-1 M1 T-1\", \"SUPPLY\": \"DECLARED\", \"VALUE\": \"1.7894e-5\", \"UNIT\": \"Pa s\", \"OVERRIDABLE\": \"NO\", \"LABEL\": \"the dynamic viscosity of air at sea level\"}, {\"NAME\": \"C_d\", \"DIMENSION\": \"1\", \"SUPPLY\": \"AUTHOR\", \"LABEL\": \"the drag coefficient of the body\"}, {\"NAME\": \"A_ref\", \"DIMENSION\": \"L2\", \"SUPPLY\": \"AUTHOR\", \"LABEL\": \"the reference area of the drag coefficient\"}, {\"NAME\": \"L_ref\", \"DIMENSION\": \"L1\", \"SUPPLY\": \"AUTHOR\", \"LABEL\": \"the reference length of the Reynolds number\"}], \"SUMS\": [{\"NAME\": \"SPEED2\", \"OVER\": \"VELOCITY\", \"EACH\": \"VELOCITY^2\"}], \"TERMS\": [{\"TARGET\": \"VELOCITY\", \"SIGN\": \"-\", \"EXPR\": \"0.5*rho_air*C_d*A_ref*sqrt(SPEED2)*VELOCITY\", \"LABEL\": \"the quadratic drag\"}], \"ASSUMPTIONS\": [{\"NAME\": \"air_still\", \"PROPOSITION\": \"the air is at rest in the frame of the body's velocity\", \"REFS\": [\"VELOCITY\"]}, {\"NAME\": \"air_uniform\", \"PROPOSITION\": \"the air density is uniform over the region of motion\", \"REFS\": [\"rho_air\"]}, {\"NAME\": \"drag_cd_constant\", \"PROPOSITION\": \"the drag coefficient C_d is constant over the motion\", \"REFS\": [\"C_d\"]}, {\"NAME\": \"drag_no_lift\", \"PROPOSITION\": \"the body experiences no lift force\", \"REFS\": [\"VELOCITY\"]}, {\"NAME\": \"drag_no_magnus\", \"PROPOSITION\": \"the body experiences no Magnus force\", \"REFS\": [\"VELOCITY\"]}], \"BOUNDARIES\": [{\"NAME\": \"drag_quadratic_regime\", \"PREDICATE\": \"1e3 < rho_air |v| L_ref / mu_air < 2e5: the Reynolds window of the quadratic law\", \"CONDITION\": \"mu_air != 0 and SPEED2 >= 0 and rho_air*sqrt(SPEED2)*L_ref/mu_air > 1000 and rho_air*sqrt(SPEED2)*L_ref/mu_air < 200000\"}], \"NOT_CHOSEN\": \"No quadratic air resistance.\", \"NOT_INCLUDED\": [\"No wind: the air is at rest.\", \"No change of air density or viscosity with altitude or temperature.\", \"No lift, Magnus or added-mass force.\", \"No drag outside the Reynolds window of the quadratic law.\"], \"EXCLUDES\": [\"AIR-LINEAR\"], \"INTERACTS_WITH\": [], \"TEST_BINDINGS\": [{\"NAME\": \"PROJECTILE_2D\", \"TPK\": {\"DOF\": [{\"NAME\": \"t\", \"DIMENSION\": \"T1\"}, {\"NAME\": \"x\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"z\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"v_x\", \"DIMENSION\": \"L1 T-1\"}, {\"NAME\": \"v_z\", \"DIMENSION\": \"L1 T-1\"}], \"CONSTANT\": [{\"NAME\": \"m\", \"DIMENSION\": \"M1\"}], \"LAW\": [{\"NAME\": \"KIN_X\", \"STATEMENT\": \"dx/dt = v_x\", \"REFS\": [\"t\", \"v_x\", \"x\"], \"ROLE\": \"EOM(x)\", \"EQUATION\": \"D(x,t)=v_x\"}, {\"NAME\": \"KIN_Z\", \"STATEMENT\": \"dz/dt = v_z\", \"REFS\": [\"t\", \"v_z\", \"z\"], \"ROLE\": \"EOM(z)\", \"EQUATION\": \"D(z,t)=v_z\"}, {\"NAME\": \"EOM_X\", \"STATEMENT\": \"m dv_x/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_x\"], \"ROLE\": \"EOM(v_x)\", \"EQUATION\": \"m*D(v_x,t)=0\"}, {\"NAME\": \"EOM_Z\", \"STATEMENT\": \"m dv_z/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_z\"], \"ROLE\": \"EOM(v_z)\", \"EQUATION\": \"m*D(v_z,t)=0\"}], \"ASSUMPTION\": [{\"NAME\": \"point_mass\", \"PROPOSITION\": \"the body is treated as a point mass\", \"REFS\": [\"m\"]}]}, \"BIND\": {\"VELOCITY\": [\"v_x\", \"v_z\"]}, \"VALUES\": {\"A_ref\": {}, \"C_d\": {}, \"L_ref\": {}}, \"ANSWERS\": {}}]}",
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it acts in this kernel only where one of your own laws states it.\", \"NO_LINE\": \"No buoyancy: the air's upthrust on the body is not included.\"}], \"TEST_BINDINGS\": [{\"NAME\": \"PROJECTILE_2D\", \"TPK\": {\"DOF\": [{\"NAME\": \"t\", \"DIMENSION\": \"T1\"}, {\"NAME\": \"x\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"z\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"v_x\", \"DIMENSION\": \"L1 T-1\"}, {\"NAME\": \"v_z\", \"DIMENSION\": \"L1 T-1\"}], \"CONSTANT\": [{\"NAME\": \"m\", \"DIMENSION\": \"M1\"}], \"LAW\": [{\"NAME\": \"KIN_X\", \"STATEMENT\": \"dx/dt = v_x\", \"REFS\": [\"t\", \"v_x\", \"x\"], \"ROLE\": \"EOM(x)\", \"EQUATION\": \"D(x,t)=v_x\"}, {\"NAME\": \"KIN_Z\", \"STATEMENT\": \"dz/dt = v_z\", \"REFS\": [\"t\", \"v_z\", \"z\"], \"ROLE\": \"EOM(z)\", \"EQUATION\": \"D(z,t)=v_z\"}, {\"NAME\": \"EOM_X\", \"STATEMENT\": \"m dv_x/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_x\"], \"ROLE\": \"EOM(v_x)\", \"EQUATION\": \"m*D(v_x,t)=0\"}, {\"NAME\": \"EOM_Z\", \"STATEMENT\": \"m dv_z/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_z\"], \"ROLE\": \"EOM(v_z)\", \"EQUATION\": \"m*D(v_z,t)=0\"}], \"ASSUMPTION\": [{\"NAME\": \"point_mass\", \"PROPOSITION\": \"the body is treated as a point mass\", \"REFS\": [\"m\"]}]}, \"BIND\": {\"HEIGHT\": [\"z\"], \"MASS\": [\"m\"], \"UP_VELOCITY\": [\"v_z\"]}, \"VALUES\": {\"h_max\": {\"VALUE\": \"100\", \"UNIT\": \"m\"}}, \"ANSWERS\": {}}, {\"NAME\": \"TABLE\", \"TPK\": {\"DOF\": [{\"NAME\": \"t\", \"DIMENSION\": \"T1\"}, {\"NAME\": \"x\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"z\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"v_x\", \"DIMENSION\": \"L1 T-1\"}, {\"NAME\": \"v_z\", \"DIMENSION\": \"L1 T-1\"}], \"CONSTANT\": [{\"NAME\": \"m\", \"DIMENSION\": \"M1\"}], \"LAW\": [{\"NAME\": \"KIN_X\", \"STATEMENT\": \"dx/dt = v_x\", \"REFS\": [\"t\", \"v_x\", \"x\"], \"ROLE\": \"EOM(x)\", \"EQUATION\": \"D(x,t)=v_x\"}, {\"NAME\": \"KIN_Z\", \"STATEMENT\": \"dz/dt = v_z\", \"REFS\": [\"t\", \"v_z\", \"z\"], \"ROLE\": \"CONSTRAINT\", \"EQUATION\": \"D(z,t)=v_z\"}, {\"NAME\": \"EOM_X\", \"STATEMENT\": \"m dv_x/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_x\"], \"ROLE\": \"EOM(v_x)\", \"EQUATION\": \"m*D(v_x,t)=0\"}], \"CONSTRAINT\": [{\"NAME\": \"C_Z\", \"TARGET\": \"z\", \"ACTION\": \"FIX\", \"VALUE\": \"0\", \"UNIT\": \"m\", \"STATEMENT\": \"the puck stays on the table top, z = 0\"}, {\"NAME\": \"C_VZ\", \"TARGET\": \"v_z\", \"ACTION\": \"FIX\", \"VALUE\": \"0\", \"UNIT\": \"m s-1\", \"STATEMENT\": \"the puck has no vertical velocity\"}]}, \"BIND\": {\"HEIGHT\": [\"z\"], \"MASS\": [\"m\"], \"UP_VELOCITY\": [\"v_z\"]}, \"VALUES\": {\"h_max\": {\"VALUE\": \"1\", \"UNIT\": \"m\"}}, \"ANSWERS\": {\"FIXED:v_z\": \"YES\"}}]}",
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"name": "I36 a catalogue that is refused"
},
{
"args": {
"answer": [
{
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{
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{
"ACT": "MODULE ADD",
"DATE": "2026-10-01",
"DIGEST": "5f3fe27b42378bce0830b0d0959f892f4a8e73b12b540ae877e39e6439d08b4d",
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{
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"{\"ID\": \"AIR-LINEAR\", \"VERSION\": \"1.0.0\", \"TITLE\": \"Air resistance at sea level, linear in the speed (Stokes drag on a sphere)\", \"SOURCE\": \"ISO 2533:1975, Standard Atmosphere, sea-level values: density 1.225 kg m-3, dynamic viscosity 1.7894e-5 Pa s\", \"PREREQUISITES\": [{\"SLOT\": \"VELOCITY\", \"KIND\": \"DOF\", \"DIMENSION\": \"L1 T-1\", \"MIN\": 1, \"MAX\": 3, \"LABEL\": \"the velocity components of the body, one per axis\"}], \"PARAMETERS\": [{\"NAME\": \"rho_air\", \"DIMENSION\": \"L-3 M1\", \"SUPPLY\": \"DECLARED\", \"VALUE\": \"1.225\", \"UNIT\": \"kg m-3\", \"OVERRIDABLE\": \"NO\", \"LABEL\": \"the density of air at sea level\"}, {\"NAME\": \"mu_air\", \"DIMENSION\": \"L-1 M1 T-1\", \"SUPPLY\": \"DECLARED\", \"VALUE\": \"1.7894e-5\", \"UNIT\": \"Pa s\", \"OVERRIDABLE\": \"NO\", \"LABEL\": \"the dynamic viscosity of air at sea level\"}, {\"NAME\": \"pi_c\", \"DIMENSION\": \"1\", \"SUPPLY\": \"DECLARED\", \"VALUE\": \"3.141592653589793\", \"UNIT\": \"1\", \"OVERRIDABLE\": \"NO\", \"LABEL\": \"pi, to 16 significant digits\"}, {\"NAME\": \"R_s\", \"DIMENSION\": \"L1\", \"SUPPLY\": \"AUTHOR\", \"LABEL\": \"the radius of the sphere\"}], \"SUMS\": [{\"NAME\": \"SPEED2\", \"OVER\": \"VELOCITY\", \"EACH\": \"VELOCITY^2\"}], \"TERMS\": [{\"TARGET\": \"VELOCITY\", \"SIGN\": \"-\", \"EXPR\": \"6*pi_c*mu_air*R_s*VELOCITY\", \"LABEL\": \"the linear (Stokes) drag\"}], \"ASSUMPTIONS\": [{\"NAME\": \"air_still\", \"PROPOSITION\": \"the air is at rest in the frame of the body's velocity\", \"REFS\": [\"VELOCITY\"]}, {\"NAME\": \"air_uniform\", \"PROPOSITION\": \"the air density is uniform over the region of motion\", \"REFS\": [\"rho_air\"]}, {\"NAME\": \"drag_sphere\", \"PROPOSITION\": \"the body is a rigid sphere of radius R_s\", \"REFS\": [\"R_s\"]}], \"BOUNDARIES\": [{\"NAME\": \"drag_linear_regime\", \"PREDICATE\": \"2 rho_air |v| R_s / mu_air < 1: the regime of the linear law\", \"CONDITION\": \"mu_air != 0 and SPEED2 >= 0 and 2*rho_air*sqrt(SPEED2)*R_s/mu_air < 1\"}], \"NOT_CHOSEN\": \"No linear (Stokes) air resistance.\", \"NOT_INCLUDED\": [\"No wind: the air is at rest.\", \"No change of air density or viscosity with altitude or temperature.\", \"No drag outside the regime of the linear law.\"], \"EXCLUDES\": [], \"INTERACTS_WITH\": [], \"TEST_BINDINGS\": [{\"NAME\": \"PROJECTILE_2D\", \"TPK\": {\"DOF\": [{\"NAME\": \"t\", \"DIMENSION\": \"T1\"}, {\"NAME\": \"x\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"z\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"v_x\", \"DIMENSION\": \"L1 T-1\"}, {\"NAME\": \"v_z\", \"DIMENSION\": \"L1 T-1\"}], \"CONSTANT\": [{\"NAME\": \"m\", \"DIMENSION\": \"M1\"}], \"LAW\": [{\"NAME\": \"KIN_X\", \"STATEMENT\": \"dx/dt = v_x\", \"REFS\": [\"t\", \"v_x\", \"x\"], \"ROLE\": \"EOM(x)\", \"EQUATION\": \"D(x,t)=v_x\"}, {\"NAME\": \"KIN_Z\", \"STATEMENT\": \"dz/dt = v_z\", \"REFS\": [\"t\", \"v_z\", \"z\"], \"ROLE\": \"EOM(z)\", \"EQUATION\": \"D(z,t)=v_z\"}, {\"NAME\": \"EOM_X\", \"STATEMENT\": \"m dv_x/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_x\"], \"ROLE\": \"EOM(v_x)\", \"EQUATION\": \"m*D(v_x,t)=0\"}, {\"NAME\": \"EOM_Z\", \"STATEMENT\": \"m dv_z/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_z\"], \"ROLE\": \"EOM(v_z)\", \"EQUATION\": \"m*D(v_z,t)=0\"}], \"ASSUMPTION\": [{\"NAME\": \"point_mass\", \"PROPOSITION\": \"the body is treated as a point mass\", \"REFS\": [\"m\"]}]}, \"BIND\": {\"VELOCITY\": [\"v_x\", \"v_z\"]}, \"VALUES\": {\"R_s\": {}}, \"ANSWERS\": {}}]}",
"{\"ID\": \"AIR-QUADRATIC\", \"VERSION\": \"1.0.0\", \"TITLE\": \"Air resistance at sea level, quadratic in the speed\", \"SOURCE\": \"ISO 2533:1975, Standard Atmosphere, sea-level values: density 1.225 kg m-3, dynamic viscosity 1.7894e-5 Pa s\", \"PREREQUISITES\": [{\"SLOT\": \"VELOCITY\", \"KIND\": \"DOF\", \"DIMENSION\": \"L1 T-1\", \"MIN\": 1, \"MAX\": 3, \"LABEL\": \"the velocity components of the body, one per axis\"}], \"PARAMETERS\": [{\"NAME\": \"rho_air\", \"DIMENSION\": \"L-3 M1\", \"SUPPLY\": \"DECLARED\", \"VALUE\": \"1.225\", \"UNIT\": \"kg m-3\", \"OVERRIDABLE\": \"NO\", \"LABEL\": \"the density of air at sea level\"}, {\"NAME\": \"mu_air\", \"DIMENSION\": \"L-1 M1 T-1\", \"SUPPLY\": \"DECLARED\", \"VALUE\": \"1.7894e-5\", \"UNIT\": \"Pa s\", \"OVERRIDABLE\": \"NO\", \"LABEL\": \"the dynamic viscosity of air at sea level\"}, {\"NAME\": \"C_d\", \"DIMENSION\": \"1\", \"SUPPLY\": \"AUTHOR\", \"LABEL\": \"the drag coefficient of the body\"}, {\"NAME\": \"A_ref\", \"DIMENSION\": \"L2\", \"SUPPLY\": \"AUTHOR\", \"LABEL\": \"the reference area of the drag coefficient\"}, {\"NAME\": \"L_ref\", \"DIMENSION\": \"L1\", \"SUPPLY\": \"AUTHOR\", \"LABEL\": \"the reference length of the Reynolds number\"}], \"SUMS\": [{\"NAME\": \"SPEED2\", \"OVER\": \"VELOCITY\", \"EACH\": \"VELOCITY^2\"}], \"TERMS\": [{\"TARGET\": \"VELOCITY\", \"SIGN\": \"-\", \"EXPR\": \"0.5*rho_air*C_d*A_ref*sqrt(SPEED2)*VELOCITY\", \"LABEL\": \"the quadratic drag\"}], \"ASSUMPTIONS\": [{\"NAME\": \"air_still\", \"PROPOSITION\": \"the air is at rest in the frame of the body's velocity\", \"REFS\": [\"VELOCITY\"]}, {\"NAME\": \"air_uniform\", \"PROPOSITION\": \"the air density is uniform over the region of motion\", \"REFS\": [\"rho_air\"]}, {\"NAME\": \"drag_cd_constant\", \"PROPOSITION\": \"the drag coefficient C_d is constant over the motion\", \"REFS\": [\"C_d\"]}, {\"NAME\": \"drag_no_lift\", \"PROPOSITION\": \"the body experiences no lift force\", \"REFS\": [\"VELOCITY\"]}, {\"NAME\": \"drag_no_magnus\", \"PROPOSITION\": \"the body experiences no Magnus force\", \"REFS\": [\"VELOCITY\"]}], \"BOUNDARIES\": [{\"NAME\": \"drag_quadratic_regime\", \"PREDICATE\": \"1e3 < rho_air |v| L_ref / mu_air < 2e5: the Reynolds window of the quadratic law\", \"CONDITION\": \"mu_air != 0 and SPEED2 >= 0 and rho_air*sqrt(SPEED2)*L_ref/mu_air > 1000 and rho_air*sqrt(SPEED2)*L_ref/mu_air < 200000\"}], \"NOT_CHOSEN\": \"No quadratic air resistance.\", \"NOT_INCLUDED\": [\"No wind: the air is at rest.\", \"No change of air density or viscosity with altitude or temperature.\", \"No lift, Magnus or added-mass force.\", \"No drag outside the Reynolds window of the quadratic law.\"], \"EXCLUDES\": [\"AIR-LINEAR\"], \"INTERACTS_WITH\": [], \"TEST_BINDINGS\": [{\"NAME\": \"PROJECTILE_2D\", \"TPK\": {\"DOF\": [{\"NAME\": \"t\", \"DIMENSION\": \"T1\"}, {\"NAME\": \"x\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"z\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"v_x\", \"DIMENSION\": \"L1 T-1\"}, {\"NAME\": \"v_z\", \"DIMENSION\": \"L1 T-1\"}], \"CONSTANT\": [{\"NAME\": \"m\", \"DIMENSION\": \"M1\"}], \"LAW\": [{\"NAME\": \"KIN_X\", \"STATEMENT\": \"dx/dt = v_x\", \"REFS\": [\"t\", \"v_x\", \"x\"], \"ROLE\": \"EOM(x)\", \"EQUATION\": \"D(x,t)=v_x\"}, {\"NAME\": \"KIN_Z\", \"STATEMENT\": \"dz/dt = v_z\", \"REFS\": [\"t\", \"v_z\", \"z\"], \"ROLE\": \"EOM(z)\", \"EQUATION\": \"D(z,t)=v_z\"}, {\"NAME\": \"EOM_X\", \"STATEMENT\": \"m dv_x/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_x\"], \"ROLE\": \"EOM(v_x)\", \"EQUATION\": \"m*D(v_x,t)=0\"}, {\"NAME\": \"EOM_Z\", \"STATEMENT\": \"m dv_z/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_z\"], \"ROLE\": \"EOM(v_z)\", \"EQUATION\": \"m*D(v_z,t)=0\"}], \"ASSUMPTION\": [{\"NAME\": \"point_mass\", \"PROPOSITION\": \"the body is treated as a point mass\", \"REFS\": [\"m\"]}]}, \"BIND\": {\"VELOCITY\": [\"v_x\", \"v_z\"]}, \"VALUES\": {\"A_ref\": {}, \"C_d\": {}, \"L_ref\": {}}, \"ANSWERS\": {}}]}",
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it acts in this kernel only where one of your own laws states it.\", \"NO_LINE\": \"No buoyancy: the air's upthrust on the body is not included.\"}], \"TEST_BINDINGS\": [{\"NAME\": \"PROJECTILE_2D\", \"TPK\": {\"DOF\": [{\"NAME\": \"t\", \"DIMENSION\": \"T1\"}, {\"NAME\": \"x\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"z\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"v_x\", \"DIMENSION\": \"L1 T-1\"}, {\"NAME\": \"v_z\", \"DIMENSION\": \"L1 T-1\"}], \"CONSTANT\": [{\"NAME\": \"m\", \"DIMENSION\": \"M1\"}], \"LAW\": [{\"NAME\": \"KIN_X\", \"STATEMENT\": \"dx/dt = v_x\", \"REFS\": [\"t\", \"v_x\", \"x\"], \"ROLE\": \"EOM(x)\", \"EQUATION\": \"D(x,t)=v_x\"}, {\"NAME\": \"KIN_Z\", \"STATEMENT\": \"dz/dt = v_z\", \"REFS\": [\"t\", \"v_z\", \"z\"], \"ROLE\": \"EOM(z)\", \"EQUATION\": \"D(z,t)=v_z\"}, {\"NAME\": \"EOM_X\", \"STATEMENT\": \"m dv_x/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_x\"], \"ROLE\": \"EOM(v_x)\", \"EQUATION\": \"m*D(v_x,t)=0\"}, {\"NAME\": \"EOM_Z\", \"STATEMENT\": \"m dv_z/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_z\"], \"ROLE\": \"EOM(v_z)\", \"EQUATION\": \"m*D(v_z,t)=0\"}], \"ASSUMPTION\": [{\"NAME\": \"point_mass\", \"PROPOSITION\": \"the body is treated as a point mass\", \"REFS\": [\"m\"]}]}, \"BIND\": {\"HEIGHT\": [\"z\"], \"MASS\": [\"m\"], \"UP_VELOCITY\": [\"v_z\"]}, \"VALUES\": {\"h_max\": {\"VALUE\": \"100\", \"UNIT\": \"m\"}}, \"ANSWERS\": {}}, {\"NAME\": \"TABLE\", \"TPK\": {\"DOF\": [{\"NAME\": \"t\", \"DIMENSION\": \"T1\"}, {\"NAME\": \"x\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"z\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"v_x\", \"DIMENSION\": \"L1 T-1\"}, {\"NAME\": \"v_z\", \"DIMENSION\": \"L1 T-1\"}], \"CONSTANT\": [{\"NAME\": \"m\", \"DIMENSION\": \"M1\"}], \"LAW\": [{\"NAME\": \"KIN_X\", \"STATEMENT\": \"dx/dt = v_x\", \"REFS\": [\"t\", \"v_x\", \"x\"], \"ROLE\": \"EOM(x)\", \"EQUATION\": \"D(x,t)=v_x\"}, {\"NAME\": \"KIN_Z\", \"STATEMENT\": \"dz/dt = v_z\", \"REFS\": [\"t\", \"v_z\", \"z\"], \"ROLE\": \"CONSTRAINT\", \"EQUATION\": \"D(z,t)=v_z\"}, {\"NAME\": \"EOM_X\", \"STATEMENT\": \"m dv_x/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_x\"], \"ROLE\": \"EOM(v_x)\", \"EQUATION\": \"m*D(v_x,t)=0\"}], \"CONSTRAINT\": [{\"NAME\": \"C_Z\", \"TARGET\": \"z\", \"ACTION\": \"FIX\", \"VALUE\": \"0\", \"UNIT\": \"m\", \"STATEMENT\": \"the puck stays on the table top, z = 0\"}, {\"NAME\": \"C_VZ\", \"TARGET\": \"v_z\", \"ACTION\": \"FIX\", \"VALUE\": \"0\", \"UNIT\": \"m s-1\", \"STATEMENT\": \"the puck has no vertical velocity\"}]}, \"BIND\": {\"HEIGHT\": [\"z\"], \"MASS\": [\"m\"], \"UP_VELOCITY\": [\"v_z\"]}, \"VALUES\": {\"h_max\": {\"VALUE\": \"1\", \"UNIT\": \"m\"}}, \"ANSWERS\": {\"FIXED:v_z\": \"YES\"}}]}",
"{\"ID\": \"MATH\", \"VERSION\": \"1.0.0\", \"TITLE\": \"The mathematical constant pi, as the CONSTANT pi_c\", \"SOURCE\": \"pi to 16 significant digits, 3.141592653589793, the nearest IEEE 754 binary64 value\", \"PREREQUISITES\": [], \"PARAMETERS\": [{\"NAME\": \"pi_c\", \"DIMENSION\": \"1\", \"SUPPLY\": \"DECLARED\", \"VALUE\": \"3.141592653589793\", \"UNIT\": \"1\", \"OVERRIDABLE\": \"NO\", \"LABEL\": \"pi, to 16 significant digits\"}], \"SUMS\": [], \"TERMS\": [], \"ASSUMPTIONS\": [], \"BOUNDARIES\": [], \"NOT_CHOSEN\": \"No mathematical constant: pi exists only if you declare it.\", \"NOT_INCLUDED\": [\"pi_c is pi rounded to 16 significant digits; no other mathematical constant is declared.\"], \"EXCLUDES\": [], \"INTERACTS_WITH\": [], \"TEST_BINDINGS\": [{\"NAME\": \"PROJECTILE_2D\", \"TPK\": {\"DOF\": [{\"NAME\": \"t\", \"DIMENSION\": \"T1\"}, {\"NAME\": \"x\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"z\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"v_x\", \"DIMENSION\": \"L1 T-1\"}, {\"NAME\": \"v_z\", \"DIMENSION\": \"L1 T-1\"}], \"CONSTANT\": [{\"NAME\": \"m\", \"DIMENSION\": \"M1\"}], \"LAW\": [{\"NAME\": \"KIN_X\", \"STATEMENT\": \"dx/dt = v_x\", \"REFS\": [\"t\", \"v_x\", \"x\"], \"ROLE\": \"EOM(x)\", \"EQUATION\": \"D(x,t)=v_x\"}, {\"NAME\": \"KIN_Z\", \"STATEMENT\": \"dz/dt = v_z\", \"REFS\": [\"t\", \"v_z\", \"z\"], \"ROLE\": \"EOM(z)\", \"EQUATION\": \"D(z,t)=v_z\"}, {\"NAME\": \"EOM_X\", \"STATEMENT\": \"m dv_x/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_x\"], \"ROLE\": \"EOM(v_x)\", \"EQUATION\": \"m*D(v_x,t)=0\"}, {\"NAME\": \"EOM_Z\", \"STATEMENT\": \"m dv_z/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_z\"], \"ROLE\": \"EOM(v_z)\", \"EQUATION\": \"m*D(v_z,t)=0\"}], \"ASSUMPTION\": [{\"NAME\": \"point_mass\", \"PROPOSITION\": \"the body is treated as a point mass\", \"REFS\": [\"m\"]}]}, \"BIND\": {}, \"VALUES\": {}, \"ANSWERS\": {}}]}"
]
},
"expected": "[\"REFUSED\",\"CLAIM GRAV-UNIFORM 1.0.5: not declared\"]",
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"name": "I37 a claim of a version never declared"
},
{
"args": {
"answer": [
{
"AT": 4,
"CHOSEN": [
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{
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"ID": "GRAV-UNIFORM",
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"lines": [
{
"ACT": "MODULE ADD",
"DATE": "2026-10-01",
"DIGEST": "5f3fe27b42378bce0830b0d0959f892f4a8e73b12b540ae877e39e6439d08b4d",
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{
"ACT": "MODULE ADD",
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{
"ACT": "MODULE ADD",
"DATE": "2026-10-01",
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"ID": "GRAV-UNIFORM",
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{
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"ID": "MATH",
"VERSION": "1.0.0"
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{
"ACT": "MODULE RETIRE",
"DATE": "2026-10-02",
"ID": "GRAV-UNIFORM",
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"modules": [
"{\"ID\": \"AIR-LINEAR\", \"VERSION\": \"1.0.0\", \"TITLE\": \"Air resistance at sea level, linear in the speed (Stokes drag on a sphere)\", \"SOURCE\": \"ISO 2533:1975, Standard Atmosphere, sea-level values: density 1.225 kg m-3, dynamic viscosity 1.7894e-5 Pa s\", \"PREREQUISITES\": [{\"SLOT\": \"VELOCITY\", \"KIND\": \"DOF\", \"DIMENSION\": \"L1 T-1\", \"MIN\": 1, \"MAX\": 3, \"LABEL\": \"the velocity components of the body, one per axis\"}], \"PARAMETERS\": [{\"NAME\": \"rho_air\", \"DIMENSION\": \"L-3 M1\", \"SUPPLY\": \"DECLARED\", \"VALUE\": \"1.225\", \"UNIT\": \"kg m-3\", \"OVERRIDABLE\": \"NO\", \"LABEL\": \"the density of air at sea level\"}, {\"NAME\": \"mu_air\", \"DIMENSION\": \"L-1 M1 T-1\", \"SUPPLY\": \"DECLARED\", \"VALUE\": \"1.7894e-5\", \"UNIT\": \"Pa s\", \"OVERRIDABLE\": \"NO\", \"LABEL\": \"the dynamic viscosity of air at sea level\"}, {\"NAME\": \"pi_c\", \"DIMENSION\": \"1\", \"SUPPLY\": \"DECLARED\", \"VALUE\": \"3.141592653589793\", \"UNIT\": \"1\", \"OVERRIDABLE\": \"NO\", \"LABEL\": \"pi, to 16 significant digits\"}, {\"NAME\": \"R_s\", \"DIMENSION\": \"L1\", \"SUPPLY\": \"AUTHOR\", \"LABEL\": \"the radius of the sphere\"}], \"SUMS\": [{\"NAME\": \"SPEED2\", \"OVER\": \"VELOCITY\", \"EACH\": \"VELOCITY^2\"}], \"TERMS\": [{\"TARGET\": \"VELOCITY\", \"SIGN\": \"-\", \"EXPR\": \"6*pi_c*mu_air*R_s*VELOCITY\", \"LABEL\": \"the linear (Stokes) drag\"}], \"ASSUMPTIONS\": [{\"NAME\": \"air_still\", \"PROPOSITION\": \"the air is at rest in the frame of the body's velocity\", \"REFS\": [\"VELOCITY\"]}, {\"NAME\": \"air_uniform\", \"PROPOSITION\": \"the air density is uniform over the region of motion\", \"REFS\": [\"rho_air\"]}, {\"NAME\": \"drag_sphere\", \"PROPOSITION\": \"the body is a rigid sphere of radius R_s\", \"REFS\": [\"R_s\"]}], \"BOUNDARIES\": [{\"NAME\": \"drag_linear_regime\", \"PREDICATE\": \"2 rho_air |v| R_s / mu_air < 1: the regime of the linear law\", \"CONDITION\": \"mu_air != 0 and SPEED2 >= 0 and 2*rho_air*sqrt(SPEED2)*R_s/mu_air < 1\"}], \"NOT_CHOSEN\": \"No linear (Stokes) air resistance.\", \"NOT_INCLUDED\": [\"No wind: the air is at rest.\", \"No change of air density or viscosity with altitude or temperature.\", \"No drag outside the regime of the linear law.\"], \"EXCLUDES\": [], \"INTERACTS_WITH\": [], \"TEST_BINDINGS\": [{\"NAME\": \"PROJECTILE_2D\", \"TPK\": {\"DOF\": [{\"NAME\": \"t\", \"DIMENSION\": \"T1\"}, {\"NAME\": \"x\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"z\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"v_x\", \"DIMENSION\": \"L1 T-1\"}, {\"NAME\": \"v_z\", \"DIMENSION\": \"L1 T-1\"}], \"CONSTANT\": [{\"NAME\": \"m\", \"DIMENSION\": \"M1\"}], \"LAW\": [{\"NAME\": \"KIN_X\", \"STATEMENT\": \"dx/dt = v_x\", \"REFS\": [\"t\", \"v_x\", \"x\"], \"ROLE\": \"EOM(x)\", \"EQUATION\": \"D(x,t)=v_x\"}, {\"NAME\": \"KIN_Z\", \"STATEMENT\": \"dz/dt = v_z\", \"REFS\": [\"t\", \"v_z\", \"z\"], \"ROLE\": \"EOM(z)\", \"EQUATION\": \"D(z,t)=v_z\"}, {\"NAME\": \"EOM_X\", \"STATEMENT\": \"m dv_x/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_x\"], \"ROLE\": \"EOM(v_x)\", \"EQUATION\": \"m*D(v_x,t)=0\"}, {\"NAME\": \"EOM_Z\", \"STATEMENT\": \"m dv_z/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_z\"], \"ROLE\": \"EOM(v_z)\", \"EQUATION\": \"m*D(v_z,t)=0\"}], \"ASSUMPTION\": [{\"NAME\": \"point_mass\", \"PROPOSITION\": \"the body is treated as a point mass\", \"REFS\": [\"m\"]}]}, \"BIND\": {\"VELOCITY\": [\"v_x\", \"v_z\"]}, \"VALUES\": {\"R_s\": {}}, \"ANSWERS\": {}}]}",
"{\"ID\": \"AIR-QUADRATIC\", \"VERSION\": \"1.0.0\", \"TITLE\": \"Air resistance at sea level, quadratic in the speed\", \"SOURCE\": \"ISO 2533:1975, Standard Atmosphere, sea-level values: density 1.225 kg m-3, dynamic viscosity 1.7894e-5 Pa s\", \"PREREQUISITES\": [{\"SLOT\": \"VELOCITY\", \"KIND\": \"DOF\", \"DIMENSION\": \"L1 T-1\", \"MIN\": 1, \"MAX\": 3, \"LABEL\": \"the velocity components of the body, one per axis\"}], \"PARAMETERS\": [{\"NAME\": \"rho_air\", \"DIMENSION\": \"L-3 M1\", \"SUPPLY\": \"DECLARED\", \"VALUE\": \"1.225\", \"UNIT\": \"kg m-3\", \"OVERRIDABLE\": \"NO\", \"LABEL\": \"the density of air at sea level\"}, {\"NAME\": \"mu_air\", \"DIMENSION\": \"L-1 M1 T-1\", \"SUPPLY\": \"DECLARED\", \"VALUE\": \"1.7894e-5\", \"UNIT\": \"Pa s\", \"OVERRIDABLE\": \"NO\", \"LABEL\": \"the dynamic viscosity of air at sea level\"}, {\"NAME\": \"C_d\", \"DIMENSION\": \"1\", \"SUPPLY\": \"AUTHOR\", \"LABEL\": \"the drag coefficient of the body\"}, {\"NAME\": \"A_ref\", \"DIMENSION\": \"L2\", \"SUPPLY\": \"AUTHOR\", \"LABEL\": \"the reference area of the drag coefficient\"}, {\"NAME\": \"L_ref\", \"DIMENSION\": \"L1\", \"SUPPLY\": \"AUTHOR\", \"LABEL\": \"the reference length of the Reynolds number\"}], \"SUMS\": [{\"NAME\": \"SPEED2\", \"OVER\": \"VELOCITY\", \"EACH\": \"VELOCITY^2\"}], \"TERMS\": [{\"TARGET\": \"VELOCITY\", \"SIGN\": \"-\", \"EXPR\": \"0.5*rho_air*C_d*A_ref*sqrt(SPEED2)*VELOCITY\", \"LABEL\": \"the quadratic drag\"}], \"ASSUMPTIONS\": [{\"NAME\": \"air_still\", \"PROPOSITION\": \"the air is at rest in the frame of the body's velocity\", \"REFS\": [\"VELOCITY\"]}, {\"NAME\": \"air_uniform\", \"PROPOSITION\": \"the air density is uniform over the region of motion\", \"REFS\": [\"rho_air\"]}, {\"NAME\": \"drag_cd_constant\", \"PROPOSITION\": \"the drag coefficient C_d is constant over the motion\", \"REFS\": [\"C_d\"]}, {\"NAME\": \"drag_no_lift\", \"PROPOSITION\": \"the body experiences no lift force\", \"REFS\": [\"VELOCITY\"]}, {\"NAME\": \"drag_no_magnus\", \"PROPOSITION\": \"the body experiences no Magnus force\", \"REFS\": [\"VELOCITY\"]}], \"BOUNDARIES\": [{\"NAME\": \"drag_quadratic_regime\", \"PREDICATE\": \"1e3 < rho_air |v| L_ref / mu_air < 2e5: the Reynolds window of the quadratic law\", \"CONDITION\": \"mu_air != 0 and SPEED2 >= 0 and rho_air*sqrt(SPEED2)*L_ref/mu_air > 1000 and rho_air*sqrt(SPEED2)*L_ref/mu_air < 200000\"}], \"NOT_CHOSEN\": \"No quadratic air resistance.\", \"NOT_INCLUDED\": [\"No wind: the air is at rest.\", \"No change of air density or viscosity with altitude or temperature.\", \"No lift, Magnus or added-mass force.\", \"No drag outside the Reynolds window of the quadratic law.\"], \"EXCLUDES\": [\"AIR-LINEAR\"], \"INTERACTS_WITH\": [], \"TEST_BINDINGS\": [{\"NAME\": \"PROJECTILE_2D\", \"TPK\": {\"DOF\": [{\"NAME\": \"t\", \"DIMENSION\": \"T1\"}, {\"NAME\": \"x\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"z\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"v_x\", \"DIMENSION\": \"L1 T-1\"}, {\"NAME\": \"v_z\", \"DIMENSION\": \"L1 T-1\"}], \"CONSTANT\": [{\"NAME\": \"m\", \"DIMENSION\": \"M1\"}], \"LAW\": [{\"NAME\": \"KIN_X\", \"STATEMENT\": \"dx/dt = v_x\", \"REFS\": [\"t\", \"v_x\", \"x\"], \"ROLE\": \"EOM(x)\", \"EQUATION\": \"D(x,t)=v_x\"}, {\"NAME\": \"KIN_Z\", \"STATEMENT\": \"dz/dt = v_z\", \"REFS\": [\"t\", \"v_z\", \"z\"], \"ROLE\": \"EOM(z)\", \"EQUATION\": \"D(z,t)=v_z\"}, {\"NAME\": \"EOM_X\", \"STATEMENT\": \"m dv_x/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_x\"], \"ROLE\": \"EOM(v_x)\", \"EQUATION\": \"m*D(v_x,t)=0\"}, {\"NAME\": \"EOM_Z\", \"STATEMENT\": \"m dv_z/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_z\"], \"ROLE\": \"EOM(v_z)\", \"EQUATION\": \"m*D(v_z,t)=0\"}], \"ASSUMPTION\": [{\"NAME\": \"point_mass\", \"PROPOSITION\": \"the body is treated as a point mass\", \"REFS\": [\"m\"]}]}, \"BIND\": {\"VELOCITY\": [\"v_x\", \"v_z\"]}, \"VALUES\": {\"A_ref\": {}, \"C_d\": {}, \"L_ref\": {}}, \"ANSWERS\": {}}]}",
"{\"ID\": \"GRAV-UNIFORM\", \"VERSION\": \"1.0.0\", \"TITLE\": \"Uniform gravity at the standard value g_n\", \"SOURCE\": \"g_n = 9.80665 m s-2, exact by definition: 3rd CGPM (1901), declaration on the unit of mass and on the definition of weight\", \"PREREQUISITES\": [{\"SLOT\": \"MASS\", \"KIND\": \"CONSTANT\", \"DIMENSION\": \"M1\", \"MIN\": 1, \"MAX\": 1, \"LABEL\": \"the mass of the body\"}, {\"SLOT\": \"UP_VELOCITY\", \"KIND\": \"DOF\", \"DIMENSION\": \"L1 T-1\", \"MIN\": 1, \"MAX\": 1, \"LABEL\": \"the velocity component pointing up; its equation of motion receives the weight\"}, {\"SLOT\": \"HEIGHT\", \"KIND\": \"DOF\", \"DIMENSION\": \"L1\", \"MIN\": 1, \"MAX\": 1, \"LABEL\": \"the position along the same upward axis\"}], \"PARAMETERS\": [{\"NAME\": \"g_n\", \"DIMENSION\": \"L1 T-2\", \"SUPPLY\": \"DECLARED\", \"VALUE\": \"9.80665\", \"UNIT\": \"m s-2\", \"OVERRIDABLE\": \"NO\", \"LABEL\": \"the standard acceleration of gravity\"}, {\"NAME\": \"h_max\", \"DIMENSION\": \"L1\", \"SUPPLY\": \"AUTHOR\", \"LABEL\": \"the largest height, above or below the origin, over which the field is taken as uniform\"}], \"SUMS\": [], \"TERMS\": [{\"TARGET\": \"UP_VELOCITY\", \"SIGN\": \"-\", \"EXPR\": \"MASS*g_n\", \"LABEL\": \"the weight\"}], \"ASSUMPTIONS\": [{\"NAME\": \"gravity_uniform\", \"PROPOSITION\": \"the gravitational field is uniform over the region abs({HEIGHT}) < h_max\", \"REFS\": [\"HEIGHT\", \"h_max\"]}, {\"NAME\": \"gravity_standard\", \"PROPOSITION\": \"the local gravitational acceleration equals the conventional standard value g_n\", \"REFS\": [\"g_n\"]}, {\"NAME\": \"frame_inertial\", \"PROPOSITION\": \"the frame in which {HEIGHT} is measured is treated as inertial\", \"REFS\": [\"HEIGHT\"]}], \"BOUNDARIES\": [{\"NAME\": \"gravity_region\", \"PREDICATE\": \"abs({HEIGHT}) < h_max\", \"CONDITION\": \"abs(HEIGHT) < h_max\"}], \"NOT_CHOSEN\": \"No gravity: no weight acts on any DOF.\", \"NOT_INCLUDED\": [\"No variation of gravity with height or latitude beyond what g_n contains.\", \"No Earth rotation (Coriolis or centrifugal force) beyond what g_n contains.\", \"No gravity of bodies other than the Earth.\"], \"EXCLUDES\": [], \"INTERACTS_WITH\": [{\"WITH\": \"AIR-*\", \"QUESTION_ID\": \"BUOYANCY\", \"QUESTION\": \"Does the air's buoyancy (upthrust) act on the body in the system you mean?\", \"YES_LINE\": \"Buoyancy acts (your answer): no module adds it; it acts in this kernel only where one of your own laws states it.\", \"NO_LINE\": \"No buoyancy: the air's upthrust on the body is not included.\"}], \"TEST_BINDINGS\": [{\"NAME\": \"PROJECTILE_2D\", \"TPK\": {\"DOF\": [{\"NAME\": \"t\", \"DIMENSION\": \"T1\"}, {\"NAME\": \"x\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"z\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"v_x\", \"DIMENSION\": \"L1 T-1\"}, {\"NAME\": \"v_z\", \"DIMENSION\": \"L1 T-1\"}], \"CONSTANT\": [{\"NAME\": \"m\", \"DIMENSION\": \"M1\"}], \"LAW\": [{\"NAME\": \"KIN_X\", \"STATEMENT\": \"dx/dt = v_x\", \"REFS\": [\"t\", \"v_x\", \"x\"], \"ROLE\": \"EOM(x)\", \"EQUATION\": \"D(x,t)=v_x\"}, {\"NAME\": \"KIN_Z\", \"STATEMENT\": \"dz/dt = v_z\", \"REFS\": [\"t\", \"v_z\", \"z\"], \"ROLE\": \"EOM(z)\", \"EQUATION\": \"D(z,t)=v_z\"}, {\"NAME\": \"EOM_X\", \"STATEMENT\": \"m dv_x/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_x\"], \"ROLE\": \"EOM(v_x)\", \"EQUATION\": \"m*D(v_x,t)=0\"}, {\"NAME\": \"EOM_Z\", \"STATEMENT\": \"m dv_z/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_z\"], \"ROLE\": \"EOM(v_z)\", \"EQUATION\": \"m*D(v_z,t)=0\"}], \"ASSUMPTION\": [{\"NAME\": \"point_mass\", \"PROPOSITION\": \"the body is treated as a point mass\", \"REFS\": [\"m\"]}]}, \"BIND\": {\"HEIGHT\": [\"z\"], \"MASS\": [\"m\"], \"UP_VELOCITY\": [\"v_z\"]}, \"VALUES\": {\"h_max\": {\"VALUE\": \"100\", \"UNIT\": \"m\"}}, \"ANSWERS\": {}}, {\"NAME\": \"TABLE\", \"TPK\": {\"DOF\": [{\"NAME\": \"t\", \"DIMENSION\": \"T1\"}, {\"NAME\": \"x\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"z\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"v_x\", \"DIMENSION\": \"L1 T-1\"}, {\"NAME\": \"v_z\", \"DIMENSION\": \"L1 T-1\"}], \"CONSTANT\": [{\"NAME\": \"m\", \"DIMENSION\": \"M1\"}], \"LAW\": [{\"NAME\": \"KIN_X\", \"STATEMENT\": \"dx/dt = v_x\", \"REFS\": [\"t\", \"v_x\", \"x\"], \"ROLE\": \"EOM(x)\", \"EQUATION\": \"D(x,t)=v_x\"}, {\"NAME\": \"KIN_Z\", \"STATEMENT\": \"dz/dt = v_z\", \"REFS\": [\"t\", \"v_z\", \"z\"], \"ROLE\": \"CONSTRAINT\", \"EQUATION\": \"D(z,t)=v_z\"}, {\"NAME\": \"EOM_X\", \"STATEMENT\": \"m dv_x/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_x\"], \"ROLE\": \"EOM(v_x)\", \"EQUATION\": \"m*D(v_x,t)=0\"}], \"CONSTRAINT\": [{\"NAME\": \"C_Z\", \"TARGET\": \"z\", \"ACTION\": \"FIX\", \"VALUE\": \"0\", \"UNIT\": \"m\", \"STATEMENT\": \"the puck stays on the table top, z = 0\"}, {\"NAME\": \"C_VZ\", \"TARGET\": \"v_z\", \"ACTION\": \"FIX\", \"VALUE\": \"0\", \"UNIT\": \"m s-1\", \"STATEMENT\": \"the puck has no vertical velocity\"}]}, \"BIND\": {\"HEIGHT\": [\"z\"], \"MASS\": [\"m\"], \"UP_VELOCITY\": [\"v_z\"]}, \"VALUES\": {\"h_max\": {\"VALUE\": \"1\", \"UNIT\": \"m\"}}, \"ANSWERS\": {\"FIXED:v_z\": \"YES\"}}]}",
"{\"ID\": \"MATH\", \"VERSION\": \"1.0.0\", \"TITLE\": \"The mathematical constant pi, as the CONSTANT pi_c\", \"SOURCE\": \"pi to 16 significant digits, 3.141592653589793, the nearest IEEE 754 binary64 value\", \"PREREQUISITES\": [], \"PARAMETERS\": [{\"NAME\": \"pi_c\", \"DIMENSION\": \"1\", \"SUPPLY\": \"DECLARED\", \"VALUE\": \"3.141592653589793\", \"UNIT\": \"1\", \"OVERRIDABLE\": \"NO\", \"LABEL\": \"pi, to 16 significant digits\"}], \"SUMS\": [], \"TERMS\": [], \"ASSUMPTIONS\": [], \"BOUNDARIES\": [], \"NOT_CHOSEN\": \"No mathematical constant: pi exists only if you declare it.\", \"NOT_INCLUDED\": [\"pi_c is pi rounded to 16 significant digits; no other mathematical constant is declared.\"], \"EXCLUDES\": [], \"INTERACTS_WITH\": [], \"TEST_BINDINGS\": [{\"NAME\": \"PROJECTILE_2D\", \"TPK\": {\"DOF\": [{\"NAME\": \"t\", \"DIMENSION\": \"T1\"}, {\"NAME\": \"x\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"z\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"v_x\", \"DIMENSION\": \"L1 T-1\"}, {\"NAME\": \"v_z\", \"DIMENSION\": \"L1 T-1\"}], \"CONSTANT\": [{\"NAME\": \"m\", \"DIMENSION\": \"M1\"}], \"LAW\": [{\"NAME\": \"KIN_X\", \"STATEMENT\": \"dx/dt = v_x\", \"REFS\": [\"t\", \"v_x\", \"x\"], \"ROLE\": \"EOM(x)\", \"EQUATION\": \"D(x,t)=v_x\"}, {\"NAME\": \"KIN_Z\", \"STATEMENT\": \"dz/dt = v_z\", \"REFS\": [\"t\", \"v_z\", \"z\"], \"ROLE\": \"EOM(z)\", \"EQUATION\": \"D(z,t)=v_z\"}, {\"NAME\": \"EOM_X\", \"STATEMENT\": \"m dv_x/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_x\"], \"ROLE\": \"EOM(v_x)\", \"EQUATION\": \"m*D(v_x,t)=0\"}, {\"NAME\": \"EOM_Z\", \"STATEMENT\": \"m dv_z/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_z\"], \"ROLE\": \"EOM(v_z)\", \"EQUATION\": \"m*D(v_z,t)=0\"}], \"ASSUMPTION\": [{\"NAME\": \"point_mass\", \"PROPOSITION\": \"the body is treated as a point mass\", \"REFS\": [\"m\"]}]}, \"BIND\": {}, \"VALUES\": {}, \"ANSWERS\": {}}]}"
]
},
"expected": "[\"OK\",[\"ASK\",[]],[\"CLAIMS\",[[\"GRAV-UNIFORM\",\"1.0.0\",\"PINNED\"]]]]",
"fn": "interview_check",
"hand_checked": true,
"name": "I38 a pinned claim whose version was RETIRED after the answer: kept"
},
{
"args": {
"answer": [
{
"AT": 4,
"CHOSEN": [
"GRAV-UNIFORM"
],
"COVERED": "all"
}
],
"carried": [],
"claims": [
{
"ANSWERS": {},
"BIND": {
"HEIGHT": [
"z"
],
"MASS": [
"m"
],
"UP_VELOCITY": [
"v_z"
]
},
"DIGEST": "24877ccb5c8ec300d29ed82ce6650592f35cf8899a3d878ccce9c08d4c72c025",
"ID": "GRAV-UNIFORM",
"VALUES": {
"h_max": {
"UNIT": "m",
"VALUE": "100"
}
},
"VERSION": "1.0.0"
}
],
"lines": [
{
"ACT": "MODULE ADD",
"DATE": "2026-10-01",
"DIGEST": "5f3fe27b42378bce0830b0d0959f892f4a8e73b12b540ae877e39e6439d08b4d",
"ID": "AIR-LINEAR",
"VERSION": "1.0.0"
},
{
"ACT": "MODULE ADD",
"DATE": "2026-10-01",
"DIGEST": "6fb53c3a6546151eead2bd6e72e9cf8334f3a2040ad0ee2f5b988ec96d6fc852",
"ID": "AIR-QUADRATIC",
"VERSION": "1.0.0"
},
{
"ACT": "MODULE ADD",
"DATE": "2026-10-01",
"DIGEST": "24877ccb5c8ec300d29ed82ce6650592f35cf8899a3d878ccce9c08d4c72c025",
"ID": "GRAV-UNIFORM",
"VERSION": "1.0.0"
},
{
"ACT": "MODULE ADD",
"DATE": "2026-10-01",
"DIGEST": "8f39a356f35527b901fcee012764590f0819c8ffdeccad4bc05195ce3d2e0bcf",
"ID": "MATH",
"VERSION": "1.0.0"
}
],
"modified": [],
"modules": [
"{\"ID\": \"AIR-LINEAR\", \"VERSION\": \"1.0.0\", \"TITLE\": \"Air resistance at sea level, linear in the speed (Stokes drag on a sphere)\", \"SOURCE\": \"ISO 2533:1975, Standard Atmosphere, sea-level values: density 1.225 kg m-3, dynamic viscosity 1.7894e-5 Pa s\", \"PREREQUISITES\": [{\"SLOT\": \"VELOCITY\", \"KIND\": \"DOF\", \"DIMENSION\": \"L1 T-1\", \"MIN\": 1, \"MAX\": 3, \"LABEL\": \"the velocity components of the body, one per axis\"}], \"PARAMETERS\": [{\"NAME\": \"rho_air\", \"DIMENSION\": \"L-3 M1\", \"SUPPLY\": \"DECLARED\", \"VALUE\": \"1.225\", \"UNIT\": \"kg m-3\", \"OVERRIDABLE\": \"NO\", \"LABEL\": \"the density of air at sea level\"}, {\"NAME\": \"mu_air\", \"DIMENSION\": \"L-1 M1 T-1\", \"SUPPLY\": \"DECLARED\", \"VALUE\": \"1.7894e-5\", \"UNIT\": \"Pa s\", \"OVERRIDABLE\": \"NO\", \"LABEL\": \"the dynamic viscosity of air at sea level\"}, {\"NAME\": \"pi_c\", \"DIMENSION\": \"1\", \"SUPPLY\": \"DECLARED\", \"VALUE\": \"3.141592653589793\", \"UNIT\": \"1\", \"OVERRIDABLE\": \"NO\", \"LABEL\": \"pi, to 16 significant digits\"}, {\"NAME\": \"R_s\", \"DIMENSION\": \"L1\", \"SUPPLY\": \"AUTHOR\", \"LABEL\": \"the radius of the sphere\"}], \"SUMS\": [{\"NAME\": \"SPEED2\", \"OVER\": \"VELOCITY\", \"EACH\": \"VELOCITY^2\"}], \"TERMS\": [{\"TARGET\": \"VELOCITY\", \"SIGN\": \"-\", \"EXPR\": \"6*pi_c*mu_air*R_s*VELOCITY\", \"LABEL\": \"the linear (Stokes) drag\"}], \"ASSUMPTIONS\": [{\"NAME\": \"air_still\", \"PROPOSITION\": \"the air is at rest in the frame of the body's velocity\", \"REFS\": [\"VELOCITY\"]}, {\"NAME\": \"air_uniform\", \"PROPOSITION\": \"the air density is uniform over the region of motion\", \"REFS\": [\"rho_air\"]}, {\"NAME\": \"drag_sphere\", \"PROPOSITION\": \"the body is a rigid sphere of radius R_s\", \"REFS\": [\"R_s\"]}], \"BOUNDARIES\": [{\"NAME\": \"drag_linear_regime\", \"PREDICATE\": \"2 rho_air |v| R_s / mu_air < 1: the regime of the linear law\", \"CONDITION\": \"mu_air != 0 and SPEED2 >= 0 and 2*rho_air*sqrt(SPEED2)*R_s/mu_air < 1\"}], \"NOT_CHOSEN\": \"No linear (Stokes) air resistance.\", \"NOT_INCLUDED\": [\"No wind: the air is at rest.\", \"No change of air density or viscosity with altitude or temperature.\", \"No drag outside the regime of the linear law.\"], \"EXCLUDES\": [], \"INTERACTS_WITH\": [], \"TEST_BINDINGS\": [{\"NAME\": \"PROJECTILE_2D\", \"TPK\": {\"DOF\": [{\"NAME\": \"t\", \"DIMENSION\": \"T1\"}, {\"NAME\": \"x\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"z\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"v_x\", \"DIMENSION\": \"L1 T-1\"}, {\"NAME\": \"v_z\", \"DIMENSION\": \"L1 T-1\"}], \"CONSTANT\": [{\"NAME\": \"m\", \"DIMENSION\": \"M1\"}], \"LAW\": [{\"NAME\": \"KIN_X\", \"STATEMENT\": \"dx/dt = v_x\", \"REFS\": [\"t\", \"v_x\", \"x\"], \"ROLE\": \"EOM(x)\", \"EQUATION\": \"D(x,t)=v_x\"}, {\"NAME\": \"KIN_Z\", \"STATEMENT\": \"dz/dt = v_z\", \"REFS\": [\"t\", \"v_z\", \"z\"], \"ROLE\": \"EOM(z)\", \"EQUATION\": \"D(z,t)=v_z\"}, {\"NAME\": \"EOM_X\", \"STATEMENT\": \"m dv_x/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_x\"], \"ROLE\": \"EOM(v_x)\", \"EQUATION\": \"m*D(v_x,t)=0\"}, {\"NAME\": \"EOM_Z\", \"STATEMENT\": \"m dv_z/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_z\"], \"ROLE\": \"EOM(v_z)\", \"EQUATION\": \"m*D(v_z,t)=0\"}], \"ASSUMPTION\": [{\"NAME\": \"point_mass\", \"PROPOSITION\": \"the body is treated as a point mass\", \"REFS\": [\"m\"]}]}, \"BIND\": {\"VELOCITY\": [\"v_x\", \"v_z\"]}, \"VALUES\": {\"R_s\": {}}, \"ANSWERS\": {}}]}",
"{\"ID\": \"AIR-QUADRATIC\", \"VERSION\": \"1.0.0\", \"TITLE\": \"Air resistance at sea level, quadratic in the speed\", \"SOURCE\": \"ISO 2533:1975, Standard Atmosphere, sea-level values: density 1.225 kg m-3, dynamic viscosity 1.7894e-5 Pa s\", \"PREREQUISITES\": [{\"SLOT\": \"VELOCITY\", \"KIND\": \"DOF\", \"DIMENSION\": \"L1 T-1\", \"MIN\": 1, \"MAX\": 3, \"LABEL\": \"the velocity components of the body, one per axis\"}], \"PARAMETERS\": [{\"NAME\": \"rho_air\", \"DIMENSION\": \"L-3 M1\", \"SUPPLY\": \"DECLARED\", \"VALUE\": \"1.225\", \"UNIT\": \"kg m-3\", \"OVERRIDABLE\": \"NO\", \"LABEL\": \"the density of air at sea level\"}, {\"NAME\": \"mu_air\", \"DIMENSION\": \"L-1 M1 T-1\", \"SUPPLY\": \"DECLARED\", \"VALUE\": \"1.7894e-5\", \"UNIT\": \"Pa s\", \"OVERRIDABLE\": \"NO\", \"LABEL\": \"the dynamic viscosity of air at sea level\"}, {\"NAME\": \"C_d\", \"DIMENSION\": \"1\", \"SUPPLY\": \"AUTHOR\", \"LABEL\": \"the drag coefficient of the body\"}, {\"NAME\": \"A_ref\", \"DIMENSION\": \"L2\", \"SUPPLY\": \"AUTHOR\", \"LABEL\": \"the reference area of the drag coefficient\"}, {\"NAME\": \"L_ref\", \"DIMENSION\": \"L1\", \"SUPPLY\": \"AUTHOR\", \"LABEL\": \"the reference length of the Reynolds number\"}], \"SUMS\": [{\"NAME\": \"SPEED2\", \"OVER\": \"VELOCITY\", \"EACH\": \"VELOCITY^2\"}], \"TERMS\": [{\"TARGET\": \"VELOCITY\", \"SIGN\": \"-\", \"EXPR\": \"0.5*rho_air*C_d*A_ref*sqrt(SPEED2)*VELOCITY\", \"LABEL\": \"the quadratic drag\"}], \"ASSUMPTIONS\": [{\"NAME\": \"air_still\", \"PROPOSITION\": \"the air is at rest in the frame of the body's velocity\", \"REFS\": [\"VELOCITY\"]}, {\"NAME\": \"air_uniform\", \"PROPOSITION\": \"the air density is uniform over the region of motion\", \"REFS\": [\"rho_air\"]}, {\"NAME\": \"drag_cd_constant\", \"PROPOSITION\": \"the drag coefficient C_d is constant over the motion\", \"REFS\": [\"C_d\"]}, {\"NAME\": \"drag_no_lift\", \"PROPOSITION\": \"the body experiences no lift force\", \"REFS\": [\"VELOCITY\"]}, {\"NAME\": \"drag_no_magnus\", \"PROPOSITION\": \"the body experiences no Magnus force\", \"REFS\": [\"VELOCITY\"]}], \"BOUNDARIES\": [{\"NAME\": \"drag_quadratic_regime\", \"PREDICATE\": \"1e3 < rho_air |v| L_ref / mu_air < 2e5: the Reynolds window of the quadratic law\", \"CONDITION\": \"mu_air != 0 and SPEED2 >= 0 and rho_air*sqrt(SPEED2)*L_ref/mu_air > 1000 and rho_air*sqrt(SPEED2)*L_ref/mu_air < 200000\"}], \"NOT_CHOSEN\": \"No quadratic air resistance.\", \"NOT_INCLUDED\": [\"No wind: the air is at rest.\", \"No change of air density or viscosity with altitude or temperature.\", \"No lift, Magnus or added-mass force.\", \"No drag outside the Reynolds window of the quadratic law.\"], \"EXCLUDES\": [\"AIR-LINEAR\"], \"INTERACTS_WITH\": [], \"TEST_BINDINGS\": [{\"NAME\": \"PROJECTILE_2D\", \"TPK\": {\"DOF\": [{\"NAME\": \"t\", \"DIMENSION\": \"T1\"}, {\"NAME\": \"x\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"z\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"v_x\", \"DIMENSION\": \"L1 T-1\"}, {\"NAME\": \"v_z\", \"DIMENSION\": \"L1 T-1\"}], \"CONSTANT\": [{\"NAME\": \"m\", \"DIMENSION\": \"M1\"}], \"LAW\": [{\"NAME\": \"KIN_X\", \"STATEMENT\": \"dx/dt = v_x\", \"REFS\": [\"t\", \"v_x\", \"x\"], \"ROLE\": \"EOM(x)\", \"EQUATION\": \"D(x,t)=v_x\"}, {\"NAME\": \"KIN_Z\", \"STATEMENT\": \"dz/dt = v_z\", \"REFS\": [\"t\", \"v_z\", \"z\"], \"ROLE\": \"EOM(z)\", \"EQUATION\": \"D(z,t)=v_z\"}, {\"NAME\": \"EOM_X\", \"STATEMENT\": \"m dv_x/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_x\"], \"ROLE\": \"EOM(v_x)\", \"EQUATION\": \"m*D(v_x,t)=0\"}, {\"NAME\": \"EOM_Z\", \"STATEMENT\": \"m dv_z/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_z\"], \"ROLE\": \"EOM(v_z)\", \"EQUATION\": \"m*D(v_z,t)=0\"}], \"ASSUMPTION\": [{\"NAME\": \"point_mass\", \"PROPOSITION\": \"the body is treated as a point mass\", \"REFS\": [\"m\"]}]}, \"BIND\": {\"VELOCITY\": [\"v_x\", \"v_z\"]}, \"VALUES\": {\"A_ref\": {}, \"C_d\": {}, \"L_ref\": {}}, \"ANSWERS\": {}}]}",
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it acts in this kernel only where one of your own laws states it.\", \"NO_LINE\": \"No buoyancy: the air's upthrust on the body is not included.\"}], \"TEST_BINDINGS\": [{\"NAME\": \"PROJECTILE_2D\", \"TPK\": {\"DOF\": [{\"NAME\": \"t\", \"DIMENSION\": \"T1\"}, {\"NAME\": \"x\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"z\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"v_x\", \"DIMENSION\": \"L1 T-1\"}, {\"NAME\": \"v_z\", \"DIMENSION\": \"L1 T-1\"}], \"CONSTANT\": [{\"NAME\": \"m\", \"DIMENSION\": \"M1\"}], \"LAW\": [{\"NAME\": \"KIN_X\", \"STATEMENT\": \"dx/dt = v_x\", \"REFS\": [\"t\", \"v_x\", \"x\"], \"ROLE\": \"EOM(x)\", \"EQUATION\": \"D(x,t)=v_x\"}, {\"NAME\": \"KIN_Z\", \"STATEMENT\": \"dz/dt = v_z\", \"REFS\": [\"t\", \"v_z\", \"z\"], \"ROLE\": \"EOM(z)\", \"EQUATION\": \"D(z,t)=v_z\"}, {\"NAME\": \"EOM_X\", \"STATEMENT\": \"m dv_x/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_x\"], \"ROLE\": \"EOM(v_x)\", \"EQUATION\": \"m*D(v_x,t)=0\"}, {\"NAME\": \"EOM_Z\", \"STATEMENT\": \"m dv_z/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_z\"], \"ROLE\": \"EOM(v_z)\", \"EQUATION\": \"m*D(v_z,t)=0\"}], \"ASSUMPTION\": [{\"NAME\": \"point_mass\", \"PROPOSITION\": \"the body is treated as a point mass\", \"REFS\": [\"m\"]}]}, \"BIND\": {\"HEIGHT\": [\"z\"], \"MASS\": [\"m\"], \"UP_VELOCITY\": [\"v_z\"]}, \"VALUES\": {\"h_max\": {\"VALUE\": \"100\", \"UNIT\": \"m\"}}, \"ANSWERS\": {}}, {\"NAME\": \"TABLE\", \"TPK\": {\"DOF\": [{\"NAME\": \"t\", \"DIMENSION\": \"T1\"}, {\"NAME\": \"x\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"z\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"v_x\", \"DIMENSION\": \"L1 T-1\"}, {\"NAME\": \"v_z\", \"DIMENSION\": \"L1 T-1\"}], \"CONSTANT\": [{\"NAME\": \"m\", \"DIMENSION\": \"M1\"}], \"LAW\": [{\"NAME\": \"KIN_X\", \"STATEMENT\": \"dx/dt = v_x\", \"REFS\": [\"t\", \"v_x\", \"x\"], \"ROLE\": \"EOM(x)\", \"EQUATION\": \"D(x,t)=v_x\"}, {\"NAME\": \"KIN_Z\", \"STATEMENT\": \"dz/dt = v_z\", \"REFS\": [\"t\", \"v_z\", \"z\"], \"ROLE\": \"CONSTRAINT\", \"EQUATION\": \"D(z,t)=v_z\"}, {\"NAME\": \"EOM_X\", \"STATEMENT\": \"m dv_x/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_x\"], \"ROLE\": \"EOM(v_x)\", \"EQUATION\": \"m*D(v_x,t)=0\"}], \"CONSTRAINT\": [{\"NAME\": \"C_Z\", \"TARGET\": \"z\", \"ACTION\": \"FIX\", \"VALUE\": \"0\", \"UNIT\": \"m\", \"STATEMENT\": \"the puck stays on the table top, z = 0\"}, {\"NAME\": \"C_VZ\", \"TARGET\": \"v_z\", \"ACTION\": \"FIX\", \"VALUE\": \"0\", \"UNIT\": \"m s-1\", \"STATEMENT\": \"the puck has no vertical velocity\"}]}, \"BIND\": {\"HEIGHT\": [\"z\"], \"MASS\": [\"m\"], \"UP_VELOCITY\": [\"v_z\"]}, \"VALUES\": {\"h_max\": {\"VALUE\": \"1\", \"UNIT\": \"m\"}}, \"ANSWERS\": {\"FIXED:v_z\": \"YES\"}}]}",
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},
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"hand_checked": true,
"name": "I39 COVERED of the wrong type"
},
{
"args": {
"answer": [
{
"AT": 4,
"CHOSEN": [
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{
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"lines": [
{
"ACT": "MODULE ADD",
"DATE": "2026-10-01",
"DIGEST": "5f3fe27b42378bce0830b0d0959f892f4a8e73b12b540ae877e39e6439d08b4d",
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{
"ACT": "MODULE ADD",
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"DIGEST": "6fb53c3a6546151eead2bd6e72e9cf8334f3a2040ad0ee2f5b988ec96d6fc852",
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{
"ACT": "MODULE ADD",
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{
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"modules": [
"{\"ID\": \"AIR-LINEAR\", \"VERSION\": \"1.0.0\", \"TITLE\": \"Air resistance at sea level, linear in the speed (Stokes drag on a sphere)\", \"SOURCE\": \"ISO 2533:1975, Standard Atmosphere, sea-level values: density 1.225 kg m-3, dynamic viscosity 1.7894e-5 Pa s\", \"PREREQUISITES\": [{\"SLOT\": \"VELOCITY\", \"KIND\": \"DOF\", \"DIMENSION\": \"L1 T-1\", \"MIN\": 1, \"MAX\": 3, \"LABEL\": \"the velocity components of the body, one per axis\"}], \"PARAMETERS\": [{\"NAME\": \"rho_air\", \"DIMENSION\": \"L-3 M1\", \"SUPPLY\": \"DECLARED\", \"VALUE\": \"1.225\", \"UNIT\": \"kg m-3\", \"OVERRIDABLE\": \"NO\", \"LABEL\": \"the density of air at sea level\"}, {\"NAME\": \"mu_air\", \"DIMENSION\": \"L-1 M1 T-1\", \"SUPPLY\": \"DECLARED\", \"VALUE\": \"1.7894e-5\", \"UNIT\": \"Pa s\", \"OVERRIDABLE\": \"NO\", \"LABEL\": \"the dynamic viscosity of air at sea level\"}, {\"NAME\": \"pi_c\", \"DIMENSION\": \"1\", \"SUPPLY\": \"DECLARED\", \"VALUE\": \"3.141592653589793\", \"UNIT\": \"1\", \"OVERRIDABLE\": \"NO\", \"LABEL\": \"pi, to 16 significant digits\"}, {\"NAME\": \"R_s\", \"DIMENSION\": \"L1\", \"SUPPLY\": \"AUTHOR\", \"LABEL\": \"the radius of the sphere\"}], \"SUMS\": [{\"NAME\": \"SPEED2\", \"OVER\": \"VELOCITY\", \"EACH\": \"VELOCITY^2\"}], \"TERMS\": [{\"TARGET\": \"VELOCITY\", \"SIGN\": \"-\", \"EXPR\": \"6*pi_c*mu_air*R_s*VELOCITY\", \"LABEL\": \"the linear (Stokes) drag\"}], \"ASSUMPTIONS\": [{\"NAME\": \"air_still\", \"PROPOSITION\": \"the air is at rest in the frame of the body's velocity\", \"REFS\": [\"VELOCITY\"]}, {\"NAME\": \"air_uniform\", \"PROPOSITION\": \"the air density is uniform over the region of motion\", \"REFS\": [\"rho_air\"]}, {\"NAME\": \"drag_sphere\", \"PROPOSITION\": \"the body is a rigid sphere of radius R_s\", \"REFS\": [\"R_s\"]}], \"BOUNDARIES\": [{\"NAME\": \"drag_linear_regime\", \"PREDICATE\": \"2 rho_air |v| R_s / mu_air < 1: the regime of the linear law\", \"CONDITION\": \"mu_air != 0 and SPEED2 >= 0 and 2*rho_air*sqrt(SPEED2)*R_s/mu_air < 1\"}], \"NOT_CHOSEN\": \"No linear (Stokes) air resistance.\", \"NOT_INCLUDED\": [\"No wind: the air is at rest.\", \"No change of air density or viscosity with altitude or temperature.\", \"No drag outside the regime of the linear law.\"], \"EXCLUDES\": [], \"INTERACTS_WITH\": [], \"TEST_BINDINGS\": [{\"NAME\": \"PROJECTILE_2D\", \"TPK\": {\"DOF\": [{\"NAME\": \"t\", \"DIMENSION\": \"T1\"}, {\"NAME\": \"x\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"z\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"v_x\", \"DIMENSION\": \"L1 T-1\"}, {\"NAME\": \"v_z\", \"DIMENSION\": \"L1 T-1\"}], \"CONSTANT\": [{\"NAME\": \"m\", \"DIMENSION\": \"M1\"}], \"LAW\": [{\"NAME\": \"KIN_X\", \"STATEMENT\": \"dx/dt = v_x\", \"REFS\": [\"t\", \"v_x\", \"x\"], \"ROLE\": \"EOM(x)\", \"EQUATION\": \"D(x,t)=v_x\"}, {\"NAME\": \"KIN_Z\", \"STATEMENT\": \"dz/dt = v_z\", \"REFS\": [\"t\", \"v_z\", \"z\"], \"ROLE\": \"EOM(z)\", \"EQUATION\": \"D(z,t)=v_z\"}, {\"NAME\": \"EOM_X\", \"STATEMENT\": \"m dv_x/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_x\"], \"ROLE\": \"EOM(v_x)\", \"EQUATION\": \"m*D(v_x,t)=0\"}, {\"NAME\": \"EOM_Z\", \"STATEMENT\": \"m dv_z/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_z\"], \"ROLE\": \"EOM(v_z)\", \"EQUATION\": \"m*D(v_z,t)=0\"}], \"ASSUMPTION\": [{\"NAME\": \"point_mass\", \"PROPOSITION\": \"the body is treated as a point mass\", \"REFS\": [\"m\"]}]}, \"BIND\": {\"VELOCITY\": [\"v_x\", \"v_z\"]}, \"VALUES\": {\"R_s\": {}}, \"ANSWERS\": {}}]}",
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it acts in this kernel only where one of your own laws states it.\", \"NO_LINE\": \"No buoyancy: the air's upthrust on the body is not included.\"}], \"TEST_BINDINGS\": [{\"NAME\": \"PROJECTILE_2D\", \"TPK\": {\"DOF\": [{\"NAME\": \"t\", \"DIMENSION\": \"T1\"}, {\"NAME\": \"x\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"z\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"v_x\", \"DIMENSION\": \"L1 T-1\"}, {\"NAME\": \"v_z\", \"DIMENSION\": \"L1 T-1\"}], \"CONSTANT\": [{\"NAME\": \"m\", \"DIMENSION\": \"M1\"}], \"LAW\": [{\"NAME\": \"KIN_X\", \"STATEMENT\": \"dx/dt = v_x\", \"REFS\": [\"t\", \"v_x\", \"x\"], \"ROLE\": \"EOM(x)\", \"EQUATION\": \"D(x,t)=v_x\"}, {\"NAME\": \"KIN_Z\", \"STATEMENT\": \"dz/dt = v_z\", \"REFS\": [\"t\", \"v_z\", \"z\"], \"ROLE\": \"EOM(z)\", \"EQUATION\": \"D(z,t)=v_z\"}, {\"NAME\": \"EOM_X\", \"STATEMENT\": \"m dv_x/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_x\"], \"ROLE\": \"EOM(v_x)\", \"EQUATION\": \"m*D(v_x,t)=0\"}, {\"NAME\": \"EOM_Z\", \"STATEMENT\": \"m dv_z/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_z\"], \"ROLE\": \"EOM(v_z)\", \"EQUATION\": \"m*D(v_z,t)=0\"}], \"ASSUMPTION\": [{\"NAME\": \"point_mass\", \"PROPOSITION\": \"the body is treated as a point mass\", \"REFS\": [\"m\"]}]}, \"BIND\": {\"HEIGHT\": [\"z\"], \"MASS\": [\"m\"], \"UP_VELOCITY\": [\"v_z\"]}, \"VALUES\": {\"h_max\": {\"VALUE\": \"100\", \"UNIT\": \"m\"}}, \"ANSWERS\": {}}, {\"NAME\": \"TABLE\", \"TPK\": {\"DOF\": [{\"NAME\": \"t\", \"DIMENSION\": \"T1\"}, {\"NAME\": \"x\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"z\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"v_x\", \"DIMENSION\": \"L1 T-1\"}, {\"NAME\": \"v_z\", \"DIMENSION\": \"L1 T-1\"}], \"CONSTANT\": [{\"NAME\": \"m\", \"DIMENSION\": \"M1\"}], \"LAW\": [{\"NAME\": \"KIN_X\", \"STATEMENT\": \"dx/dt = v_x\", \"REFS\": [\"t\", \"v_x\", \"x\"], \"ROLE\": \"EOM(x)\", \"EQUATION\": \"D(x,t)=v_x\"}, {\"NAME\": \"KIN_Z\", \"STATEMENT\": \"dz/dt = v_z\", \"REFS\": [\"t\", \"v_z\", \"z\"], \"ROLE\": \"CONSTRAINT\", \"EQUATION\": \"D(z,t)=v_z\"}, {\"NAME\": \"EOM_X\", \"STATEMENT\": \"m dv_x/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_x\"], \"ROLE\": \"EOM(v_x)\", \"EQUATION\": \"m*D(v_x,t)=0\"}], \"CONSTRAINT\": [{\"NAME\": \"C_Z\", \"TARGET\": \"z\", \"ACTION\": \"FIX\", \"VALUE\": \"0\", \"UNIT\": \"m\", \"STATEMENT\": \"the puck stays on the table top, z = 0\"}, {\"NAME\": \"C_VZ\", \"TARGET\": \"v_z\", \"ACTION\": \"FIX\", \"VALUE\": \"0\", \"UNIT\": \"m s-1\", \"STATEMENT\": \"the puck has no vertical velocity\"}]}, \"BIND\": {\"HEIGHT\": [\"z\"], \"MASS\": [\"m\"], \"UP_VELOCITY\": [\"v_z\"]}, \"VALUES\": {\"h_max\": {\"VALUE\": \"1\", \"UNIT\": \"m\"}}, \"ANSWERS\": {\"FIXED:v_z\": \"YES\"}}]}",
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"hand_checked": true,
"name": "I40 CARRIED with a DIGEST not the declared one"
},
{
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{
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"lines": [
{
"ACT": "MODULE ADD",
"DATE": "2026-10-01",
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{
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"modules": [
"{\"ID\": \"AIR-LINEAR\", \"VERSION\": \"1.0.0\", \"TITLE\": \"Air resistance at sea level, linear in the speed (Stokes drag on a sphere)\", \"SOURCE\": \"ISO 2533:1975, Standard Atmosphere, sea-level values: density 1.225 kg m-3, dynamic viscosity 1.7894e-5 Pa s\", \"PREREQUISITES\": [{\"SLOT\": \"VELOCITY\", \"KIND\": \"DOF\", \"DIMENSION\": \"L1 T-1\", \"MIN\": 1, \"MAX\": 3, \"LABEL\": \"the velocity components of the body, one per axis\"}], \"PARAMETERS\": [{\"NAME\": \"rho_air\", \"DIMENSION\": \"L-3 M1\", \"SUPPLY\": \"DECLARED\", \"VALUE\": \"1.225\", \"UNIT\": \"kg m-3\", \"OVERRIDABLE\": \"NO\", \"LABEL\": \"the density of air at sea level\"}, {\"NAME\": \"mu_air\", \"DIMENSION\": \"L-1 M1 T-1\", \"SUPPLY\": \"DECLARED\", \"VALUE\": \"1.7894e-5\", \"UNIT\": \"Pa s\", \"OVERRIDABLE\": \"NO\", \"LABEL\": \"the dynamic viscosity of air at sea level\"}, {\"NAME\": \"pi_c\", \"DIMENSION\": \"1\", \"SUPPLY\": \"DECLARED\", \"VALUE\": \"3.141592653589793\", \"UNIT\": \"1\", \"OVERRIDABLE\": \"NO\", \"LABEL\": \"pi, to 16 significant digits\"}, {\"NAME\": \"R_s\", \"DIMENSION\": \"L1\", \"SUPPLY\": \"AUTHOR\", \"LABEL\": \"the radius of the sphere\"}], \"SUMS\": [{\"NAME\": \"SPEED2\", \"OVER\": \"VELOCITY\", \"EACH\": \"VELOCITY^2\"}], \"TERMS\": [{\"TARGET\": \"VELOCITY\", \"SIGN\": \"-\", \"EXPR\": \"6*pi_c*mu_air*R_s*VELOCITY\", \"LABEL\": \"the linear (Stokes) drag\"}], \"ASSUMPTIONS\": [{\"NAME\": \"air_still\", \"PROPOSITION\": \"the air is at rest in the frame of the body's velocity\", \"REFS\": [\"VELOCITY\"]}, {\"NAME\": \"air_uniform\", \"PROPOSITION\": \"the air density is uniform over the region of motion\", \"REFS\": [\"rho_air\"]}, {\"NAME\": \"drag_sphere\", \"PROPOSITION\": \"the body is a rigid sphere of radius R_s\", \"REFS\": [\"R_s\"]}], \"BOUNDARIES\": [{\"NAME\": \"drag_linear_regime\", \"PREDICATE\": \"2 rho_air |v| R_s / mu_air < 1: the regime of the linear law\", \"CONDITION\": \"mu_air != 0 and SPEED2 >= 0 and 2*rho_air*sqrt(SPEED2)*R_s/mu_air < 1\"}], \"NOT_CHOSEN\": \"No linear (Stokes) air resistance.\", \"NOT_INCLUDED\": [\"No wind: the air is at rest.\", \"No change of air density or viscosity with altitude or temperature.\", \"No drag outside the regime of the linear law.\"], \"EXCLUDES\": [], \"INTERACTS_WITH\": [], \"TEST_BINDINGS\": [{\"NAME\": \"PROJECTILE_2D\", \"TPK\": {\"DOF\": [{\"NAME\": \"t\", \"DIMENSION\": \"T1\"}, {\"NAME\": \"x\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"z\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"v_x\", \"DIMENSION\": \"L1 T-1\"}, {\"NAME\": \"v_z\", \"DIMENSION\": \"L1 T-1\"}], \"CONSTANT\": [{\"NAME\": \"m\", \"DIMENSION\": \"M1\"}], \"LAW\": [{\"NAME\": \"KIN_X\", \"STATEMENT\": \"dx/dt = v_x\", \"REFS\": [\"t\", \"v_x\", \"x\"], \"ROLE\": \"EOM(x)\", \"EQUATION\": \"D(x,t)=v_x\"}, {\"NAME\": \"KIN_Z\", \"STATEMENT\": \"dz/dt = v_z\", \"REFS\": [\"t\", \"v_z\", \"z\"], \"ROLE\": \"EOM(z)\", \"EQUATION\": \"D(z,t)=v_z\"}, {\"NAME\": \"EOM_X\", \"STATEMENT\": \"m dv_x/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_x\"], \"ROLE\": \"EOM(v_x)\", \"EQUATION\": \"m*D(v_x,t)=0\"}, {\"NAME\": \"EOM_Z\", \"STATEMENT\": \"m dv_z/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_z\"], \"ROLE\": \"EOM(v_z)\", \"EQUATION\": \"m*D(v_z,t)=0\"}], \"ASSUMPTION\": [{\"NAME\": \"point_mass\", \"PROPOSITION\": \"the body is treated as a point mass\", \"REFS\": [\"m\"]}]}, \"BIND\": {\"VELOCITY\": [\"v_x\", \"v_z\"]}, \"VALUES\": {\"R_s\": {}}, \"ANSWERS\": {}}]}",
"{\"ID\": \"AIR-QUADRATIC\", \"VERSION\": \"1.0.0\", \"TITLE\": \"Air resistance at sea level, quadratic in the speed\", \"SOURCE\": \"ISO 2533:1975, Standard Atmosphere, sea-level values: density 1.225 kg m-3, dynamic viscosity 1.7894e-5 Pa s\", \"PREREQUISITES\": [{\"SLOT\": \"VELOCITY\", \"KIND\": \"DOF\", \"DIMENSION\": \"L1 T-1\", \"MIN\": 1, \"MAX\": 3, \"LABEL\": \"the velocity components of the body, one per axis\"}], \"PARAMETERS\": [{\"NAME\": \"rho_air\", \"DIMENSION\": \"L-3 M1\", \"SUPPLY\": \"DECLARED\", \"VALUE\": \"1.225\", \"UNIT\": \"kg m-3\", \"OVERRIDABLE\": \"NO\", \"LABEL\": \"the density of air at sea level\"}, {\"NAME\": \"mu_air\", \"DIMENSION\": \"L-1 M1 T-1\", \"SUPPLY\": \"DECLARED\", \"VALUE\": \"1.7894e-5\", \"UNIT\": \"Pa s\", \"OVERRIDABLE\": \"NO\", \"LABEL\": \"the dynamic viscosity of air at sea level\"}, {\"NAME\": \"C_d\", \"DIMENSION\": \"1\", \"SUPPLY\": \"AUTHOR\", \"LABEL\": \"the drag coefficient of the body\"}, {\"NAME\": \"A_ref\", \"DIMENSION\": \"L2\", \"SUPPLY\": \"AUTHOR\", \"LABEL\": \"the reference area of the drag coefficient\"}, {\"NAME\": \"L_ref\", \"DIMENSION\": \"L1\", \"SUPPLY\": \"AUTHOR\", \"LABEL\": \"the reference length of the Reynolds number\"}], \"SUMS\": [{\"NAME\": \"SPEED2\", \"OVER\": \"VELOCITY\", \"EACH\": \"VELOCITY^2\"}], \"TERMS\": [{\"TARGET\": \"VELOCITY\", \"SIGN\": \"-\", \"EXPR\": \"0.5*rho_air*C_d*A_ref*sqrt(SPEED2)*VELOCITY\", \"LABEL\": \"the quadratic drag\"}], \"ASSUMPTIONS\": [{\"NAME\": \"air_still\", \"PROPOSITION\": \"the air is at rest in the frame of the body's velocity\", \"REFS\": [\"VELOCITY\"]}, {\"NAME\": \"air_uniform\", \"PROPOSITION\": \"the air density is uniform over the region of motion\", \"REFS\": [\"rho_air\"]}, {\"NAME\": \"drag_cd_constant\", \"PROPOSITION\": \"the drag coefficient C_d is constant over the motion\", \"REFS\": [\"C_d\"]}, {\"NAME\": \"drag_no_lift\", \"PROPOSITION\": \"the body experiences no lift force\", \"REFS\": [\"VELOCITY\"]}, {\"NAME\": \"drag_no_magnus\", \"PROPOSITION\": \"the body experiences no Magnus force\", \"REFS\": [\"VELOCITY\"]}], \"BOUNDARIES\": [{\"NAME\": \"drag_quadratic_regime\", \"PREDICATE\": \"1e3 < rho_air |v| L_ref / mu_air < 2e5: the Reynolds window of the quadratic law\", \"CONDITION\": \"mu_air != 0 and SPEED2 >= 0 and rho_air*sqrt(SPEED2)*L_ref/mu_air > 1000 and rho_air*sqrt(SPEED2)*L_ref/mu_air < 200000\"}], \"NOT_CHOSEN\": \"No quadratic air resistance.\", \"NOT_INCLUDED\": [\"No wind: the air is at rest.\", \"No change of air density or viscosity with altitude or temperature.\", \"No lift, Magnus or added-mass force.\", \"No drag outside the Reynolds window of the quadratic law.\"], \"EXCLUDES\": [\"AIR-LINEAR\"], \"INTERACTS_WITH\": [], \"TEST_BINDINGS\": [{\"NAME\": \"PROJECTILE_2D\", \"TPK\": {\"DOF\": [{\"NAME\": \"t\", \"DIMENSION\": \"T1\"}, {\"NAME\": \"x\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"z\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"v_x\", \"DIMENSION\": \"L1 T-1\"}, {\"NAME\": \"v_z\", \"DIMENSION\": \"L1 T-1\"}], \"CONSTANT\": [{\"NAME\": \"m\", \"DIMENSION\": \"M1\"}], \"LAW\": [{\"NAME\": \"KIN_X\", \"STATEMENT\": \"dx/dt = v_x\", \"REFS\": [\"t\", \"v_x\", \"x\"], \"ROLE\": \"EOM(x)\", \"EQUATION\": \"D(x,t)=v_x\"}, {\"NAME\": \"KIN_Z\", \"STATEMENT\": \"dz/dt = v_z\", \"REFS\": [\"t\", \"v_z\", \"z\"], \"ROLE\": \"EOM(z)\", \"EQUATION\": \"D(z,t)=v_z\"}, {\"NAME\": \"EOM_X\", \"STATEMENT\": \"m dv_x/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_x\"], \"ROLE\": \"EOM(v_x)\", \"EQUATION\": \"m*D(v_x,t)=0\"}, {\"NAME\": \"EOM_Z\", \"STATEMENT\": \"m dv_z/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_z\"], \"ROLE\": \"EOM(v_z)\", \"EQUATION\": \"m*D(v_z,t)=0\"}], \"ASSUMPTION\": [{\"NAME\": \"point_mass\", \"PROPOSITION\": \"the body is treated as a point mass\", \"REFS\": [\"m\"]}]}, \"BIND\": {\"VELOCITY\": [\"v_x\", \"v_z\"]}, \"VALUES\": {\"A_ref\": {}, \"C_d\": {}, \"L_ref\": {}}, \"ANSWERS\": {}}]}",
"{\"ID\": \"GRAV-UNIFORM\", \"VERSION\": \"1.0.0\", \"TITLE\": \"Uniform gravity at the standard value g_n\", \"SOURCE\": \"g_n = 9.80665 m s-2, exact by definition: 3rd CGPM (1901), declaration on the unit of mass and on the definition of weight\", \"PREREQUISITES\": [{\"SLOT\": \"MASS\", \"KIND\": \"CONSTANT\", \"DIMENSION\": \"M1\", \"MIN\": 1, \"MAX\": 1, \"LABEL\": \"the mass of the body\"}, {\"SLOT\": \"UP_VELOCITY\", \"KIND\": \"DOF\", \"DIMENSION\": \"L1 T-1\", \"MIN\": 1, \"MAX\": 1, \"LABEL\": \"the velocity component pointing up; its equation of motion receives the weight\"}, {\"SLOT\": \"HEIGHT\", \"KIND\": \"DOF\", \"DIMENSION\": \"L1\", \"MIN\": 1, \"MAX\": 1, \"LABEL\": \"the position along the same upward axis\"}], \"PARAMETERS\": [{\"NAME\": \"g_n\", \"DIMENSION\": \"L1 T-2\", \"SUPPLY\": \"DECLARED\", \"VALUE\": \"9.80665\", \"UNIT\": \"m s-2\", \"OVERRIDABLE\": \"NO\", \"LABEL\": \"the standard acceleration of gravity\"}, {\"NAME\": \"h_max\", \"DIMENSION\": \"L1\", \"SUPPLY\": \"AUTHOR\", \"LABEL\": \"the largest height, above or below the origin, over which the field is taken as uniform\"}], \"SUMS\": [], \"TERMS\": [{\"TARGET\": \"UP_VELOCITY\", \"SIGN\": \"-\", \"EXPR\": \"MASS*g_n\", \"LABEL\": \"the weight\"}], \"ASSUMPTIONS\": [{\"NAME\": \"gravity_uniform\", \"PROPOSITION\": \"the gravitational field is uniform over the region abs({HEIGHT}) < h_max\", \"REFS\": [\"HEIGHT\", \"h_max\"]}, {\"NAME\": \"gravity_standard\", \"PROPOSITION\": \"the local gravitational acceleration equals the conventional standard value g_n\", \"REFS\": [\"g_n\"]}, {\"NAME\": \"frame_inertial\", \"PROPOSITION\": \"the frame in which {HEIGHT} is measured is treated as inertial\", \"REFS\": [\"HEIGHT\"]}], \"BOUNDARIES\": [{\"NAME\": \"gravity_region\", \"PREDICATE\": \"abs({HEIGHT}) < h_max\", \"CONDITION\": \"abs(HEIGHT) < h_max\"}], \"NOT_CHOSEN\": \"No gravity: no weight acts on any DOF.\", \"NOT_INCLUDED\": [\"No variation of gravity with height or latitude beyond what g_n contains.\", \"No Earth rotation (Coriolis or centrifugal force) beyond what g_n contains.\", \"No gravity of bodies other than the Earth.\"], \"EXCLUDES\": [], \"INTERACTS_WITH\": [{\"WITH\": \"AIR-*\", \"QUESTION_ID\": \"BUOYANCY\", \"QUESTION\": \"Does the air's buoyancy (upthrust) act on the body in the system you mean?\", \"YES_LINE\": \"Buoyancy acts (your answer): no module adds it; it acts in this kernel only where one of your own laws states it.\", \"NO_LINE\": \"No buoyancy: the air's upthrust on the body is not included.\"}], \"TEST_BINDINGS\": [{\"NAME\": \"PROJECTILE_2D\", \"TPK\": {\"DOF\": [{\"NAME\": \"t\", \"DIMENSION\": \"T1\"}, {\"NAME\": \"x\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"z\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"v_x\", \"DIMENSION\": \"L1 T-1\"}, {\"NAME\": \"v_z\", \"DIMENSION\": \"L1 T-1\"}], \"CONSTANT\": [{\"NAME\": \"m\", \"DIMENSION\": \"M1\"}], \"LAW\": [{\"NAME\": \"KIN_X\", \"STATEMENT\": \"dx/dt = v_x\", \"REFS\": [\"t\", \"v_x\", \"x\"], \"ROLE\": \"EOM(x)\", \"EQUATION\": \"D(x,t)=v_x\"}, {\"NAME\": \"KIN_Z\", \"STATEMENT\": \"dz/dt = v_z\", \"REFS\": [\"t\", \"v_z\", \"z\"], \"ROLE\": \"EOM(z)\", \"EQUATION\": \"D(z,t)=v_z\"}, {\"NAME\": \"EOM_X\", \"STATEMENT\": \"m dv_x/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_x\"], \"ROLE\": \"EOM(v_x)\", \"EQUATION\": \"m*D(v_x,t)=0\"}, {\"NAME\": \"EOM_Z\", \"STATEMENT\": \"m dv_z/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_z\"], \"ROLE\": \"EOM(v_z)\", \"EQUATION\": \"m*D(v_z,t)=0\"}], \"ASSUMPTION\": [{\"NAME\": \"point_mass\", \"PROPOSITION\": \"the body is treated as a point mass\", \"REFS\": [\"m\"]}]}, \"BIND\": {\"HEIGHT\": [\"z\"], \"MASS\": [\"m\"], \"UP_VELOCITY\": [\"v_z\"]}, \"VALUES\": {\"h_max\": {\"VALUE\": \"100\", \"UNIT\": \"m\"}}, \"ANSWERS\": {}}, {\"NAME\": \"TABLE\", \"TPK\": {\"DOF\": [{\"NAME\": \"t\", \"DIMENSION\": \"T1\"}, {\"NAME\": \"x\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"z\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"v_x\", \"DIMENSION\": \"L1 T-1\"}, {\"NAME\": \"v_z\", \"DIMENSION\": \"L1 T-1\"}], \"CONSTANT\": [{\"NAME\": \"m\", \"DIMENSION\": \"M1\"}], \"LAW\": [{\"NAME\": \"KIN_X\", \"STATEMENT\": \"dx/dt = v_x\", \"REFS\": [\"t\", \"v_x\", \"x\"], \"ROLE\": \"EOM(x)\", \"EQUATION\": \"D(x,t)=v_x\"}, {\"NAME\": \"KIN_Z\", \"STATEMENT\": \"dz/dt = v_z\", \"REFS\": [\"t\", \"v_z\", \"z\"], \"ROLE\": \"CONSTRAINT\", \"EQUATION\": \"D(z,t)=v_z\"}, {\"NAME\": \"EOM_X\", \"STATEMENT\": \"m dv_x/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_x\"], \"ROLE\": \"EOM(v_x)\", \"EQUATION\": \"m*D(v_x,t)=0\"}], \"CONSTRAINT\": [{\"NAME\": \"C_Z\", \"TARGET\": \"z\", \"ACTION\": \"FIX\", \"VALUE\": \"0\", \"UNIT\": \"m\", \"STATEMENT\": \"the puck stays on the table top, z = 0\"}, {\"NAME\": \"C_VZ\", \"TARGET\": \"v_z\", \"ACTION\": \"FIX\", \"VALUE\": \"0\", \"UNIT\": \"m s-1\", \"STATEMENT\": \"the puck has no vertical velocity\"}]}, \"BIND\": {\"HEIGHT\": [\"z\"], \"MASS\": [\"m\"], \"UP_VELOCITY\": [\"v_z\"]}, \"VALUES\": {\"h_max\": {\"VALUE\": \"1\", \"UNIT\": \"m\"}}, \"ANSWERS\": {\"FIXED:v_z\": \"YES\"}}]}",
"{\"ID\": \"MATH\", \"VERSION\": \"1.0.0\", \"TITLE\": \"The mathematical constant pi, as the CONSTANT pi_c\", \"SOURCE\": \"pi to 16 significant digits, 3.141592653589793, the nearest IEEE 754 binary64 value\", \"PREREQUISITES\": [], \"PARAMETERS\": [{\"NAME\": \"pi_c\", \"DIMENSION\": \"1\", \"SUPPLY\": \"DECLARED\", \"VALUE\": \"3.141592653589793\", \"UNIT\": \"1\", \"OVERRIDABLE\": \"NO\", \"LABEL\": \"pi, to 16 significant digits\"}], \"SUMS\": [], \"TERMS\": [], \"ASSUMPTIONS\": [], \"BOUNDARIES\": [], \"NOT_CHOSEN\": \"No mathematical constant: pi exists only if you declare it.\", \"NOT_INCLUDED\": [\"pi_c is pi rounded to 16 significant digits; no other mathematical constant is declared.\"], \"EXCLUDES\": [], \"INTERACTS_WITH\": [], \"TEST_BINDINGS\": [{\"NAME\": \"PROJECTILE_2D\", \"TPK\": {\"DOF\": [{\"NAME\": \"t\", \"DIMENSION\": \"T1\"}, {\"NAME\": \"x\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"z\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"v_x\", \"DIMENSION\": \"L1 T-1\"}, {\"NAME\": \"v_z\", \"DIMENSION\": \"L1 T-1\"}], \"CONSTANT\": [{\"NAME\": \"m\", \"DIMENSION\": \"M1\"}], \"LAW\": [{\"NAME\": \"KIN_X\", \"STATEMENT\": \"dx/dt = v_x\", \"REFS\": [\"t\", \"v_x\", \"x\"], \"ROLE\": \"EOM(x)\", \"EQUATION\": \"D(x,t)=v_x\"}, {\"NAME\": \"KIN_Z\", \"STATEMENT\": \"dz/dt = v_z\", \"REFS\": [\"t\", \"v_z\", \"z\"], \"ROLE\": \"EOM(z)\", \"EQUATION\": \"D(z,t)=v_z\"}, {\"NAME\": \"EOM_X\", \"STATEMENT\": \"m dv_x/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_x\"], \"ROLE\": \"EOM(v_x)\", \"EQUATION\": \"m*D(v_x,t)=0\"}, {\"NAME\": \"EOM_Z\", \"STATEMENT\": \"m dv_z/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_z\"], \"ROLE\": \"EOM(v_z)\", \"EQUATION\": \"m*D(v_z,t)=0\"}], \"ASSUMPTION\": [{\"NAME\": \"point_mass\", \"PROPOSITION\": \"the body is treated as a point mass\", \"REFS\": [\"m\"]}]}, \"BIND\": {}, \"VALUES\": {}, \"ANSWERS\": {}}]}",
"{\"ID\": \"GRAV-UNIFORM\", \"VERSION\": \"1.1.0\", \"TITLE\": \"Uniform gravity at the standard value g_n (text revised)\", \"SOURCE\": \"g_n = 9.80665 m s-2, exact by definition: 3rd CGPM (1901), declaration on the unit of mass and on the definition of weight\", \"PREREQUISITES\": [{\"SLOT\": \"MASS\", \"KIND\": \"CONSTANT\", \"DIMENSION\": \"M1\", \"MIN\": 1, \"MAX\": 1, \"LABEL\": \"the mass of the body\"}, {\"SLOT\": \"UP_VELOCITY\", \"KIND\": \"DOF\", \"DIMENSION\": \"L1 T-1\", \"MIN\": 1, \"MAX\": 1, \"LABEL\": \"the velocity component pointing up; its equation of motion receives the weight\"}, {\"SLOT\": \"HEIGHT\", \"KIND\": \"DOF\", \"DIMENSION\": \"L1\", \"MIN\": 1, \"MAX\": 1, \"LABEL\": \"the position along the same upward axis\"}], \"PARAMETERS\": [{\"NAME\": \"g_n\", \"DIMENSION\": \"L1 T-2\", \"SUPPLY\": \"DECLARED\", \"VALUE\": \"9.80665\", \"UNIT\": \"m s-2\", \"OVERRIDABLE\": \"NO\", \"LABEL\": \"the standard acceleration of gravity\"}, {\"NAME\": \"h_max\", \"DIMENSION\": \"L1\", \"SUPPLY\": \"AUTHOR\", \"LABEL\": \"the largest height, above or below the origin, over which the field is taken as uniform\"}], \"SUMS\": [], \"TERMS\": [{\"TARGET\": \"UP_VELOCITY\", \"SIGN\": \"-\", \"EXPR\": \"MASS*g_n\", \"LABEL\": \"the weight\"}], \"ASSUMPTIONS\": [{\"NAME\": \"gravity_uniform\", \"PROPOSITION\": \"the gravitational field is uniform over the region abs({HEIGHT}) < h_max\", \"REFS\": [\"HEIGHT\", \"h_max\"]}, {\"NAME\": \"gravity_standard\", \"PROPOSITION\": \"the local gravitational acceleration equals the conventional standard value g_n\", \"REFS\": [\"g_n\"]}, {\"NAME\": \"frame_inertial\", \"PROPOSITION\": \"the frame in which {HEIGHT} is measured is treated as inertial\", \"REFS\": [\"HEIGHT\"]}], \"BOUNDARIES\": [{\"NAME\": \"gravity_region\", \"PREDICATE\": \"abs({HEIGHT}) < h_max\", \"CONDITION\": \"abs(HEIGHT) < h_max\"}], \"NOT_CHOSEN\": \"No gravity: no weight acts on any DOF.\", \"NOT_INCLUDED\": [\"No variation of gravity with height or latitude beyond what g_n contains.\", \"No Earth rotation (Coriolis or centrifugal force) beyond what g_n contains.\", \"No gravity of bodies other than the Earth.\"], \"EXCLUDES\": [], \"INTERACTS_WITH\": [{\"WITH\": \"AIR-*\", \"QUESTION_ID\": \"BUOYANCY\", \"QUESTION\": \"Does the air's buoyancy (upthrust) act on the body in the system you mean?\", \"YES_LINE\": \"Buoyancy acts (your answer): no module adds it; it acts in this kernel only where one of your own laws states it.\", \"NO_LINE\": \"No buoyancy: the air's upthrust on the body is not included.\"}], \"TEST_BINDINGS\": [{\"NAME\": \"PROJECTILE_2D\", \"TPK\": {\"DOF\": [{\"NAME\": \"t\", \"DIMENSION\": \"T1\"}, {\"NAME\": \"x\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"z\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"v_x\", \"DIMENSION\": \"L1 T-1\"}, {\"NAME\": \"v_z\", \"DIMENSION\": \"L1 T-1\"}], \"CONSTANT\": [{\"NAME\": \"m\", \"DIMENSION\": \"M1\"}], \"LAW\": [{\"NAME\": \"KIN_X\", \"STATEMENT\": \"dx/dt = v_x\", \"REFS\": [\"t\", \"v_x\", \"x\"], \"ROLE\": \"EOM(x)\", \"EQUATION\": \"D(x,t)=v_x\"}, {\"NAME\": \"KIN_Z\", \"STATEMENT\": \"dz/dt = v_z\", \"REFS\": [\"t\", \"v_z\", \"z\"], \"ROLE\": \"EOM(z)\", \"EQUATION\": \"D(z,t)=v_z\"}, {\"NAME\": \"EOM_X\", \"STATEMENT\": \"m dv_x/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_x\"], \"ROLE\": \"EOM(v_x)\", \"EQUATION\": \"m*D(v_x,t)=0\"}, {\"NAME\": \"EOM_Z\", \"STATEMENT\": \"m dv_z/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_z\"], \"ROLE\": \"EOM(v_z)\", \"EQUATION\": \"m*D(v_z,t)=0\"}], \"ASSUMPTION\": [{\"NAME\": \"point_mass\", \"PROPOSITION\": \"the body is treated as a point mass\", \"REFS\": [\"m\"]}]}, \"BIND\": {\"HEIGHT\": [\"z\"], \"MASS\": [\"m\"], \"UP_VELOCITY\": [\"v_z\"]}, \"VALUES\": {\"h_max\": {\"VALUE\": \"100\", \"UNIT\": \"m\"}}, \"ANSWERS\": {}}, {\"NAME\": \"TABLE\", \"TPK\": {\"DOF\": [{\"NAME\": \"t\", \"DIMENSION\": \"T1\"}, {\"NAME\": \"x\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"z\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"v_x\", \"DIMENSION\": \"L1 T-1\"}, {\"NAME\": \"v_z\", \"DIMENSION\": \"L1 T-1\"}], \"CONSTANT\": [{\"NAME\": \"m\", \"DIMENSION\": \"M1\"}], \"LAW\": [{\"NAME\": \"KIN_X\", \"STATEMENT\": \"dx/dt = v_x\", \"REFS\": [\"t\", \"v_x\", \"x\"], \"ROLE\": \"EOM(x)\", \"EQUATION\": \"D(x,t)=v_x\"}, {\"NAME\": \"KIN_Z\", \"STATEMENT\": \"dz/dt = v_z\", \"REFS\": [\"t\", \"v_z\", \"z\"], \"ROLE\": \"CONSTRAINT\", \"EQUATION\": \"D(z,t)=v_z\"}, {\"NAME\": \"EOM_X\", \"STATEMENT\": \"m dv_x/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_x\"], \"ROLE\": \"EOM(v_x)\", \"EQUATION\": \"m*D(v_x,t)=0\"}], \"CONSTRAINT\": [{\"NAME\": \"C_Z\", \"TARGET\": \"z\", \"ACTION\": \"FIX\", \"VALUE\": \"0\", \"UNIT\": \"m\", \"STATEMENT\": \"the puck stays on the table top, z = 0\"}, {\"NAME\": \"C_VZ\", \"TARGET\": \"v_z\", \"ACTION\": \"FIX\", \"VALUE\": \"0\", \"UNIT\": \"m s-1\", \"STATEMENT\": \"the puck has no vertical velocity\"}]}, \"BIND\": {\"HEIGHT\": [\"z\"], \"MASS\": [\"m\"], \"UP_VELOCITY\": [\"v_z\"]}, \"VALUES\": {\"h_max\": {\"VALUE\": \"1\", \"UNIT\": \"m\"}}, \"ANSWERS\": {\"FIXED:v_z\": \"YES\"}}]}"
]
},
"expected": "[\"OK\",[\"ASK\",[]],[\"CLAIMS\",[[\"GRAV-UNIFORM\",\"1.1.0\",\"PINNED\"]]]]",
"fn": "interview_check",
"hand_checked": true,
"name": "I41 a re-selection round takes the OFFERED version: PINNED to it"
},
{
"args": {
"answer": [
{
"AT": 4,
"CHOSEN": [
"GRAV-UNIFORM"
],
"COVERED": [
[
"AIR-LINEAR",
"1.0.0",
"5f3fe27b42378bce0830b0d0959f892f4a8e73b12b540ae877e39e6439d08b4d"
],
[
"AIR-QUADRATIC",
"1.0.0",
"6fb53c3a6546151eead2bd6e72e9cf8334f3a2040ad0ee2f5b988ec96d6fc852"
],
[
"GRAV-UNIFORM",
"1.0.0",
"24877ccb5c8ec300d29ed82ce6650592f35cf8899a3d878ccce9c08d4c72c025"
],
[
"MATH",
"1.0.0",
"8f39a356f35527b901fcee012764590f0819c8ffdeccad4bc05195ce3d2e0bcf"
]
]
},
{
"AT": 5,
"CHOSEN": [
"GRAV-UNIFORM"
],
"COVERED": [
[
"GRAV-UNIFORM",
"1.1.0",
"5be3923c28dc8f8ff910b033c2d17154f267f2a20fdb32c74a07293a37dfe338"
]
],
"RESELECT": [
"GRAV-UNIFORM"
]
}
],
"carried": [],
"claims": [
{
"ANSWERS": {},
"BIND": {
"HEIGHT": [
"z"
],
"MASS": [
"m"
],
"UP_VELOCITY": [
"v_z"
]
},
"DIGEST": "24877ccb5c8ec300d29ed82ce6650592f35cf8899a3d878ccce9c08d4c72c025",
"ID": "GRAV-UNIFORM",
"VALUES": {
"h_max": {
"UNIT": "m",
"VALUE": "100"
}
},
"VERSION": "1.0.0"
}
],
"lines": [
{
"ACT": "MODULE ADD",
"DATE": "2026-10-01",
"DIGEST": "5f3fe27b42378bce0830b0d0959f892f4a8e73b12b540ae877e39e6439d08b4d",
"ID": "AIR-LINEAR",
"VERSION": "1.0.0"
},
{
"ACT": "MODULE ADD",
"DATE": "2026-10-01",
"DIGEST": "6fb53c3a6546151eead2bd6e72e9cf8334f3a2040ad0ee2f5b988ec96d6fc852",
"ID": "AIR-QUADRATIC",
"VERSION": "1.0.0"
},
{
"ACT": "MODULE ADD",
"DATE": "2026-10-01",
"DIGEST": "24877ccb5c8ec300d29ed82ce6650592f35cf8899a3d878ccce9c08d4c72c025",
"ID": "GRAV-UNIFORM",
"VERSION": "1.0.0"
},
{
"ACT": "MODULE ADD",
"DATE": "2026-10-01",
"DIGEST": "8f39a356f35527b901fcee012764590f0819c8ffdeccad4bc05195ce3d2e0bcf",
"ID": "MATH",
"VERSION": "1.0.0"
},
{
"ACT": "MODULE VERSION",
"DATE": "2026-10-02",
"DIGEST": "5be3923c28dc8f8ff910b033c2d17154f267f2a20fdb32c74a07293a37dfe338",
"ID": "GRAV-UNIFORM",
"VERSION": "1.1.0"
}
],
"modified": [],
"modules": [
"{\"ID\": \"AIR-LINEAR\", \"VERSION\": \"1.0.0\", \"TITLE\": \"Air resistance at sea level, linear in the speed (Stokes drag on a sphere)\", \"SOURCE\": \"ISO 2533:1975, Standard Atmosphere, sea-level values: density 1.225 kg m-3, dynamic viscosity 1.7894e-5 Pa s\", \"PREREQUISITES\": [{\"SLOT\": \"VELOCITY\", \"KIND\": \"DOF\", \"DIMENSION\": \"L1 T-1\", \"MIN\": 1, \"MAX\": 3, \"LABEL\": \"the velocity components of the body, one per axis\"}], \"PARAMETERS\": [{\"NAME\": \"rho_air\", \"DIMENSION\": \"L-3 M1\", \"SUPPLY\": \"DECLARED\", \"VALUE\": \"1.225\", \"UNIT\": \"kg m-3\", \"OVERRIDABLE\": \"NO\", \"LABEL\": \"the density of air at sea level\"}, {\"NAME\": \"mu_air\", \"DIMENSION\": \"L-1 M1 T-1\", \"SUPPLY\": \"DECLARED\", \"VALUE\": \"1.7894e-5\", \"UNIT\": \"Pa s\", \"OVERRIDABLE\": \"NO\", \"LABEL\": \"the dynamic viscosity of air at sea level\"}, {\"NAME\": \"pi_c\", \"DIMENSION\": \"1\", \"SUPPLY\": \"DECLARED\", \"VALUE\": \"3.141592653589793\", \"UNIT\": \"1\", \"OVERRIDABLE\": \"NO\", \"LABEL\": \"pi, to 16 significant digits\"}, {\"NAME\": \"R_s\", \"DIMENSION\": \"L1\", \"SUPPLY\": \"AUTHOR\", \"LABEL\": \"the radius of the sphere\"}], \"SUMS\": [{\"NAME\": \"SPEED2\", \"OVER\": \"VELOCITY\", \"EACH\": \"VELOCITY^2\"}], \"TERMS\": [{\"TARGET\": \"VELOCITY\", \"SIGN\": \"-\", \"EXPR\": \"6*pi_c*mu_air*R_s*VELOCITY\", \"LABEL\": \"the linear (Stokes) drag\"}], \"ASSUMPTIONS\": [{\"NAME\": \"air_still\", \"PROPOSITION\": \"the air is at rest in the frame of the body's velocity\", \"REFS\": [\"VELOCITY\"]}, {\"NAME\": \"air_uniform\", \"PROPOSITION\": \"the air density is uniform over the region of motion\", \"REFS\": [\"rho_air\"]}, {\"NAME\": \"drag_sphere\", \"PROPOSITION\": \"the body is a rigid sphere of radius R_s\", \"REFS\": [\"R_s\"]}], \"BOUNDARIES\": [{\"NAME\": \"drag_linear_regime\", \"PREDICATE\": \"2 rho_air |v| R_s / mu_air < 1: the regime of the linear law\", \"CONDITION\": \"mu_air != 0 and SPEED2 >= 0 and 2*rho_air*sqrt(SPEED2)*R_s/mu_air < 1\"}], \"NOT_CHOSEN\": \"No linear (Stokes) air resistance.\", \"NOT_INCLUDED\": [\"No wind: the air is at rest.\", \"No change of air density or viscosity with altitude or temperature.\", \"No drag outside the regime of the linear law.\"], \"EXCLUDES\": [], \"INTERACTS_WITH\": [], \"TEST_BINDINGS\": [{\"NAME\": \"PROJECTILE_2D\", \"TPK\": {\"DOF\": [{\"NAME\": \"t\", \"DIMENSION\": \"T1\"}, {\"NAME\": \"x\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"z\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"v_x\", \"DIMENSION\": \"L1 T-1\"}, {\"NAME\": \"v_z\", \"DIMENSION\": \"L1 T-1\"}], \"CONSTANT\": [{\"NAME\": \"m\", \"DIMENSION\": \"M1\"}], \"LAW\": [{\"NAME\": \"KIN_X\", \"STATEMENT\": \"dx/dt = v_x\", \"REFS\": [\"t\", \"v_x\", \"x\"], \"ROLE\": \"EOM(x)\", \"EQUATION\": \"D(x,t)=v_x\"}, {\"NAME\": \"KIN_Z\", \"STATEMENT\": \"dz/dt = v_z\", \"REFS\": [\"t\", \"v_z\", \"z\"], \"ROLE\": \"EOM(z)\", \"EQUATION\": \"D(z,t)=v_z\"}, {\"NAME\": \"EOM_X\", \"STATEMENT\": \"m dv_x/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_x\"], \"ROLE\": \"EOM(v_x)\", \"EQUATION\": \"m*D(v_x,t)=0\"}, {\"NAME\": \"EOM_Z\", \"STATEMENT\": \"m dv_z/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_z\"], \"ROLE\": \"EOM(v_z)\", \"EQUATION\": \"m*D(v_z,t)=0\"}], \"ASSUMPTION\": [{\"NAME\": \"point_mass\", \"PROPOSITION\": \"the body is treated as a point mass\", \"REFS\": [\"m\"]}]}, \"BIND\": {\"VELOCITY\": [\"v_x\", \"v_z\"]}, \"VALUES\": {\"R_s\": {}}, \"ANSWERS\": {}}]}",
"{\"ID\": \"AIR-QUADRATIC\", \"VERSION\": \"1.0.0\", \"TITLE\": \"Air resistance at sea level, quadratic in the speed\", \"SOURCE\": \"ISO 2533:1975, Standard Atmosphere, sea-level values: density 1.225 kg m-3, dynamic viscosity 1.7894e-5 Pa s\", \"PREREQUISITES\": [{\"SLOT\": \"VELOCITY\", \"KIND\": \"DOF\", \"DIMENSION\": \"L1 T-1\", \"MIN\": 1, \"MAX\": 3, \"LABEL\": \"the velocity components of the body, one per axis\"}], \"PARAMETERS\": [{\"NAME\": \"rho_air\", \"DIMENSION\": \"L-3 M1\", \"SUPPLY\": \"DECLARED\", \"VALUE\": \"1.225\", \"UNIT\": \"kg m-3\", \"OVERRIDABLE\": \"NO\", \"LABEL\": \"the density of air at sea level\"}, {\"NAME\": \"mu_air\", \"DIMENSION\": \"L-1 M1 T-1\", \"SUPPLY\": \"DECLARED\", \"VALUE\": \"1.7894e-5\", \"UNIT\": \"Pa s\", \"OVERRIDABLE\": \"NO\", \"LABEL\": \"the dynamic viscosity of air at sea level\"}, {\"NAME\": \"C_d\", \"DIMENSION\": \"1\", \"SUPPLY\": \"AUTHOR\", \"LABEL\": \"the drag coefficient of the body\"}, {\"NAME\": \"A_ref\", \"DIMENSION\": \"L2\", \"SUPPLY\": \"AUTHOR\", \"LABEL\": \"the reference area of the drag coefficient\"}, {\"NAME\": \"L_ref\", \"DIMENSION\": \"L1\", \"SUPPLY\": \"AUTHOR\", \"LABEL\": \"the reference length of the Reynolds number\"}], \"SUMS\": [{\"NAME\": \"SPEED2\", \"OVER\": \"VELOCITY\", \"EACH\": \"VELOCITY^2\"}], \"TERMS\": [{\"TARGET\": \"VELOCITY\", \"SIGN\": \"-\", \"EXPR\": \"0.5*rho_air*C_d*A_ref*sqrt(SPEED2)*VELOCITY\", \"LABEL\": \"the quadratic drag\"}], \"ASSUMPTIONS\": [{\"NAME\": \"air_still\", \"PROPOSITION\": \"the air is at rest in the frame of the body's velocity\", \"REFS\": [\"VELOCITY\"]}, {\"NAME\": \"air_uniform\", \"PROPOSITION\": \"the air density is uniform over the region of motion\", \"REFS\": [\"rho_air\"]}, {\"NAME\": \"drag_cd_constant\", \"PROPOSITION\": \"the drag coefficient C_d is constant over the motion\", \"REFS\": [\"C_d\"]}, {\"NAME\": \"drag_no_lift\", \"PROPOSITION\": \"the body experiences no lift force\", \"REFS\": [\"VELOCITY\"]}, {\"NAME\": \"drag_no_magnus\", \"PROPOSITION\": \"the body experiences no Magnus force\", \"REFS\": [\"VELOCITY\"]}], \"BOUNDARIES\": [{\"NAME\": \"drag_quadratic_regime\", \"PREDICATE\": \"1e3 < rho_air |v| L_ref / mu_air < 2e5: the Reynolds window of the quadratic law\", \"CONDITION\": \"mu_air != 0 and SPEED2 >= 0 and rho_air*sqrt(SPEED2)*L_ref/mu_air > 1000 and rho_air*sqrt(SPEED2)*L_ref/mu_air < 200000\"}], \"NOT_CHOSEN\": \"No quadratic air resistance.\", \"NOT_INCLUDED\": [\"No wind: the air is at rest.\", \"No change of air density or viscosity with altitude or temperature.\", \"No lift, Magnus or added-mass force.\", \"No drag outside the Reynolds window of the quadratic law.\"], \"EXCLUDES\": [\"AIR-LINEAR\"], \"INTERACTS_WITH\": [], \"TEST_BINDINGS\": [{\"NAME\": \"PROJECTILE_2D\", \"TPK\": {\"DOF\": [{\"NAME\": \"t\", \"DIMENSION\": \"T1\"}, {\"NAME\": \"x\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"z\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"v_x\", \"DIMENSION\": \"L1 T-1\"}, {\"NAME\": \"v_z\", \"DIMENSION\": \"L1 T-1\"}], \"CONSTANT\": [{\"NAME\": \"m\", \"DIMENSION\": \"M1\"}], \"LAW\": [{\"NAME\": \"KIN_X\", \"STATEMENT\": \"dx/dt = v_x\", \"REFS\": [\"t\", \"v_x\", \"x\"], \"ROLE\": \"EOM(x)\", \"EQUATION\": \"D(x,t)=v_x\"}, {\"NAME\": \"KIN_Z\", \"STATEMENT\": \"dz/dt = v_z\", \"REFS\": [\"t\", \"v_z\", \"z\"], \"ROLE\": \"EOM(z)\", \"EQUATION\": \"D(z,t)=v_z\"}, {\"NAME\": \"EOM_X\", \"STATEMENT\": \"m dv_x/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_x\"], \"ROLE\": \"EOM(v_x)\", \"EQUATION\": \"m*D(v_x,t)=0\"}, {\"NAME\": \"EOM_Z\", \"STATEMENT\": \"m dv_z/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_z\"], \"ROLE\": \"EOM(v_z)\", \"EQUATION\": \"m*D(v_z,t)=0\"}], \"ASSUMPTION\": [{\"NAME\": \"point_mass\", \"PROPOSITION\": \"the body is treated as a point mass\", \"REFS\": [\"m\"]}]}, \"BIND\": {\"VELOCITY\": [\"v_x\", \"v_z\"]}, \"VALUES\": {\"A_ref\": {}, \"C_d\": {}, \"L_ref\": {}}, \"ANSWERS\": {}}]}",
"{\"ID\": \"GRAV-UNIFORM\", \"VERSION\": \"1.0.0\", \"TITLE\": \"Uniform gravity at the standard value g_n\", \"SOURCE\": \"g_n = 9.80665 m s-2, exact by definition: 3rd CGPM (1901), declaration on the unit of mass and on the definition of weight\", \"PREREQUISITES\": [{\"SLOT\": \"MASS\", \"KIND\": \"CONSTANT\", \"DIMENSION\": \"M1\", \"MIN\": 1, \"MAX\": 1, \"LABEL\": \"the mass of the body\"}, {\"SLOT\": \"UP_VELOCITY\", \"KIND\": \"DOF\", \"DIMENSION\": \"L1 T-1\", \"MIN\": 1, \"MAX\": 1, \"LABEL\": \"the velocity component pointing up; its equation of motion receives the weight\"}, {\"SLOT\": \"HEIGHT\", \"KIND\": \"DOF\", \"DIMENSION\": \"L1\", \"MIN\": 1, \"MAX\": 1, \"LABEL\": \"the position along the same upward axis\"}], \"PARAMETERS\": [{\"NAME\": \"g_n\", \"DIMENSION\": \"L1 T-2\", \"SUPPLY\": \"DECLARED\", \"VALUE\": \"9.80665\", \"UNIT\": \"m s-2\", \"OVERRIDABLE\": \"NO\", \"LABEL\": \"the standard acceleration of gravity\"}, {\"NAME\": \"h_max\", \"DIMENSION\": \"L1\", \"SUPPLY\": \"AUTHOR\", \"LABEL\": \"the largest height, above or below the origin, over which the field is taken as uniform\"}], \"SUMS\": [], \"TERMS\": [{\"TARGET\": \"UP_VELOCITY\", \"SIGN\": \"-\", \"EXPR\": \"MASS*g_n\", \"LABEL\": \"the weight\"}], \"ASSUMPTIONS\": [{\"NAME\": \"gravity_uniform\", \"PROPOSITION\": \"the gravitational field is uniform over the region abs({HEIGHT}) < h_max\", \"REFS\": [\"HEIGHT\", \"h_max\"]}, {\"NAME\": \"gravity_standard\", \"PROPOSITION\": \"the local gravitational acceleration equals the conventional standard value g_n\", \"REFS\": [\"g_n\"]}, {\"NAME\": \"frame_inertial\", \"PROPOSITION\": \"the frame in which {HEIGHT} is measured is treated as inertial\", \"REFS\": [\"HEIGHT\"]}], \"BOUNDARIES\": [{\"NAME\": \"gravity_region\", \"PREDICATE\": \"abs({HEIGHT}) < h_max\", \"CONDITION\": \"abs(HEIGHT) < h_max\"}], \"NOT_CHOSEN\": \"No gravity: no weight acts on any DOF.\", \"NOT_INCLUDED\": [\"No variation of gravity with height or latitude beyond what g_n contains.\", \"No Earth rotation (Coriolis or centrifugal force) beyond what g_n contains.\", \"No gravity of bodies other than the Earth.\"], \"EXCLUDES\": [], \"INTERACTS_WITH\": [{\"WITH\": \"AIR-*\", \"QUESTION_ID\": \"BUOYANCY\", \"QUESTION\": \"Does the air's buoyancy (upthrust) act on the body in the system you mean?\", \"YES_LINE\": \"Buoyancy acts (your answer): no module adds it; it acts in this kernel only where one of your own laws states it.\", \"NO_LINE\": \"No buoyancy: the air's upthrust on the body is not included.\"}], \"TEST_BINDINGS\": [{\"NAME\": \"PROJECTILE_2D\", \"TPK\": {\"DOF\": [{\"NAME\": \"t\", \"DIMENSION\": \"T1\"}, {\"NAME\": \"x\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"z\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"v_x\", \"DIMENSION\": \"L1 T-1\"}, {\"NAME\": \"v_z\", \"DIMENSION\": \"L1 T-1\"}], \"CONSTANT\": [{\"NAME\": \"m\", \"DIMENSION\": \"M1\"}], \"LAW\": [{\"NAME\": \"KIN_X\", \"STATEMENT\": \"dx/dt = v_x\", \"REFS\": [\"t\", \"v_x\", \"x\"], \"ROLE\": \"EOM(x)\", \"EQUATION\": \"D(x,t)=v_x\"}, {\"NAME\": \"KIN_Z\", \"STATEMENT\": \"dz/dt = v_z\", \"REFS\": [\"t\", \"v_z\", \"z\"], \"ROLE\": \"EOM(z)\", \"EQUATION\": \"D(z,t)=v_z\"}, {\"NAME\": \"EOM_X\", \"STATEMENT\": \"m dv_x/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_x\"], \"ROLE\": \"EOM(v_x)\", \"EQUATION\": \"m*D(v_x,t)=0\"}, {\"NAME\": \"EOM_Z\", \"STATEMENT\": \"m dv_z/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_z\"], \"ROLE\": \"EOM(v_z)\", \"EQUATION\": \"m*D(v_z,t)=0\"}], \"ASSUMPTION\": [{\"NAME\": \"point_mass\", \"PROPOSITION\": \"the body is treated as a point mass\", \"REFS\": [\"m\"]}]}, \"BIND\": {\"HEIGHT\": [\"z\"], \"MASS\": [\"m\"], \"UP_VELOCITY\": [\"v_z\"]}, \"VALUES\": {\"h_max\": {\"VALUE\": \"100\", \"UNIT\": \"m\"}}, \"ANSWERS\": {}}, {\"NAME\": \"TABLE\", \"TPK\": {\"DOF\": [{\"NAME\": \"t\", \"DIMENSION\": \"T1\"}, {\"NAME\": \"x\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"z\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"v_x\", \"DIMENSION\": \"L1 T-1\"}, {\"NAME\": \"v_z\", \"DIMENSION\": \"L1 T-1\"}], \"CONSTANT\": [{\"NAME\": \"m\", \"DIMENSION\": \"M1\"}], \"LAW\": [{\"NAME\": \"KIN_X\", \"STATEMENT\": \"dx/dt = v_x\", \"REFS\": [\"t\", \"v_x\", \"x\"], \"ROLE\": \"EOM(x)\", \"EQUATION\": \"D(x,t)=v_x\"}, {\"NAME\": \"KIN_Z\", \"STATEMENT\": \"dz/dt = v_z\", \"REFS\": [\"t\", \"v_z\", \"z\"], \"ROLE\": \"CONSTRAINT\", \"EQUATION\": \"D(z,t)=v_z\"}, {\"NAME\": \"EOM_X\", \"STATEMENT\": \"m dv_x/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_x\"], \"ROLE\": \"EOM(v_x)\", \"EQUATION\": \"m*D(v_x,t)=0\"}], \"CONSTRAINT\": [{\"NAME\": \"C_Z\", \"TARGET\": \"z\", \"ACTION\": \"FIX\", \"VALUE\": \"0\", \"UNIT\": \"m\", \"STATEMENT\": \"the puck stays on the table top, z = 0\"}, {\"NAME\": \"C_VZ\", \"TARGET\": \"v_z\", \"ACTION\": \"FIX\", \"VALUE\": \"0\", \"UNIT\": \"m s-1\", \"STATEMENT\": \"the puck has no vertical velocity\"}]}, \"BIND\": {\"HEIGHT\": [\"z\"], \"MASS\": [\"m\"], \"UP_VELOCITY\": [\"v_z\"]}, \"VALUES\": {\"h_max\": {\"VALUE\": \"1\", \"UNIT\": \"m\"}}, \"ANSWERS\": {\"FIXED:v_z\": \"YES\"}}]}",
"{\"ID\": \"MATH\", \"VERSION\": \"1.0.0\", \"TITLE\": \"The mathematical constant pi, as the CONSTANT pi_c\", \"SOURCE\": \"pi to 16 significant digits, 3.141592653589793, the nearest IEEE 754 binary64 value\", \"PREREQUISITES\": [], \"PARAMETERS\": [{\"NAME\": \"pi_c\", \"DIMENSION\": \"1\", \"SUPPLY\": \"DECLARED\", \"VALUE\": \"3.141592653589793\", \"UNIT\": \"1\", \"OVERRIDABLE\": \"NO\", \"LABEL\": \"pi, to 16 significant digits\"}], \"SUMS\": [], \"TERMS\": [], \"ASSUMPTIONS\": [], \"BOUNDARIES\": [], \"NOT_CHOSEN\": \"No mathematical constant: pi exists only if you declare it.\", \"NOT_INCLUDED\": [\"pi_c is pi rounded to 16 significant digits; no other mathematical constant is declared.\"], \"EXCLUDES\": [], \"INTERACTS_WITH\": [], \"TEST_BINDINGS\": [{\"NAME\": \"PROJECTILE_2D\", \"TPK\": {\"DOF\": [{\"NAME\": \"t\", \"DIMENSION\": \"T1\"}, {\"NAME\": \"x\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"z\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"v_x\", \"DIMENSION\": \"L1 T-1\"}, {\"NAME\": \"v_z\", \"DIMENSION\": \"L1 T-1\"}], \"CONSTANT\": [{\"NAME\": \"m\", \"DIMENSION\": \"M1\"}], \"LAW\": [{\"NAME\": \"KIN_X\", \"STATEMENT\": \"dx/dt = v_x\", \"REFS\": [\"t\", \"v_x\", \"x\"], \"ROLE\": \"EOM(x)\", \"EQUATION\": \"D(x,t)=v_x\"}, {\"NAME\": \"KIN_Z\", \"STATEMENT\": \"dz/dt = v_z\", \"REFS\": [\"t\", \"v_z\", \"z\"], \"ROLE\": \"EOM(z)\", \"EQUATION\": \"D(z,t)=v_z\"}, {\"NAME\": \"EOM_X\", \"STATEMENT\": \"m dv_x/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_x\"], \"ROLE\": \"EOM(v_x)\", \"EQUATION\": \"m*D(v_x,t)=0\"}, {\"NAME\": \"EOM_Z\", \"STATEMENT\": \"m dv_z/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_z\"], \"ROLE\": \"EOM(v_z)\", \"EQUATION\": \"m*D(v_z,t)=0\"}], \"ASSUMPTION\": [{\"NAME\": \"point_mass\", \"PROPOSITION\": \"the body is treated as a point mass\", \"REFS\": [\"m\"]}]}, \"BIND\": {}, \"VALUES\": {}, \"ANSWERS\": {}}]}",
"{\"ID\": \"GRAV-UNIFORM\", \"VERSION\": \"1.1.0\", \"TITLE\": \"Uniform gravity at the standard value g_n (text revised)\", \"SOURCE\": \"g_n = 9.80665 m s-2, exact by definition: 3rd CGPM (1901), declaration on the unit of mass and on the definition of weight\", \"PREREQUISITES\": [{\"SLOT\": \"MASS\", \"KIND\": \"CONSTANT\", \"DIMENSION\": \"M1\", \"MIN\": 1, \"MAX\": 1, \"LABEL\": \"the mass of the body\"}, {\"SLOT\": \"UP_VELOCITY\", \"KIND\": \"DOF\", \"DIMENSION\": \"L1 T-1\", \"MIN\": 1, \"MAX\": 1, \"LABEL\": \"the velocity component pointing up; its equation of motion receives the weight\"}, {\"SLOT\": \"HEIGHT\", \"KIND\": \"DOF\", \"DIMENSION\": \"L1\", \"MIN\": 1, \"MAX\": 1, \"LABEL\": \"the position along the same upward axis\"}], \"PARAMETERS\": [{\"NAME\": \"g_n\", \"DIMENSION\": \"L1 T-2\", \"SUPPLY\": \"DECLARED\", \"VALUE\": \"9.80665\", \"UNIT\": \"m s-2\", \"OVERRIDABLE\": \"NO\", \"LABEL\": \"the standard acceleration of gravity\"}, {\"NAME\": \"h_max\", \"DIMENSION\": \"L1\", \"SUPPLY\": \"AUTHOR\", \"LABEL\": \"the largest height, above or below the origin, over which the field is taken as uniform\"}], \"SUMS\": [], \"TERMS\": [{\"TARGET\": \"UP_VELOCITY\", \"SIGN\": \"-\", \"EXPR\": \"MASS*g_n\", \"LABEL\": \"the weight\"}], \"ASSUMPTIONS\": [{\"NAME\": \"gravity_uniform\", \"PROPOSITION\": \"the gravitational field is uniform over the region abs({HEIGHT}) < h_max\", \"REFS\": [\"HEIGHT\", \"h_max\"]}, {\"NAME\": \"gravity_standard\", \"PROPOSITION\": \"the local gravitational acceleration equals the conventional standard value g_n\", \"REFS\": [\"g_n\"]}, {\"NAME\": \"frame_inertial\", \"PROPOSITION\": \"the frame in which {HEIGHT} is measured is treated as inertial\", \"REFS\": [\"HEIGHT\"]}], \"BOUNDARIES\": [{\"NAME\": \"gravity_region\", \"PREDICATE\": \"abs({HEIGHT}) < h_max\", \"CONDITION\": \"abs(HEIGHT) < h_max\"}], \"NOT_CHOSEN\": \"No gravity: no weight acts on any DOF.\", \"NOT_INCLUDED\": [\"No variation of gravity with height or latitude beyond what g_n contains.\", \"No Earth rotation (Coriolis or centrifugal force) beyond what g_n contains.\", \"No gravity of bodies other than the Earth.\"], \"EXCLUDES\": [], \"INTERACTS_WITH\": [{\"WITH\": \"AIR-*\", \"QUESTION_ID\": \"BUOYANCY\", \"QUESTION\": \"Does the air's buoyancy (upthrust) act on the body in the system you mean?\", \"YES_LINE\": \"Buoyancy acts (your answer): no module adds it; it acts in this kernel only where one of your own laws states it.\", \"NO_LINE\": \"No buoyancy: the air's upthrust on the body is not included.\"}], \"TEST_BINDINGS\": [{\"NAME\": \"PROJECTILE_2D\", \"TPK\": {\"DOF\": [{\"NAME\": \"t\", \"DIMENSION\": \"T1\"}, {\"NAME\": \"x\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"z\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"v_x\", \"DIMENSION\": \"L1 T-1\"}, {\"NAME\": \"v_z\", \"DIMENSION\": \"L1 T-1\"}], \"CONSTANT\": [{\"NAME\": \"m\", \"DIMENSION\": \"M1\"}], \"LAW\": [{\"NAME\": \"KIN_X\", \"STATEMENT\": \"dx/dt = v_x\", \"REFS\": [\"t\", \"v_x\", \"x\"], \"ROLE\": \"EOM(x)\", \"EQUATION\": \"D(x,t)=v_x\"}, {\"NAME\": \"KIN_Z\", \"STATEMENT\": \"dz/dt = v_z\", \"REFS\": [\"t\", \"v_z\", \"z\"], \"ROLE\": \"EOM(z)\", \"EQUATION\": \"D(z,t)=v_z\"}, {\"NAME\": \"EOM_X\", \"STATEMENT\": \"m dv_x/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_x\"], \"ROLE\": \"EOM(v_x)\", \"EQUATION\": \"m*D(v_x,t)=0\"}, {\"NAME\": \"EOM_Z\", \"STATEMENT\": \"m dv_z/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_z\"], \"ROLE\": \"EOM(v_z)\", \"EQUATION\": \"m*D(v_z,t)=0\"}], \"ASSUMPTION\": [{\"NAME\": \"point_mass\", \"PROPOSITION\": \"the body is treated as a point mass\", \"REFS\": [\"m\"]}]}, \"BIND\": {\"HEIGHT\": [\"z\"], \"MASS\": [\"m\"], \"UP_VELOCITY\": [\"v_z\"]}, \"VALUES\": {\"h_max\": {\"VALUE\": \"100\", \"UNIT\": \"m\"}}, \"ANSWERS\": {}}, {\"NAME\": \"TABLE\", \"TPK\": {\"DOF\": [{\"NAME\": \"t\", \"DIMENSION\": \"T1\"}, {\"NAME\": \"x\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"z\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"v_x\", \"DIMENSION\": \"L1 T-1\"}, {\"NAME\": \"v_z\", \"DIMENSION\": \"L1 T-1\"}], \"CONSTANT\": [{\"NAME\": \"m\", \"DIMENSION\": \"M1\"}], \"LAW\": [{\"NAME\": \"KIN_X\", \"STATEMENT\": \"dx/dt = v_x\", \"REFS\": [\"t\", \"v_x\", \"x\"], \"ROLE\": \"EOM(x)\", \"EQUATION\": \"D(x,t)=v_x\"}, {\"NAME\": \"KIN_Z\", \"STATEMENT\": \"dz/dt = v_z\", \"REFS\": [\"t\", \"v_z\", \"z\"], \"ROLE\": \"CONSTRAINT\", \"EQUATION\": \"D(z,t)=v_z\"}, {\"NAME\": \"EOM_X\", \"STATEMENT\": \"m dv_x/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_x\"], \"ROLE\": \"EOM(v_x)\", \"EQUATION\": \"m*D(v_x,t)=0\"}], \"CONSTRAINT\": [{\"NAME\": \"C_Z\", \"TARGET\": \"z\", \"ACTION\": \"FIX\", \"VALUE\": \"0\", \"UNIT\": \"m\", \"STATEMENT\": \"the puck stays on the table top, z = 0\"}, {\"NAME\": \"C_VZ\", \"TARGET\": \"v_z\", \"ACTION\": \"FIX\", \"VALUE\": \"0\", \"UNIT\": \"m s-1\", \"STATEMENT\": \"the puck has no vertical velocity\"}]}, \"BIND\": {\"HEIGHT\": [\"z\"], \"MASS\": [\"m\"], \"UP_VELOCITY\": [\"v_z\"]}, \"VALUES\": {\"h_max\": {\"VALUE\": \"1\", \"UNIT\": \"m\"}}, \"ANSWERS\": {\"FIXED:v_z\": \"YES\"}}]}"
]
},
"expected": "[\"REFUSED\",\"CLAIM GRAV-UNIFORM 1.0.0: not OFFERED when chosen (a new claim names the OFFERED version)\"]",
"fn": "interview_check",
"hand_checked": true,
"name": "I42 the same round, the claim still on the old version: refused (DR-7)"
},
{
"args": {
"answer": [
{
"AT": 4,
"CHOSEN": "NONE",
"COVERED": [
[
"AIR-LINEAR",
"1.0.0",
"5f3fe27b42378bce0830b0d0959f892f4a8e73b12b540ae877e39e6439d08b4d"
],
[
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[
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"MATH",
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]
]
},
{
"AT": 5,
"CHOSEN": "NONE",
"COVERED": [
[
"TEST-X",
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]
],
"RESELECT": [
"TEST-X"
]
}
],
"carried": [],
"claims": [],
"lines": [
{
"ACT": "MODULE ADD",
"DATE": "2026-10-01",
"DIGEST": "5f3fe27b42378bce0830b0d0959f892f4a8e73b12b540ae877e39e6439d08b4d",
"ID": "AIR-LINEAR",
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},
{
"ACT": "MODULE ADD",
"DATE": "2026-10-01",
"DIGEST": "6fb53c3a6546151eead2bd6e72e9cf8334f3a2040ad0ee2f5b988ec96d6fc852",
"ID": "AIR-QUADRATIC",
"VERSION": "1.0.0"
},
{
"ACT": "MODULE ADD",
"DATE": "2026-10-01",
"DIGEST": "24877ccb5c8ec300d29ed82ce6650592f35cf8899a3d878ccce9c08d4c72c025",
"ID": "GRAV-UNIFORM",
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},
{
"ACT": "MODULE ADD",
"DATE": "2026-10-01",
"DIGEST": "8f39a356f35527b901fcee012764590f0819c8ffdeccad4bc05195ce3d2e0bcf",
"ID": "MATH",
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},
{
"ACT": "MODULE ADD",
"DATE": "2026-10-02",
"DIGEST": "3ecd3a5b540cc15ae65165e5246c4814ef6cb2e7fd293e3578041cbe66efbcb3",
"ID": "TEST-X",
"VERSION": "1.0.0"
}
],
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"modules": [
"{\"ID\": \"AIR-LINEAR\", \"VERSION\": \"1.0.0\", \"TITLE\": \"Air resistance at sea level, linear in the speed (Stokes drag on a sphere)\", \"SOURCE\": \"ISO 2533:1975, Standard Atmosphere, sea-level values: density 1.225 kg m-3, dynamic viscosity 1.7894e-5 Pa s\", \"PREREQUISITES\": [{\"SLOT\": \"VELOCITY\", \"KIND\": \"DOF\", \"DIMENSION\": \"L1 T-1\", \"MIN\": 1, \"MAX\": 3, \"LABEL\": \"the velocity components of the body, one per axis\"}], \"PARAMETERS\": [{\"NAME\": \"rho_air\", \"DIMENSION\": \"L-3 M1\", \"SUPPLY\": \"DECLARED\", \"VALUE\": \"1.225\", \"UNIT\": \"kg m-3\", \"OVERRIDABLE\": \"NO\", \"LABEL\": \"the density of air at sea level\"}, {\"NAME\": \"mu_air\", \"DIMENSION\": \"L-1 M1 T-1\", \"SUPPLY\": \"DECLARED\", \"VALUE\": \"1.7894e-5\", \"UNIT\": \"Pa s\", \"OVERRIDABLE\": \"NO\", \"LABEL\": \"the dynamic viscosity of air at sea level\"}, {\"NAME\": \"pi_c\", \"DIMENSION\": \"1\", \"SUPPLY\": \"DECLARED\", \"VALUE\": \"3.141592653589793\", \"UNIT\": \"1\", \"OVERRIDABLE\": \"NO\", \"LABEL\": \"pi, to 16 significant digits\"}, {\"NAME\": \"R_s\", \"DIMENSION\": \"L1\", \"SUPPLY\": \"AUTHOR\", \"LABEL\": \"the radius of the sphere\"}], \"SUMS\": [{\"NAME\": \"SPEED2\", \"OVER\": \"VELOCITY\", \"EACH\": \"VELOCITY^2\"}], \"TERMS\": [{\"TARGET\": \"VELOCITY\", \"SIGN\": \"-\", \"EXPR\": \"6*pi_c*mu_air*R_s*VELOCITY\", \"LABEL\": \"the linear (Stokes) drag\"}], \"ASSUMPTIONS\": [{\"NAME\": \"air_still\", \"PROPOSITION\": \"the air is at rest in the frame of the body's velocity\", \"REFS\": [\"VELOCITY\"]}, {\"NAME\": \"air_uniform\", \"PROPOSITION\": \"the air density is uniform over the region of motion\", \"REFS\": [\"rho_air\"]}, {\"NAME\": \"drag_sphere\", \"PROPOSITION\": \"the body is a rigid sphere of radius R_s\", \"REFS\": [\"R_s\"]}], \"BOUNDARIES\": [{\"NAME\": \"drag_linear_regime\", \"PREDICATE\": \"2 rho_air |v| R_s / mu_air < 1: the regime of the linear law\", \"CONDITION\": \"mu_air != 0 and SPEED2 >= 0 and 2*rho_air*sqrt(SPEED2)*R_s/mu_air < 1\"}], \"NOT_CHOSEN\": \"No linear (Stokes) air resistance.\", \"NOT_INCLUDED\": [\"No wind: the air is at rest.\", \"No change of air density or viscosity with altitude or temperature.\", \"No drag outside the regime of the linear law.\"], \"EXCLUDES\": [], \"INTERACTS_WITH\": [], \"TEST_BINDINGS\": [{\"NAME\": \"PROJECTILE_2D\", \"TPK\": {\"DOF\": [{\"NAME\": \"t\", \"DIMENSION\": \"T1\"}, {\"NAME\": \"x\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"z\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"v_x\", \"DIMENSION\": \"L1 T-1\"}, {\"NAME\": \"v_z\", \"DIMENSION\": \"L1 T-1\"}], \"CONSTANT\": [{\"NAME\": \"m\", \"DIMENSION\": \"M1\"}], \"LAW\": [{\"NAME\": \"KIN_X\", \"STATEMENT\": \"dx/dt = v_x\", \"REFS\": [\"t\", \"v_x\", \"x\"], \"ROLE\": \"EOM(x)\", \"EQUATION\": \"D(x,t)=v_x\"}, {\"NAME\": \"KIN_Z\", \"STATEMENT\": \"dz/dt = v_z\", \"REFS\": [\"t\", \"v_z\", \"z\"], \"ROLE\": \"EOM(z)\", \"EQUATION\": \"D(z,t)=v_z\"}, {\"NAME\": \"EOM_X\", \"STATEMENT\": \"m dv_x/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_x\"], \"ROLE\": \"EOM(v_x)\", \"EQUATION\": \"m*D(v_x,t)=0\"}, {\"NAME\": \"EOM_Z\", \"STATEMENT\": \"m dv_z/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_z\"], \"ROLE\": \"EOM(v_z)\", \"EQUATION\": \"m*D(v_z,t)=0\"}], \"ASSUMPTION\": [{\"NAME\": \"point_mass\", \"PROPOSITION\": \"the body is treated as a point mass\", \"REFS\": [\"m\"]}]}, \"BIND\": {\"VELOCITY\": [\"v_x\", \"v_z\"]}, \"VALUES\": {\"R_s\": {}}, \"ANSWERS\": {}}]}",
"{\"ID\": \"AIR-QUADRATIC\", \"VERSION\": \"1.0.0\", \"TITLE\": \"Air resistance at sea level, quadratic in the speed\", \"SOURCE\": \"ISO 2533:1975, Standard Atmosphere, sea-level values: density 1.225 kg m-3, dynamic viscosity 1.7894e-5 Pa s\", \"PREREQUISITES\": [{\"SLOT\": \"VELOCITY\", \"KIND\": \"DOF\", \"DIMENSION\": \"L1 T-1\", \"MIN\": 1, \"MAX\": 3, \"LABEL\": \"the velocity components of the body, one per axis\"}], \"PARAMETERS\": [{\"NAME\": \"rho_air\", \"DIMENSION\": \"L-3 M1\", \"SUPPLY\": \"DECLARED\", \"VALUE\": \"1.225\", \"UNIT\": \"kg m-3\", \"OVERRIDABLE\": \"NO\", \"LABEL\": \"the density of air at sea level\"}, {\"NAME\": \"mu_air\", \"DIMENSION\": \"L-1 M1 T-1\", \"SUPPLY\": \"DECLARED\", \"VALUE\": \"1.7894e-5\", \"UNIT\": \"Pa s\", \"OVERRIDABLE\": \"NO\", \"LABEL\": \"the dynamic viscosity of air at sea level\"}, {\"NAME\": \"C_d\", \"DIMENSION\": \"1\", \"SUPPLY\": \"AUTHOR\", \"LABEL\": \"the drag coefficient of the body\"}, {\"NAME\": \"A_ref\", \"DIMENSION\": \"L2\", \"SUPPLY\": \"AUTHOR\", \"LABEL\": \"the reference area of the drag coefficient\"}, {\"NAME\": \"L_ref\", \"DIMENSION\": \"L1\", \"SUPPLY\": \"AUTHOR\", \"LABEL\": \"the reference length of the Reynolds number\"}], \"SUMS\": [{\"NAME\": \"SPEED2\", \"OVER\": \"VELOCITY\", \"EACH\": \"VELOCITY^2\"}], \"TERMS\": [{\"TARGET\": \"VELOCITY\", \"SIGN\": \"-\", \"EXPR\": \"0.5*rho_air*C_d*A_ref*sqrt(SPEED2)*VELOCITY\", \"LABEL\": \"the quadratic drag\"}], \"ASSUMPTIONS\": [{\"NAME\": \"air_still\", \"PROPOSITION\": \"the air is at rest in the frame of the body's velocity\", \"REFS\": [\"VELOCITY\"]}, {\"NAME\": \"air_uniform\", \"PROPOSITION\": \"the air density is uniform over the region of motion\", \"REFS\": [\"rho_air\"]}, {\"NAME\": \"drag_cd_constant\", \"PROPOSITION\": \"the drag coefficient C_d is constant over the motion\", \"REFS\": [\"C_d\"]}, {\"NAME\": \"drag_no_lift\", \"PROPOSITION\": \"the body experiences no lift force\", \"REFS\": [\"VELOCITY\"]}, {\"NAME\": \"drag_no_magnus\", \"PROPOSITION\": \"the body experiences no Magnus force\", \"REFS\": [\"VELOCITY\"]}], \"BOUNDARIES\": [{\"NAME\": \"drag_quadratic_regime\", \"PREDICATE\": \"1e3 < rho_air |v| L_ref / mu_air < 2e5: the Reynolds window of the quadratic law\", \"CONDITION\": \"mu_air != 0 and SPEED2 >= 0 and rho_air*sqrt(SPEED2)*L_ref/mu_air > 1000 and rho_air*sqrt(SPEED2)*L_ref/mu_air < 200000\"}], \"NOT_CHOSEN\": \"No quadratic air resistance.\", \"NOT_INCLUDED\": [\"No wind: the air is at rest.\", \"No change of air density or viscosity with altitude or temperature.\", \"No lift, Magnus or added-mass force.\", \"No drag outside the Reynolds window of the quadratic law.\"], \"EXCLUDES\": [\"AIR-LINEAR\"], \"INTERACTS_WITH\": [], \"TEST_BINDINGS\": [{\"NAME\": \"PROJECTILE_2D\", \"TPK\": {\"DOF\": [{\"NAME\": \"t\", \"DIMENSION\": \"T1\"}, {\"NAME\": \"x\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"z\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"v_x\", \"DIMENSION\": \"L1 T-1\"}, {\"NAME\": \"v_z\", \"DIMENSION\": \"L1 T-1\"}], \"CONSTANT\": [{\"NAME\": \"m\", \"DIMENSION\": \"M1\"}], \"LAW\": [{\"NAME\": \"KIN_X\", \"STATEMENT\": \"dx/dt = v_x\", \"REFS\": [\"t\", \"v_x\", \"x\"], \"ROLE\": \"EOM(x)\", \"EQUATION\": \"D(x,t)=v_x\"}, {\"NAME\": \"KIN_Z\", \"STATEMENT\": \"dz/dt = v_z\", \"REFS\": [\"t\", \"v_z\", \"z\"], \"ROLE\": \"EOM(z)\", \"EQUATION\": \"D(z,t)=v_z\"}, {\"NAME\": \"EOM_X\", \"STATEMENT\": \"m dv_x/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_x\"], \"ROLE\": \"EOM(v_x)\", \"EQUATION\": \"m*D(v_x,t)=0\"}, {\"NAME\": \"EOM_Z\", \"STATEMENT\": \"m dv_z/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_z\"], \"ROLE\": \"EOM(v_z)\", \"EQUATION\": \"m*D(v_z,t)=0\"}], \"ASSUMPTION\": [{\"NAME\": \"point_mass\", \"PROPOSITION\": \"the body is treated as a point mass\", \"REFS\": [\"m\"]}]}, \"BIND\": {\"VELOCITY\": [\"v_x\", \"v_z\"]}, \"VALUES\": {\"A_ref\": {}, \"C_d\": {}, \"L_ref\": {}}, \"ANSWERS\": {}}]}",
"{\"ID\": \"GRAV-UNIFORM\", \"VERSION\": \"1.0.0\", \"TITLE\": \"Uniform gravity at the standard value g_n\", \"SOURCE\": \"g_n = 9.80665 m s-2, exact by definition: 3rd CGPM (1901), declaration on the unit of mass and on the definition of weight\", \"PREREQUISITES\": [{\"SLOT\": \"MASS\", \"KIND\": \"CONSTANT\", \"DIMENSION\": \"M1\", \"MIN\": 1, \"MAX\": 1, \"LABEL\": \"the mass of the body\"}, {\"SLOT\": \"UP_VELOCITY\", \"KIND\": \"DOF\", \"DIMENSION\": \"L1 T-1\", \"MIN\": 1, \"MAX\": 1, \"LABEL\": \"the velocity component pointing up; its equation of motion receives the weight\"}, {\"SLOT\": \"HEIGHT\", \"KIND\": \"DOF\", \"DIMENSION\": \"L1\", \"MIN\": 1, \"MAX\": 1, \"LABEL\": \"the position along the same upward axis\"}], \"PARAMETERS\": [{\"NAME\": \"g_n\", \"DIMENSION\": \"L1 T-2\", \"SUPPLY\": \"DECLARED\", \"VALUE\": \"9.80665\", \"UNIT\": \"m s-2\", \"OVERRIDABLE\": \"NO\", \"LABEL\": \"the standard acceleration of gravity\"}, {\"NAME\": \"h_max\", \"DIMENSION\": \"L1\", \"SUPPLY\": \"AUTHOR\", \"LABEL\": \"the largest height, above or below the origin, over which the field is taken as uniform\"}], \"SUMS\": [], \"TERMS\": [{\"TARGET\": \"UP_VELOCITY\", \"SIGN\": \"-\", \"EXPR\": \"MASS*g_n\", \"LABEL\": \"the weight\"}], \"ASSUMPTIONS\": [{\"NAME\": \"gravity_uniform\", \"PROPOSITION\": \"the gravitational field is uniform over the region abs({HEIGHT}) < h_max\", \"REFS\": [\"HEIGHT\", \"h_max\"]}, {\"NAME\": \"gravity_standard\", \"PROPOSITION\": \"the local gravitational acceleration equals the conventional standard value g_n\", \"REFS\": [\"g_n\"]}, {\"NAME\": \"frame_inertial\", \"PROPOSITION\": \"the frame in which {HEIGHT} is measured is treated as inertial\", \"REFS\": [\"HEIGHT\"]}], \"BOUNDARIES\": [{\"NAME\": \"gravity_region\", \"PREDICATE\": \"abs({HEIGHT}) < h_max\", \"CONDITION\": \"abs(HEIGHT) < h_max\"}], \"NOT_CHOSEN\": \"No gravity: no weight acts on any DOF.\", \"NOT_INCLUDED\": [\"No variation of gravity with height or latitude beyond what g_n contains.\", \"No Earth rotation (Coriolis or centrifugal force) beyond what g_n contains.\", \"No gravity of bodies other than the Earth.\"], \"EXCLUDES\": [], \"INTERACTS_WITH\": [{\"WITH\": \"AIR-*\", \"QUESTION_ID\": \"BUOYANCY\", \"QUESTION\": \"Does the air's buoyancy (upthrust) act on the body in the system you mean?\", \"YES_LINE\": \"Buoyancy acts (your answer): no module adds it; it acts in this kernel only where one of your own laws states it.\", \"NO_LINE\": \"No buoyancy: the air's upthrust on the body is not included.\"}], \"TEST_BINDINGS\": [{\"NAME\": \"PROJECTILE_2D\", \"TPK\": {\"DOF\": [{\"NAME\": \"t\", \"DIMENSION\": \"T1\"}, {\"NAME\": \"x\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"z\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"v_x\", \"DIMENSION\": \"L1 T-1\"}, {\"NAME\": \"v_z\", \"DIMENSION\": \"L1 T-1\"}], \"CONSTANT\": [{\"NAME\": \"m\", \"DIMENSION\": \"M1\"}], \"LAW\": [{\"NAME\": \"KIN_X\", \"STATEMENT\": \"dx/dt = v_x\", \"REFS\": [\"t\", \"v_x\", \"x\"], \"ROLE\": \"EOM(x)\", \"EQUATION\": \"D(x,t)=v_x\"}, {\"NAME\": \"KIN_Z\", \"STATEMENT\": \"dz/dt = v_z\", \"REFS\": [\"t\", \"v_z\", \"z\"], \"ROLE\": \"EOM(z)\", \"EQUATION\": \"D(z,t)=v_z\"}, {\"NAME\": \"EOM_X\", \"STATEMENT\": \"m dv_x/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_x\"], \"ROLE\": \"EOM(v_x)\", \"EQUATION\": \"m*D(v_x,t)=0\"}, {\"NAME\": \"EOM_Z\", \"STATEMENT\": \"m dv_z/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_z\"], \"ROLE\": \"EOM(v_z)\", \"EQUATION\": \"m*D(v_z,t)=0\"}], \"ASSUMPTION\": [{\"NAME\": \"point_mass\", \"PROPOSITION\": \"the body is treated as a point mass\", \"REFS\": [\"m\"]}]}, \"BIND\": {\"HEIGHT\": [\"z\"], \"MASS\": [\"m\"], \"UP_VELOCITY\": [\"v_z\"]}, \"VALUES\": {\"h_max\": {\"VALUE\": \"100\", \"UNIT\": \"m\"}}, \"ANSWERS\": {}}, {\"NAME\": \"TABLE\", \"TPK\": {\"DOF\": [{\"NAME\": \"t\", \"DIMENSION\": \"T1\"}, {\"NAME\": \"x\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"z\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"v_x\", \"DIMENSION\": \"L1 T-1\"}, {\"NAME\": \"v_z\", \"DIMENSION\": \"L1 T-1\"}], \"CONSTANT\": [{\"NAME\": \"m\", \"DIMENSION\": \"M1\"}], \"LAW\": [{\"NAME\": \"KIN_X\", \"STATEMENT\": \"dx/dt = v_x\", \"REFS\": [\"t\", \"v_x\", \"x\"], \"ROLE\": \"EOM(x)\", \"EQUATION\": \"D(x,t)=v_x\"}, {\"NAME\": \"KIN_Z\", \"STATEMENT\": \"dz/dt = v_z\", \"REFS\": [\"t\", \"v_z\", \"z\"], \"ROLE\": \"CONSTRAINT\", \"EQUATION\": \"D(z,t)=v_z\"}, {\"NAME\": \"EOM_X\", \"STATEMENT\": \"m dv_x/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_x\"], \"ROLE\": \"EOM(v_x)\", \"EQUATION\": \"m*D(v_x,t)=0\"}], \"CONSTRAINT\": [{\"NAME\": \"C_Z\", \"TARGET\": \"z\", \"ACTION\": \"FIX\", \"VALUE\": \"0\", \"UNIT\": \"m\", \"STATEMENT\": \"the puck stays on the table top, z = 0\"}, {\"NAME\": \"C_VZ\", \"TARGET\": \"v_z\", \"ACTION\": \"FIX\", \"VALUE\": \"0\", \"UNIT\": \"m s-1\", \"STATEMENT\": \"the puck has no vertical velocity\"}]}, \"BIND\": {\"HEIGHT\": [\"z\"], \"MASS\": [\"m\"], \"UP_VELOCITY\": [\"v_z\"]}, \"VALUES\": {\"h_max\": {\"VALUE\": \"1\", \"UNIT\": \"m\"}}, \"ANSWERS\": {\"FIXED:v_z\": \"YES\"}}]}",
"{\"ID\": \"MATH\", \"VERSION\": \"1.0.0\", \"TITLE\": \"The mathematical constant pi, as the CONSTANT pi_c\", \"SOURCE\": \"pi to 16 significant digits, 3.141592653589793, the nearest IEEE 754 binary64 value\", \"PREREQUISITES\": [], \"PARAMETERS\": [{\"NAME\": \"pi_c\", \"DIMENSION\": \"1\", \"SUPPLY\": \"DECLARED\", \"VALUE\": \"3.141592653589793\", \"UNIT\": \"1\", \"OVERRIDABLE\": \"NO\", \"LABEL\": \"pi, to 16 significant digits\"}], \"SUMS\": [], \"TERMS\": [], \"ASSUMPTIONS\": [], \"BOUNDARIES\": [], \"NOT_CHOSEN\": \"No mathematical constant: pi exists only if you declare it.\", \"NOT_INCLUDED\": [\"pi_c is pi rounded to 16 significant digits; no other mathematical constant is declared.\"], \"EXCLUDES\": [], \"INTERACTS_WITH\": [], \"TEST_BINDINGS\": [{\"NAME\": \"PROJECTILE_2D\", \"TPK\": {\"DOF\": [{\"NAME\": \"t\", \"DIMENSION\": \"T1\"}, {\"NAME\": \"x\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"z\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"v_x\", \"DIMENSION\": \"L1 T-1\"}, {\"NAME\": \"v_z\", \"DIMENSION\": \"L1 T-1\"}], \"CONSTANT\": [{\"NAME\": \"m\", \"DIMENSION\": \"M1\"}], \"LAW\": [{\"NAME\": \"KIN_X\", \"STATEMENT\": \"dx/dt = v_x\", \"REFS\": [\"t\", \"v_x\", \"x\"], \"ROLE\": \"EOM(x)\", \"EQUATION\": \"D(x,t)=v_x\"}, {\"NAME\": \"KIN_Z\", \"STATEMENT\": \"dz/dt = v_z\", \"REFS\": [\"t\", \"v_z\", \"z\"], \"ROLE\": \"EOM(z)\", \"EQUATION\": \"D(z,t)=v_z\"}, {\"NAME\": \"EOM_X\", \"STATEMENT\": \"m dv_x/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_x\"], \"ROLE\": \"EOM(v_x)\", \"EQUATION\": \"m*D(v_x,t)=0\"}, {\"NAME\": \"EOM_Z\", \"STATEMENT\": \"m dv_z/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_z\"], \"ROLE\": \"EOM(v_z)\", \"EQUATION\": \"m*D(v_z,t)=0\"}], \"ASSUMPTION\": [{\"NAME\": \"point_mass\", \"PROPOSITION\": \"the body is treated as a point mass\", \"REFS\": [\"m\"]}]}, \"BIND\": {}, \"VALUES\": {}, \"ANSWERS\": {}}]}",
"{\"ID\": \"TEST-X\", \"VERSION\": \"1.0.0\", \"TITLE\": \"Test interaction X\", \"SOURCE\": \"synthetic fixture\", \"PREREQUISITES\": [], \"PARAMETERS\": [{\"NAME\": \"x_test\", \"DIMENSION\": \"1\", \"SUPPLY\": \"DECLARED\", \"VALUE\": \"1\", \"UNIT\": \"1\", \"OVERRIDABLE\": \"NO\", \"LABEL\": \"a test constant\"}], \"SUMS\": [], \"TERMS\": [], \"ASSUMPTIONS\": [], \"BOUNDARIES\": [], \"NOT_CHOSEN\": \"No test interaction X.\", \"NOT_INCLUDED\": [\"Test X adds only a constant.\"], \"EXCLUDES\": [], \"INTERACTS_WITH\": [], \"TEST_BINDINGS\": [{\"NAME\": \"SOLO\", \"TPK\": {\"DOF\": [{\"NAME\": \"t\", \"DIMENSION\": \"T1\"}, {\"NAME\": \"q\", \"DIMENSION\": \"L1\"}], \"LAW\": [{\"NAME\": \"EQ_Q\", \"STATEMENT\": \"dq/dt = 0\", \"REFS\": [\"q\", \"t\"], \"ROLE\": \"EOM(q)\", \"EQUATION\": \"D(q,t)=0\"}]}, \"BIND\": {}, \"VALUES\": {}, \"ANSWERS\": {}}]}"
]
},
"expected": "[\"REFUSED\",\"ANSWER ROUND 2: RESELECT TEST-X was not covered before\"]",
"fn": "interview_check",
"hand_checked": true,
"name": "I43 RESELECT of an ID no earlier round covered"
},
{
"args": {
"answer": [
{
"AT": 4,
"CHOSEN": [
"GRAV-UNIFORM"
],
"COVERED": [
[
"AIR-LINEAR",
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"5f3fe27b42378bce0830b0d0959f892f4a8e73b12b540ae877e39e6439d08b4d"
],
[
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],
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]
}
],
"carried": [],
"claims": [],
"lines": [
{
"ACT": "MODULE ADD",
"DATE": "2026-10-01",
"DIGEST": "5f3fe27b42378bce0830b0d0959f892f4a8e73b12b540ae877e39e6439d08b4d",
"ID": "AIR-LINEAR",
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{
"ACT": "MODULE ADD",
"DATE": "2026-10-01",
"DIGEST": "6fb53c3a6546151eead2bd6e72e9cf8334f3a2040ad0ee2f5b988ec96d6fc852",
"ID": "AIR-QUADRATIC",
"VERSION": "1.0.0"
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{
"ACT": "MODULE ADD",
"DATE": "2026-10-01",
"DIGEST": "24877ccb5c8ec300d29ed82ce6650592f35cf8899a3d878ccce9c08d4c72c025",
"ID": "GRAV-UNIFORM",
"VERSION": "1.0.0"
},
{
"ACT": "MODULE ADD",
"DATE": "2026-10-01",
"DIGEST": "8f39a356f35527b901fcee012764590f0819c8ffdeccad4bc05195ce3d2e0bcf",
"ID": "MATH",
"VERSION": "1.0.0"
}
],
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[
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],
"modules": [
"{\"ID\": \"AIR-LINEAR\", \"VERSION\": \"1.0.0\", \"TITLE\": \"Air resistance at sea level, linear in the speed (Stokes drag on a sphere)\", \"SOURCE\": \"ISO 2533:1975, Standard Atmosphere, sea-level values: density 1.225 kg m-3, dynamic viscosity 1.7894e-5 Pa s\", \"PREREQUISITES\": [{\"SLOT\": \"VELOCITY\", \"KIND\": \"DOF\", \"DIMENSION\": \"L1 T-1\", \"MIN\": 1, \"MAX\": 3, \"LABEL\": \"the velocity components of the body, one per axis\"}], \"PARAMETERS\": [{\"NAME\": \"rho_air\", \"DIMENSION\": \"L-3 M1\", \"SUPPLY\": \"DECLARED\", \"VALUE\": \"1.225\", \"UNIT\": \"kg m-3\", \"OVERRIDABLE\": \"NO\", \"LABEL\": \"the density of air at sea level\"}, {\"NAME\": \"mu_air\", \"DIMENSION\": \"L-1 M1 T-1\", \"SUPPLY\": \"DECLARED\", \"VALUE\": \"1.7894e-5\", \"UNIT\": \"Pa s\", \"OVERRIDABLE\": \"NO\", \"LABEL\": \"the dynamic viscosity of air at sea level\"}, {\"NAME\": \"pi_c\", \"DIMENSION\": \"1\", \"SUPPLY\": \"DECLARED\", \"VALUE\": \"3.141592653589793\", \"UNIT\": \"1\", \"OVERRIDABLE\": \"NO\", \"LABEL\": \"pi, to 16 significant digits\"}, {\"NAME\": \"R_s\", \"DIMENSION\": \"L1\", \"SUPPLY\": \"AUTHOR\", \"LABEL\": \"the radius of the sphere\"}], \"SUMS\": [{\"NAME\": \"SPEED2\", \"OVER\": \"VELOCITY\", \"EACH\": \"VELOCITY^2\"}], \"TERMS\": [{\"TARGET\": \"VELOCITY\", \"SIGN\": \"-\", \"EXPR\": \"6*pi_c*mu_air*R_s*VELOCITY\", \"LABEL\": \"the linear (Stokes) drag\"}], \"ASSUMPTIONS\": [{\"NAME\": \"air_still\", \"PROPOSITION\": \"the air is at rest in the frame of the body's velocity\", \"REFS\": [\"VELOCITY\"]}, {\"NAME\": \"air_uniform\", \"PROPOSITION\": \"the air density is uniform over the region of motion\", \"REFS\": [\"rho_air\"]}, {\"NAME\": \"drag_sphere\", \"PROPOSITION\": \"the body is a rigid sphere of radius R_s\", \"REFS\": [\"R_s\"]}], \"BOUNDARIES\": [{\"NAME\": \"drag_linear_regime\", \"PREDICATE\": \"2 rho_air |v| R_s / mu_air < 1: the regime of the linear law\", \"CONDITION\": \"mu_air != 0 and SPEED2 >= 0 and 2*rho_air*sqrt(SPEED2)*R_s/mu_air < 1\"}], \"NOT_CHOSEN\": \"No linear (Stokes) air resistance.\", \"NOT_INCLUDED\": [\"No wind: the air is at rest.\", \"No change of air density or viscosity with altitude or temperature.\", \"No drag outside the regime of the linear law.\"], \"EXCLUDES\": [], \"INTERACTS_WITH\": [], \"TEST_BINDINGS\": [{\"NAME\": \"PROJECTILE_2D\", \"TPK\": {\"DOF\": [{\"NAME\": \"t\", \"DIMENSION\": \"T1\"}, {\"NAME\": \"x\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"z\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"v_x\", \"DIMENSION\": \"L1 T-1\"}, {\"NAME\": \"v_z\", \"DIMENSION\": \"L1 T-1\"}], \"CONSTANT\": [{\"NAME\": \"m\", \"DIMENSION\": \"M1\"}], \"LAW\": [{\"NAME\": \"KIN_X\", \"STATEMENT\": \"dx/dt = v_x\", \"REFS\": [\"t\", \"v_x\", \"x\"], \"ROLE\": \"EOM(x)\", \"EQUATION\": \"D(x,t)=v_x\"}, {\"NAME\": \"KIN_Z\", \"STATEMENT\": \"dz/dt = v_z\", \"REFS\": [\"t\", \"v_z\", \"z\"], \"ROLE\": \"EOM(z)\", \"EQUATION\": \"D(z,t)=v_z\"}, {\"NAME\": \"EOM_X\", \"STATEMENT\": \"m dv_x/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_x\"], \"ROLE\": \"EOM(v_x)\", \"EQUATION\": \"m*D(v_x,t)=0\"}, {\"NAME\": \"EOM_Z\", \"STATEMENT\": \"m dv_z/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_z\"], \"ROLE\": \"EOM(v_z)\", \"EQUATION\": \"m*D(v_z,t)=0\"}], \"ASSUMPTION\": [{\"NAME\": \"point_mass\", \"PROPOSITION\": \"the body is treated as a point mass\", \"REFS\": [\"m\"]}]}, \"BIND\": {\"VELOCITY\": [\"v_x\", \"v_z\"]}, \"VALUES\": {\"R_s\": {}}, \"ANSWERS\": {}}]}",
"{\"ID\": \"AIR-QUADRATIC\", \"VERSION\": \"1.0.0\", \"TITLE\": \"Air resistance at sea level, quadratic in the speed\", \"SOURCE\": \"ISO 2533:1975, Standard Atmosphere, sea-level values: density 1.225 kg m-3, dynamic viscosity 1.7894e-5 Pa s\", \"PREREQUISITES\": [{\"SLOT\": \"VELOCITY\", \"KIND\": \"DOF\", \"DIMENSION\": \"L1 T-1\", \"MIN\": 1, \"MAX\": 3, \"LABEL\": \"the velocity components of the body, one per axis\"}], \"PARAMETERS\": [{\"NAME\": \"rho_air\", \"DIMENSION\": \"L-3 M1\", \"SUPPLY\": \"DECLARED\", \"VALUE\": \"1.225\", \"UNIT\": \"kg m-3\", \"OVERRIDABLE\": \"NO\", \"LABEL\": \"the density of air at sea level\"}, {\"NAME\": \"mu_air\", \"DIMENSION\": \"L-1 M1 T-1\", \"SUPPLY\": \"DECLARED\", \"VALUE\": \"1.7894e-5\", \"UNIT\": \"Pa s\", \"OVERRIDABLE\": \"NO\", \"LABEL\": \"the dynamic viscosity of air at sea level\"}, {\"NAME\": \"C_d\", \"DIMENSION\": \"1\", \"SUPPLY\": \"AUTHOR\", \"LABEL\": \"the drag coefficient of the body\"}, {\"NAME\": \"A_ref\", \"DIMENSION\": \"L2\", \"SUPPLY\": \"AUTHOR\", \"LABEL\": \"the reference area of the drag coefficient\"}, {\"NAME\": \"L_ref\", \"DIMENSION\": \"L1\", \"SUPPLY\": \"AUTHOR\", \"LABEL\": \"the reference length of the Reynolds number\"}], \"SUMS\": [{\"NAME\": \"SPEED2\", \"OVER\": \"VELOCITY\", \"EACH\": \"VELOCITY^2\"}], \"TERMS\": [{\"TARGET\": \"VELOCITY\", \"SIGN\": \"-\", \"EXPR\": \"0.5*rho_air*C_d*A_ref*sqrt(SPEED2)*VELOCITY\", \"LABEL\": \"the quadratic drag\"}], \"ASSUMPTIONS\": [{\"NAME\": \"air_still\", \"PROPOSITION\": \"the air is at rest in the frame of the body's velocity\", \"REFS\": [\"VELOCITY\"]}, {\"NAME\": \"air_uniform\", \"PROPOSITION\": \"the air density is uniform over the region of motion\", \"REFS\": [\"rho_air\"]}, {\"NAME\": \"drag_cd_constant\", \"PROPOSITION\": \"the drag coefficient C_d is constant over the motion\", \"REFS\": [\"C_d\"]}, {\"NAME\": \"drag_no_lift\", \"PROPOSITION\": \"the body experiences no lift force\", \"REFS\": [\"VELOCITY\"]}, {\"NAME\": \"drag_no_magnus\", \"PROPOSITION\": \"the body experiences no Magnus force\", \"REFS\": [\"VELOCITY\"]}], \"BOUNDARIES\": [{\"NAME\": \"drag_quadratic_regime\", \"PREDICATE\": \"1e3 < rho_air |v| L_ref / mu_air < 2e5: the Reynolds window of the quadratic law\", \"CONDITION\": \"mu_air != 0 and SPEED2 >= 0 and rho_air*sqrt(SPEED2)*L_ref/mu_air > 1000 and rho_air*sqrt(SPEED2)*L_ref/mu_air < 200000\"}], \"NOT_CHOSEN\": \"No quadratic air resistance.\", \"NOT_INCLUDED\": [\"No wind: the air is at rest.\", \"No change of air density or viscosity with altitude or temperature.\", \"No lift, Magnus or added-mass force.\", \"No drag outside the Reynolds window of the quadratic law.\"], \"EXCLUDES\": [\"AIR-LINEAR\"], \"INTERACTS_WITH\": [], \"TEST_BINDINGS\": [{\"NAME\": \"PROJECTILE_2D\", \"TPK\": {\"DOF\": [{\"NAME\": \"t\", \"DIMENSION\": \"T1\"}, {\"NAME\": \"x\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"z\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"v_x\", \"DIMENSION\": \"L1 T-1\"}, {\"NAME\": \"v_z\", \"DIMENSION\": \"L1 T-1\"}], \"CONSTANT\": [{\"NAME\": \"m\", \"DIMENSION\": \"M1\"}], \"LAW\": [{\"NAME\": \"KIN_X\", \"STATEMENT\": \"dx/dt = v_x\", \"REFS\": [\"t\", \"v_x\", \"x\"], \"ROLE\": \"EOM(x)\", \"EQUATION\": \"D(x,t)=v_x\"}, {\"NAME\": \"KIN_Z\", \"STATEMENT\": \"dz/dt = v_z\", \"REFS\": [\"t\", \"v_z\", \"z\"], \"ROLE\": \"EOM(z)\", \"EQUATION\": \"D(z,t)=v_z\"}, {\"NAME\": \"EOM_X\", \"STATEMENT\": \"m dv_x/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_x\"], \"ROLE\": \"EOM(v_x)\", \"EQUATION\": \"m*D(v_x,t)=0\"}, {\"NAME\": \"EOM_Z\", \"STATEMENT\": \"m dv_z/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_z\"], \"ROLE\": \"EOM(v_z)\", \"EQUATION\": \"m*D(v_z,t)=0\"}], \"ASSUMPTION\": [{\"NAME\": \"point_mass\", \"PROPOSITION\": \"the body is treated as a point mass\", \"REFS\": [\"m\"]}]}, \"BIND\": {\"VELOCITY\": [\"v_x\", \"v_z\"]}, \"VALUES\": {\"A_ref\": {}, \"C_d\": {}, \"L_ref\": {}}, \"ANSWERS\": {}}]}",
"{\"ID\": \"GRAV-UNIFORM\", \"VERSION\": \"1.0.0\", \"TITLE\": \"Uniform gravity at the standard value g_n\", \"SOURCE\": \"g_n = 9.80665 m s-2, exact by definition: 3rd CGPM (1901), declaration on the unit of mass and on the definition of weight\", \"PREREQUISITES\": [{\"SLOT\": \"MASS\", \"KIND\": \"CONSTANT\", \"DIMENSION\": \"M1\", \"MIN\": 1, \"MAX\": 1, \"LABEL\": \"the mass of the body\"}, {\"SLOT\": \"UP_VELOCITY\", \"KIND\": \"DOF\", \"DIMENSION\": \"L1 T-1\", \"MIN\": 1, \"MAX\": 1, \"LABEL\": \"the velocity component pointing up; its equation of motion receives the weight\"}, {\"SLOT\": \"HEIGHT\", \"KIND\": \"DOF\", \"DIMENSION\": \"L1\", \"MIN\": 1, \"MAX\": 1, \"LABEL\": \"the position along the same upward axis\"}], \"PARAMETERS\": [{\"NAME\": \"g_n\", \"DIMENSION\": \"L1 T-2\", \"SUPPLY\": \"DECLARED\", \"VALUE\": \"9.80665\", \"UNIT\": \"m s-2\", \"OVERRIDABLE\": \"NO\", \"LABEL\": \"the standard acceleration of gravity\"}, {\"NAME\": \"h_max\", \"DIMENSION\": \"L1\", \"SUPPLY\": \"AUTHOR\", \"LABEL\": \"the largest height, above or below the origin, over which the field is taken as uniform\"}], \"SUMS\": [], \"TERMS\": [{\"TARGET\": \"UP_VELOCITY\", \"SIGN\": \"-\", \"EXPR\": \"MASS*g_n\", \"LABEL\": \"the weight\"}], \"ASSUMPTIONS\": [{\"NAME\": \"gravity_uniform\", \"PROPOSITION\": \"the gravitational field is uniform over the region abs({HEIGHT}) < h_max\", \"REFS\": [\"HEIGHT\", \"h_max\"]}, {\"NAME\": \"gravity_standard\", \"PROPOSITION\": \"the local gravitational acceleration equals the conventional standard value g_n\", \"REFS\": [\"g_n\"]}, {\"NAME\": \"frame_inertial\", \"PROPOSITION\": \"the frame in which {HEIGHT} is measured is treated as inertial\", \"REFS\": [\"HEIGHT\"]}], \"BOUNDARIES\": [{\"NAME\": \"gravity_region\", \"PREDICATE\": \"abs({HEIGHT}) < h_max\", \"CONDITION\": \"abs(HEIGHT) < h_max\"}], \"NOT_CHOSEN\": \"No gravity: no weight acts on any DOF.\", \"NOT_INCLUDED\": [\"No variation of gravity with height or latitude beyond what g_n contains.\", \"No Earth rotation (Coriolis or centrifugal force) beyond what g_n contains.\", \"No gravity of bodies other than the Earth.\"], \"EXCLUDES\": [], \"INTERACTS_WITH\": [{\"WITH\": \"AIR-*\", \"QUESTION_ID\": \"BUOYANCY\", \"QUESTION\": \"Does the air's buoyancy (upthrust) act on the body in the system you mean?\", \"YES_LINE\": \"Buoyancy acts (your answer): no module adds it; it acts in this kernel only where one of your own laws states it.\", \"NO_LINE\": \"No buoyancy: the air's upthrust on the body is not included.\"}], \"TEST_BINDINGS\": [{\"NAME\": \"PROJECTILE_2D\", \"TPK\": {\"DOF\": [{\"NAME\": \"t\", \"DIMENSION\": \"T1\"}, {\"NAME\": \"x\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"z\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"v_x\", \"DIMENSION\": \"L1 T-1\"}, {\"NAME\": \"v_z\", \"DIMENSION\": \"L1 T-1\"}], \"CONSTANT\": [{\"NAME\": \"m\", \"DIMENSION\": \"M1\"}], \"LAW\": [{\"NAME\": \"KIN_X\", \"STATEMENT\": \"dx/dt = v_x\", \"REFS\": [\"t\", \"v_x\", \"x\"], \"ROLE\": \"EOM(x)\", \"EQUATION\": \"D(x,t)=v_x\"}, {\"NAME\": \"KIN_Z\", \"STATEMENT\": \"dz/dt = v_z\", \"REFS\": [\"t\", \"v_z\", \"z\"], \"ROLE\": \"EOM(z)\", \"EQUATION\": \"D(z,t)=v_z\"}, {\"NAME\": \"EOM_X\", \"STATEMENT\": \"m dv_x/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_x\"], \"ROLE\": \"EOM(v_x)\", \"EQUATION\": \"m*D(v_x,t)=0\"}, {\"NAME\": \"EOM_Z\", \"STATEMENT\": \"m dv_z/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_z\"], \"ROLE\": \"EOM(v_z)\", \"EQUATION\": \"m*D(v_z,t)=0\"}], \"ASSUMPTION\": [{\"NAME\": \"point_mass\", \"PROPOSITION\": \"the body is treated as a point mass\", \"REFS\": [\"m\"]}]}, \"BIND\": {\"HEIGHT\": [\"z\"], \"MASS\": [\"m\"], \"UP_VELOCITY\": [\"v_z\"]}, \"VALUES\": {\"h_max\": {\"VALUE\": \"100\", \"UNIT\": \"m\"}}, \"ANSWERS\": {}}, {\"NAME\": \"TABLE\", \"TPK\": {\"DOF\": [{\"NAME\": \"t\", \"DIMENSION\": \"T1\"}, {\"NAME\": \"x\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"z\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"v_x\", \"DIMENSION\": \"L1 T-1\"}, {\"NAME\": \"v_z\", \"DIMENSION\": \"L1 T-1\"}], \"CONSTANT\": [{\"NAME\": \"m\", \"DIMENSION\": \"M1\"}], \"LAW\": [{\"NAME\": \"KIN_X\", \"STATEMENT\": \"dx/dt = v_x\", \"REFS\": [\"t\", \"v_x\", \"x\"], \"ROLE\": \"EOM(x)\", \"EQUATION\": \"D(x,t)=v_x\"}, {\"NAME\": \"KIN_Z\", \"STATEMENT\": \"dz/dt = v_z\", \"REFS\": [\"t\", \"v_z\", \"z\"], \"ROLE\": \"CONSTRAINT\", \"EQUATION\": \"D(z,t)=v_z\"}, {\"NAME\": \"EOM_X\", \"STATEMENT\": \"m dv_x/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_x\"], \"ROLE\": \"EOM(v_x)\", \"EQUATION\": \"m*D(v_x,t)=0\"}], \"CONSTRAINT\": [{\"NAME\": \"C_Z\", \"TARGET\": \"z\", \"ACTION\": \"FIX\", \"VALUE\": \"0\", \"UNIT\": \"m\", \"STATEMENT\": \"the puck stays on the table top, z = 0\"}, {\"NAME\": \"C_VZ\", \"TARGET\": \"v_z\", \"ACTION\": \"FIX\", \"VALUE\": \"0\", \"UNIT\": \"m s-1\", \"STATEMENT\": \"the puck has no vertical velocity\"}]}, \"BIND\": {\"HEIGHT\": [\"z\"], \"MASS\": [\"m\"], \"UP_VELOCITY\": [\"v_z\"]}, \"VALUES\": {\"h_max\": {\"VALUE\": \"1\", \"UNIT\": \"m\"}}, \"ANSWERS\": {\"FIXED:v_z\": \"YES\"}}]}",
"{\"ID\": \"MATH\", \"VERSION\": \"1.0.0\", \"TITLE\": \"The mathematical constant pi, as the CONSTANT pi_c\", \"SOURCE\": \"pi to 16 significant digits, 3.141592653589793, the nearest IEEE 754 binary64 value\", \"PREREQUISITES\": [], \"PARAMETERS\": [{\"NAME\": \"pi_c\", \"DIMENSION\": \"1\", \"SUPPLY\": \"DECLARED\", \"VALUE\": \"3.141592653589793\", \"UNIT\": \"1\", \"OVERRIDABLE\": \"NO\", \"LABEL\": \"pi, to 16 significant digits\"}], \"SUMS\": [], \"TERMS\": [], \"ASSUMPTIONS\": [], \"BOUNDARIES\": [], \"NOT_CHOSEN\": \"No mathematical constant: pi exists only if you declare it.\", \"NOT_INCLUDED\": [\"pi_c is pi rounded to 16 significant digits; no other mathematical constant is declared.\"], \"EXCLUDES\": [], \"INTERACTS_WITH\": [], \"TEST_BINDINGS\": [{\"NAME\": \"PROJECTILE_2D\", \"TPK\": {\"DOF\": [{\"NAME\": \"t\", \"DIMENSION\": \"T1\"}, {\"NAME\": \"x\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"z\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"v_x\", \"DIMENSION\": \"L1 T-1\"}, {\"NAME\": \"v_z\", \"DIMENSION\": \"L1 T-1\"}], \"CONSTANT\": [{\"NAME\": \"m\", \"DIMENSION\": \"M1\"}], \"LAW\": [{\"NAME\": \"KIN_X\", \"STATEMENT\": \"dx/dt = v_x\", \"REFS\": [\"t\", \"v_x\", \"x\"], \"ROLE\": \"EOM(x)\", \"EQUATION\": \"D(x,t)=v_x\"}, {\"NAME\": \"KIN_Z\", \"STATEMENT\": \"dz/dt = v_z\", \"REFS\": [\"t\", \"v_z\", \"z\"], \"ROLE\": \"EOM(z)\", \"EQUATION\": \"D(z,t)=v_z\"}, {\"NAME\": \"EOM_X\", \"STATEMENT\": \"m dv_x/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_x\"], \"ROLE\": \"EOM(v_x)\", \"EQUATION\": \"m*D(v_x,t)=0\"}, {\"NAME\": \"EOM_Z\", \"STATEMENT\": \"m dv_z/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_z\"], \"ROLE\": \"EOM(v_z)\", \"EQUATION\": \"m*D(v_z,t)=0\"}], \"ASSUMPTION\": [{\"NAME\": \"point_mass\", \"PROPOSITION\": \"the body is treated as a point mass\", \"REFS\": [\"m\"]}]}, \"BIND\": {}, \"VALUES\": {}, \"ANSWERS\": {}}]}"
]
},
"expected": "[\"OK\",[\"ASK\",[]],[\"CLAIMS\",[]]]",
"fn": "interview_check",
"hand_checked": true,
"name": "I44 a chosen module the author edited by hand: MODIFIED, not claimed"
},
{
"args": {
"answer": [
{
"AT": 4,
"CHOSEN": [
"GRAV-UNIFORM"
],
"COVERED": [
[
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[
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[
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]
]
}
],
"carried": [],
"claims": [],
"lines": [
{
"ACT": "MODULE ADD",
"DATE": "2026-10-01",
"DIGEST": "5f3fe27b42378bce0830b0d0959f892f4a8e73b12b540ae877e39e6439d08b4d",
"ID": "AIR-LINEAR",
"VERSION": "1.0.0"
},
{
"ACT": "MODULE ADD",
"DATE": "2026-10-01",
"DIGEST": "6fb53c3a6546151eead2bd6e72e9cf8334f3a2040ad0ee2f5b988ec96d6fc852",
"ID": "AIR-QUADRATIC",
"VERSION": "1.0.0"
},
{
"ACT": "MODULE ADD",
"DATE": "2026-10-01",
"DIGEST": "24877ccb5c8ec300d29ed82ce6650592f35cf8899a3d878ccce9c08d4c72c025",
"ID": "GRAV-UNIFORM",
"VERSION": "1.0.0"
},
{
"ACT": "MODULE ADD",
"DATE": "2026-10-01",
"DIGEST": "8f39a356f35527b901fcee012764590f0819c8ffdeccad4bc05195ce3d2e0bcf",
"ID": "MATH",
"VERSION": "1.0.0"
}
],
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[
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"modules": [
"{\"ID\": \"AIR-LINEAR\", \"VERSION\": \"1.0.0\", \"TITLE\": \"Air resistance at sea level, linear in the speed (Stokes drag on a sphere)\", \"SOURCE\": \"ISO 2533:1975, Standard Atmosphere, sea-level values: density 1.225 kg m-3, dynamic viscosity 1.7894e-5 Pa s\", \"PREREQUISITES\": [{\"SLOT\": \"VELOCITY\", \"KIND\": \"DOF\", \"DIMENSION\": \"L1 T-1\", \"MIN\": 1, \"MAX\": 3, \"LABEL\": \"the velocity components of the body, one per axis\"}], \"PARAMETERS\": [{\"NAME\": \"rho_air\", \"DIMENSION\": \"L-3 M1\", \"SUPPLY\": \"DECLARED\", \"VALUE\": \"1.225\", \"UNIT\": \"kg m-3\", \"OVERRIDABLE\": \"NO\", \"LABEL\": \"the density of air at sea level\"}, {\"NAME\": \"mu_air\", \"DIMENSION\": \"L-1 M1 T-1\", \"SUPPLY\": \"DECLARED\", \"VALUE\": \"1.7894e-5\", \"UNIT\": \"Pa s\", \"OVERRIDABLE\": \"NO\", \"LABEL\": \"the dynamic viscosity of air at sea level\"}, {\"NAME\": \"pi_c\", \"DIMENSION\": \"1\", \"SUPPLY\": \"DECLARED\", \"VALUE\": \"3.141592653589793\", \"UNIT\": \"1\", \"OVERRIDABLE\": \"NO\", \"LABEL\": \"pi, to 16 significant digits\"}, {\"NAME\": \"R_s\", \"DIMENSION\": \"L1\", \"SUPPLY\": \"AUTHOR\", \"LABEL\": \"the radius of the sphere\"}], \"SUMS\": [{\"NAME\": \"SPEED2\", \"OVER\": \"VELOCITY\", \"EACH\": \"VELOCITY^2\"}], \"TERMS\": [{\"TARGET\": \"VELOCITY\", \"SIGN\": \"-\", \"EXPR\": \"6*pi_c*mu_air*R_s*VELOCITY\", \"LABEL\": \"the linear (Stokes) drag\"}], \"ASSUMPTIONS\": [{\"NAME\": \"air_still\", \"PROPOSITION\": \"the air is at rest in the frame of the body's velocity\", \"REFS\": [\"VELOCITY\"]}, {\"NAME\": \"air_uniform\", \"PROPOSITION\": \"the air density is uniform over the region of motion\", \"REFS\": [\"rho_air\"]}, {\"NAME\": \"drag_sphere\", \"PROPOSITION\": \"the body is a rigid sphere of radius R_s\", \"REFS\": [\"R_s\"]}], \"BOUNDARIES\": [{\"NAME\": \"drag_linear_regime\", \"PREDICATE\": \"2 rho_air |v| R_s / mu_air < 1: the regime of the linear law\", \"CONDITION\": \"mu_air != 0 and SPEED2 >= 0 and 2*rho_air*sqrt(SPEED2)*R_s/mu_air < 1\"}], \"NOT_CHOSEN\": \"No linear (Stokes) air resistance.\", \"NOT_INCLUDED\": [\"No wind: the air is at rest.\", \"No change of air density or viscosity with altitude or temperature.\", \"No drag outside the regime of the linear law.\"], \"EXCLUDES\": [], \"INTERACTS_WITH\": [], \"TEST_BINDINGS\": [{\"NAME\": \"PROJECTILE_2D\", \"TPK\": {\"DOF\": [{\"NAME\": \"t\", \"DIMENSION\": \"T1\"}, {\"NAME\": \"x\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"z\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"v_x\", \"DIMENSION\": \"L1 T-1\"}, {\"NAME\": \"v_z\", \"DIMENSION\": \"L1 T-1\"}], \"CONSTANT\": [{\"NAME\": \"m\", \"DIMENSION\": \"M1\"}], \"LAW\": [{\"NAME\": \"KIN_X\", \"STATEMENT\": \"dx/dt = v_x\", \"REFS\": [\"t\", \"v_x\", \"x\"], \"ROLE\": \"EOM(x)\", \"EQUATION\": \"D(x,t)=v_x\"}, {\"NAME\": \"KIN_Z\", \"STATEMENT\": \"dz/dt = v_z\", \"REFS\": [\"t\", \"v_z\", \"z\"], \"ROLE\": \"EOM(z)\", \"EQUATION\": \"D(z,t)=v_z\"}, {\"NAME\": \"EOM_X\", \"STATEMENT\": \"m dv_x/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_x\"], \"ROLE\": \"EOM(v_x)\", \"EQUATION\": \"m*D(v_x,t)=0\"}, {\"NAME\": \"EOM_Z\", \"STATEMENT\": \"m dv_z/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_z\"], \"ROLE\": \"EOM(v_z)\", \"EQUATION\": \"m*D(v_z,t)=0\"}], \"ASSUMPTION\": [{\"NAME\": \"point_mass\", \"PROPOSITION\": \"the body is treated as a point mass\", \"REFS\": [\"m\"]}]}, \"BIND\": {\"VELOCITY\": [\"v_x\", \"v_z\"]}, \"VALUES\": {\"R_s\": {}}, \"ANSWERS\": {}}]}",
"{\"ID\": \"AIR-QUADRATIC\", \"VERSION\": \"1.0.0\", \"TITLE\": \"Air resistance at sea level, quadratic in the speed\", \"SOURCE\": \"ISO 2533:1975, Standard Atmosphere, sea-level values: density 1.225 kg m-3, dynamic viscosity 1.7894e-5 Pa s\", \"PREREQUISITES\": [{\"SLOT\": \"VELOCITY\", \"KIND\": \"DOF\", \"DIMENSION\": \"L1 T-1\", \"MIN\": 1, \"MAX\": 3, \"LABEL\": \"the velocity components of the body, one per axis\"}], \"PARAMETERS\": [{\"NAME\": \"rho_air\", \"DIMENSION\": \"L-3 M1\", \"SUPPLY\": \"DECLARED\", \"VALUE\": \"1.225\", \"UNIT\": \"kg m-3\", \"OVERRIDABLE\": \"NO\", \"LABEL\": \"the density of air at sea level\"}, {\"NAME\": \"mu_air\", \"DIMENSION\": \"L-1 M1 T-1\", \"SUPPLY\": \"DECLARED\", \"VALUE\": \"1.7894e-5\", \"UNIT\": \"Pa s\", \"OVERRIDABLE\": \"NO\", \"LABEL\": \"the dynamic viscosity of air at sea level\"}, {\"NAME\": \"C_d\", \"DIMENSION\": \"1\", \"SUPPLY\": \"AUTHOR\", \"LABEL\": \"the drag coefficient of the body\"}, {\"NAME\": \"A_ref\", \"DIMENSION\": \"L2\", \"SUPPLY\": \"AUTHOR\", \"LABEL\": \"the reference area of the drag coefficient\"}, {\"NAME\": \"L_ref\", \"DIMENSION\": \"L1\", \"SUPPLY\": \"AUTHOR\", \"LABEL\": \"the reference length of the Reynolds number\"}], \"SUMS\": [{\"NAME\": \"SPEED2\", \"OVER\": \"VELOCITY\", \"EACH\": \"VELOCITY^2\"}], \"TERMS\": [{\"TARGET\": \"VELOCITY\", \"SIGN\": \"-\", \"EXPR\": \"0.5*rho_air*C_d*A_ref*sqrt(SPEED2)*VELOCITY\", \"LABEL\": \"the quadratic drag\"}], \"ASSUMPTIONS\": [{\"NAME\": \"air_still\", \"PROPOSITION\": \"the air is at rest in the frame of the body's velocity\", \"REFS\": [\"VELOCITY\"]}, {\"NAME\": \"air_uniform\", \"PROPOSITION\": \"the air density is uniform over the region of motion\", \"REFS\": [\"rho_air\"]}, {\"NAME\": \"drag_cd_constant\", \"PROPOSITION\": \"the drag coefficient C_d is constant over the motion\", \"REFS\": [\"C_d\"]}, {\"NAME\": \"drag_no_lift\", \"PROPOSITION\": \"the body experiences no lift force\", \"REFS\": [\"VELOCITY\"]}, {\"NAME\": \"drag_no_magnus\", \"PROPOSITION\": \"the body experiences no Magnus force\", \"REFS\": [\"VELOCITY\"]}], \"BOUNDARIES\": [{\"NAME\": \"drag_quadratic_regime\", \"PREDICATE\": \"1e3 < rho_air |v| L_ref / mu_air < 2e5: the Reynolds window of the quadratic law\", \"CONDITION\": \"mu_air != 0 and SPEED2 >= 0 and rho_air*sqrt(SPEED2)*L_ref/mu_air > 1000 and rho_air*sqrt(SPEED2)*L_ref/mu_air < 200000\"}], \"NOT_CHOSEN\": \"No quadratic air resistance.\", \"NOT_INCLUDED\": [\"No wind: the air is at rest.\", \"No change of air density or viscosity with altitude or temperature.\", \"No lift, Magnus or added-mass force.\", \"No drag outside the Reynolds window of the quadratic law.\"], \"EXCLUDES\": [\"AIR-LINEAR\"], \"INTERACTS_WITH\": [], \"TEST_BINDINGS\": [{\"NAME\": \"PROJECTILE_2D\", \"TPK\": {\"DOF\": [{\"NAME\": \"t\", \"DIMENSION\": \"T1\"}, {\"NAME\": \"x\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"z\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"v_x\", \"DIMENSION\": \"L1 T-1\"}, {\"NAME\": \"v_z\", \"DIMENSION\": \"L1 T-1\"}], \"CONSTANT\": [{\"NAME\": \"m\", \"DIMENSION\": \"M1\"}], \"LAW\": [{\"NAME\": \"KIN_X\", \"STATEMENT\": \"dx/dt = v_x\", \"REFS\": [\"t\", \"v_x\", \"x\"], \"ROLE\": \"EOM(x)\", \"EQUATION\": \"D(x,t)=v_x\"}, {\"NAME\": \"KIN_Z\", \"STATEMENT\": \"dz/dt = v_z\", \"REFS\": [\"t\", \"v_z\", \"z\"], \"ROLE\": \"EOM(z)\", \"EQUATION\": \"D(z,t)=v_z\"}, {\"NAME\": \"EOM_X\", \"STATEMENT\": \"m dv_x/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_x\"], \"ROLE\": \"EOM(v_x)\", \"EQUATION\": \"m*D(v_x,t)=0\"}, {\"NAME\": \"EOM_Z\", \"STATEMENT\": \"m dv_z/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_z\"], \"ROLE\": \"EOM(v_z)\", \"EQUATION\": \"m*D(v_z,t)=0\"}], \"ASSUMPTION\": [{\"NAME\": \"point_mass\", \"PROPOSITION\": \"the body is treated as a point mass\", \"REFS\": [\"m\"]}]}, \"BIND\": {\"VELOCITY\": [\"v_x\", \"v_z\"]}, \"VALUES\": {\"A_ref\": {}, \"C_d\": {}, \"L_ref\": {}}, \"ANSWERS\": {}}]}",
"{\"ID\": \"GRAV-UNIFORM\", \"VERSION\": \"1.0.0\", \"TITLE\": \"Uniform gravity at the standard value g_n\", \"SOURCE\": \"g_n = 9.80665 m s-2, exact by definition: 3rd CGPM (1901), declaration on the unit of mass and on the definition of weight\", \"PREREQUISITES\": [{\"SLOT\": \"MASS\", \"KIND\": \"CONSTANT\", \"DIMENSION\": \"M1\", \"MIN\": 1, \"MAX\": 1, \"LABEL\": \"the mass of the body\"}, {\"SLOT\": \"UP_VELOCITY\", \"KIND\": \"DOF\", \"DIMENSION\": \"L1 T-1\", \"MIN\": 1, \"MAX\": 1, \"LABEL\": \"the velocity component pointing up; its equation of motion receives the weight\"}, {\"SLOT\": \"HEIGHT\", \"KIND\": \"DOF\", \"DIMENSION\": \"L1\", \"MIN\": 1, \"MAX\": 1, \"LABEL\": \"the position along the same upward axis\"}], \"PARAMETERS\": [{\"NAME\": \"g_n\", \"DIMENSION\": \"L1 T-2\", \"SUPPLY\": \"DECLARED\", \"VALUE\": \"9.80665\", \"UNIT\": \"m s-2\", \"OVERRIDABLE\": \"NO\", \"LABEL\": \"the standard acceleration of gravity\"}, {\"NAME\": \"h_max\", \"DIMENSION\": \"L1\", \"SUPPLY\": \"AUTHOR\", \"LABEL\": \"the largest height, above or below the origin, over which the field is taken as uniform\"}], \"SUMS\": [], \"TERMS\": [{\"TARGET\": \"UP_VELOCITY\", \"SIGN\": \"-\", \"EXPR\": \"MASS*g_n\", \"LABEL\": \"the weight\"}], \"ASSUMPTIONS\": [{\"NAME\": \"gravity_uniform\", \"PROPOSITION\": \"the gravitational field is uniform over the region abs({HEIGHT}) < h_max\", \"REFS\": [\"HEIGHT\", \"h_max\"]}, {\"NAME\": \"gravity_standard\", \"PROPOSITION\": \"the local gravitational acceleration equals the conventional standard value g_n\", \"REFS\": [\"g_n\"]}, {\"NAME\": \"frame_inertial\", \"PROPOSITION\": \"the frame in which {HEIGHT} is measured is treated as inertial\", \"REFS\": [\"HEIGHT\"]}], \"BOUNDARIES\": [{\"NAME\": \"gravity_region\", \"PREDICATE\": \"abs({HEIGHT}) < h_max\", \"CONDITION\": \"abs(HEIGHT) < h_max\"}], \"NOT_CHOSEN\": \"No gravity: no weight acts on any DOF.\", \"NOT_INCLUDED\": [\"No variation of gravity with height or latitude beyond what g_n contains.\", \"No Earth rotation (Coriolis or centrifugal force) beyond what g_n contains.\", \"No gravity of bodies other than the Earth.\"], \"EXCLUDES\": [], \"INTERACTS_WITH\": [{\"WITH\": \"AIR-*\", \"QUESTION_ID\": \"BUOYANCY\", \"QUESTION\": \"Does the air's buoyancy (upthrust) act on the body in the system you mean?\", \"YES_LINE\": \"Buoyancy acts (your answer): no module adds it; it acts in this kernel only where one of your own laws states it.\", \"NO_LINE\": \"No buoyancy: the air's upthrust on the body is not included.\"}], \"TEST_BINDINGS\": [{\"NAME\": \"PROJECTILE_2D\", \"TPK\": {\"DOF\": [{\"NAME\": \"t\", \"DIMENSION\": \"T1\"}, {\"NAME\": \"x\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"z\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"v_x\", \"DIMENSION\": \"L1 T-1\"}, {\"NAME\": \"v_z\", \"DIMENSION\": \"L1 T-1\"}], \"CONSTANT\": [{\"NAME\": \"m\", \"DIMENSION\": \"M1\"}], \"LAW\": [{\"NAME\": \"KIN_X\", \"STATEMENT\": \"dx/dt = v_x\", \"REFS\": [\"t\", \"v_x\", \"x\"], \"ROLE\": \"EOM(x)\", \"EQUATION\": \"D(x,t)=v_x\"}, {\"NAME\": \"KIN_Z\", \"STATEMENT\": \"dz/dt = v_z\", \"REFS\": [\"t\", \"v_z\", \"z\"], \"ROLE\": \"EOM(z)\", \"EQUATION\": \"D(z,t)=v_z\"}, {\"NAME\": \"EOM_X\", \"STATEMENT\": \"m dv_x/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_x\"], \"ROLE\": \"EOM(v_x)\", \"EQUATION\": \"m*D(v_x,t)=0\"}, {\"NAME\": \"EOM_Z\", \"STATEMENT\": \"m dv_z/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_z\"], \"ROLE\": \"EOM(v_z)\", \"EQUATION\": \"m*D(v_z,t)=0\"}], \"ASSUMPTION\": [{\"NAME\": \"point_mass\", \"PROPOSITION\": \"the body is treated as a point mass\", \"REFS\": [\"m\"]}]}, \"BIND\": {\"HEIGHT\": [\"z\"], \"MASS\": [\"m\"], \"UP_VELOCITY\": [\"v_z\"]}, \"VALUES\": {\"h_max\": {\"VALUE\": \"100\", \"UNIT\": \"m\"}}, \"ANSWERS\": {}}, {\"NAME\": \"TABLE\", \"TPK\": {\"DOF\": [{\"NAME\": \"t\", \"DIMENSION\": \"T1\"}, {\"NAME\": \"x\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"z\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"v_x\", \"DIMENSION\": \"L1 T-1\"}, {\"NAME\": \"v_z\", \"DIMENSION\": \"L1 T-1\"}], \"CONSTANT\": [{\"NAME\": \"m\", \"DIMENSION\": \"M1\"}], \"LAW\": [{\"NAME\": \"KIN_X\", \"STATEMENT\": \"dx/dt = v_x\", \"REFS\": [\"t\", \"v_x\", \"x\"], \"ROLE\": \"EOM(x)\", \"EQUATION\": \"D(x,t)=v_x\"}, {\"NAME\": \"KIN_Z\", \"STATEMENT\": \"dz/dt = v_z\", \"REFS\": [\"t\", \"v_z\", \"z\"], \"ROLE\": \"CONSTRAINT\", \"EQUATION\": \"D(z,t)=v_z\"}, {\"NAME\": \"EOM_X\", \"STATEMENT\": \"m dv_x/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_x\"], \"ROLE\": \"EOM(v_x)\", \"EQUATION\": \"m*D(v_x,t)=0\"}], \"CONSTRAINT\": [{\"NAME\": \"C_Z\", \"TARGET\": \"z\", \"ACTION\": \"FIX\", \"VALUE\": \"0\", \"UNIT\": \"m\", \"STATEMENT\": \"the puck stays on the table top, z = 0\"}, {\"NAME\": \"C_VZ\", \"TARGET\": \"v_z\", \"ACTION\": \"FIX\", \"VALUE\": \"0\", \"UNIT\": \"m s-1\", \"STATEMENT\": \"the puck has no vertical velocity\"}]}, \"BIND\": {\"HEIGHT\": [\"z\"], \"MASS\": [\"m\"], \"UP_VELOCITY\": [\"v_z\"]}, \"VALUES\": {\"h_max\": {\"VALUE\": \"1\", \"UNIT\": \"m\"}}, \"ANSWERS\": {\"FIXED:v_z\": \"YES\"}}]}",
"{\"ID\": \"MATH\", \"VERSION\": \"1.0.0\", \"TITLE\": \"The mathematical constant pi, as the CONSTANT pi_c\", \"SOURCE\": \"pi to 16 significant digits, 3.141592653589793, the nearest IEEE 754 binary64 value\", \"PREREQUISITES\": [], \"PARAMETERS\": [{\"NAME\": \"pi_c\", \"DIMENSION\": \"1\", \"SUPPLY\": \"DECLARED\", \"VALUE\": \"3.141592653589793\", \"UNIT\": \"1\", \"OVERRIDABLE\": \"NO\", \"LABEL\": \"pi, to 16 significant digits\"}], \"SUMS\": [], \"TERMS\": [], \"ASSUMPTIONS\": [], \"BOUNDARIES\": [], \"NOT_CHOSEN\": \"No mathematical constant: pi exists only if you declare it.\", \"NOT_INCLUDED\": [\"pi_c is pi rounded to 16 significant digits; no other mathematical constant is declared.\"], \"EXCLUDES\": [], \"INTERACTS_WITH\": [], \"TEST_BINDINGS\": [{\"NAME\": \"PROJECTILE_2D\", \"TPK\": {\"DOF\": [{\"NAME\": \"t\", \"DIMENSION\": \"T1\"}, {\"NAME\": \"x\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"z\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"v_x\", \"DIMENSION\": \"L1 T-1\"}, {\"NAME\": \"v_z\", \"DIMENSION\": \"L1 T-1\"}], \"CONSTANT\": [{\"NAME\": \"m\", \"DIMENSION\": \"M1\"}], \"LAW\": [{\"NAME\": \"KIN_X\", \"STATEMENT\": \"dx/dt = v_x\", \"REFS\": [\"t\", \"v_x\", \"x\"], \"ROLE\": \"EOM(x)\", \"EQUATION\": \"D(x,t)=v_x\"}, {\"NAME\": \"KIN_Z\", \"STATEMENT\": \"dz/dt = v_z\", \"REFS\": [\"t\", \"v_z\", \"z\"], \"ROLE\": \"EOM(z)\", \"EQUATION\": \"D(z,t)=v_z\"}, {\"NAME\": \"EOM_X\", \"STATEMENT\": \"m dv_x/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_x\"], \"ROLE\": \"EOM(v_x)\", \"EQUATION\": \"m*D(v_x,t)=0\"}, {\"NAME\": \"EOM_Z\", \"STATEMENT\": \"m dv_z/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_z\"], \"ROLE\": \"EOM(v_z)\", \"EQUATION\": \"m*D(v_z,t)=0\"}], \"ASSUMPTION\": [{\"NAME\": \"point_mass\", \"PROPOSITION\": \"the body is treated as a point mass\", \"REFS\": [\"m\"]}]}, \"BIND\": {}, \"VALUES\": {}, \"ANSWERS\": {}}]}"
]
},
"expected": "[\"REFUSED\",\"MODIFIED: not a list of [ID, VERSION]\"]",
"fn": "interview_check",
"hand_checked": true,
"name": "I45 MODIFIED not a list of pairs"
},
{
"args": {
"answer": [
{
"AT": 4,
"CHOSEN": [
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"claims": [],
"lines": [
{
"ACT": "MODULE ADD",
"DATE": "2026-10-01",
"DIGEST": "5f3fe27b42378bce0830b0d0959f892f4a8e73b12b540ae877e39e6439d08b4d",
"ID": "AIR-LINEAR",
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{
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{
"ACT": "MODULE ADD",
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"{\"ID\": \"AIR-LINEAR\", \"VERSION\": \"1.0.0\", \"TITLE\": \"Air resistance at sea level, linear in the speed (Stokes drag on a sphere)\", \"SOURCE\": \"ISO 2533:1975, Standard Atmosphere, sea-level values: density 1.225 kg m-3, dynamic viscosity 1.7894e-5 Pa s\", \"PREREQUISITES\": [{\"SLOT\": \"VELOCITY\", \"KIND\": \"DOF\", \"DIMENSION\": \"L1 T-1\", \"MIN\": 1, \"MAX\": 3, \"LABEL\": \"the velocity components of the body, one per axis\"}], \"PARAMETERS\": [{\"NAME\": \"rho_air\", \"DIMENSION\": \"L-3 M1\", \"SUPPLY\": \"DECLARED\", \"VALUE\": \"1.225\", \"UNIT\": \"kg m-3\", \"OVERRIDABLE\": \"NO\", \"LABEL\": \"the density of air at sea level\"}, {\"NAME\": \"mu_air\", \"DIMENSION\": \"L-1 M1 T-1\", \"SUPPLY\": \"DECLARED\", \"VALUE\": \"1.7894e-5\", \"UNIT\": \"Pa s\", \"OVERRIDABLE\": \"NO\", \"LABEL\": \"the dynamic viscosity of air at sea level\"}, {\"NAME\": \"pi_c\", \"DIMENSION\": \"1\", \"SUPPLY\": \"DECLARED\", \"VALUE\": \"3.141592653589793\", \"UNIT\": \"1\", \"OVERRIDABLE\": \"NO\", \"LABEL\": \"pi, to 16 significant digits\"}, {\"NAME\": \"R_s\", \"DIMENSION\": \"L1\", \"SUPPLY\": \"AUTHOR\", \"LABEL\": \"the radius of the sphere\"}], \"SUMS\": [{\"NAME\": \"SPEED2\", \"OVER\": \"VELOCITY\", \"EACH\": \"VELOCITY^2\"}], \"TERMS\": [{\"TARGET\": \"VELOCITY\", \"SIGN\": \"-\", \"EXPR\": \"6*pi_c*mu_air*R_s*VELOCITY\", \"LABEL\": \"the linear (Stokes) drag\"}], \"ASSUMPTIONS\": [{\"NAME\": \"air_still\", \"PROPOSITION\": \"the air is at rest in the frame of the body's velocity\", \"REFS\": [\"VELOCITY\"]}, {\"NAME\": \"air_uniform\", \"PROPOSITION\": \"the air density is uniform over the region of motion\", \"REFS\": [\"rho_air\"]}, {\"NAME\": \"drag_sphere\", \"PROPOSITION\": \"the body is a rigid sphere of radius R_s\", \"REFS\": [\"R_s\"]}], \"BOUNDARIES\": [{\"NAME\": \"drag_linear_regime\", \"PREDICATE\": \"2 rho_air |v| R_s / mu_air < 1: the regime of the linear law\", \"CONDITION\": \"mu_air != 0 and SPEED2 >= 0 and 2*rho_air*sqrt(SPEED2)*R_s/mu_air < 1\"}], \"NOT_CHOSEN\": \"No linear (Stokes) air resistance.\", \"NOT_INCLUDED\": [\"No wind: the air is at rest.\", \"No change of air density or viscosity with altitude or temperature.\", \"No drag outside the regime of the linear law.\"], \"EXCLUDES\": [], \"INTERACTS_WITH\": [], \"TEST_BINDINGS\": [{\"NAME\": \"PROJECTILE_2D\", \"TPK\": {\"DOF\": [{\"NAME\": \"t\", \"DIMENSION\": \"T1\"}, {\"NAME\": \"x\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"z\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"v_x\", \"DIMENSION\": \"L1 T-1\"}, {\"NAME\": \"v_z\", \"DIMENSION\": \"L1 T-1\"}], \"CONSTANT\": [{\"NAME\": \"m\", \"DIMENSION\": \"M1\"}], \"LAW\": [{\"NAME\": \"KIN_X\", \"STATEMENT\": \"dx/dt = v_x\", \"REFS\": [\"t\", \"v_x\", \"x\"], \"ROLE\": \"EOM(x)\", \"EQUATION\": \"D(x,t)=v_x\"}, {\"NAME\": \"KIN_Z\", \"STATEMENT\": \"dz/dt = v_z\", \"REFS\": [\"t\", \"v_z\", \"z\"], \"ROLE\": \"EOM(z)\", \"EQUATION\": \"D(z,t)=v_z\"}, {\"NAME\": \"EOM_X\", \"STATEMENT\": \"m dv_x/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_x\"], \"ROLE\": \"EOM(v_x)\", \"EQUATION\": \"m*D(v_x,t)=0\"}, {\"NAME\": \"EOM_Z\", \"STATEMENT\": \"m dv_z/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_z\"], \"ROLE\": \"EOM(v_z)\", \"EQUATION\": \"m*D(v_z,t)=0\"}], \"ASSUMPTION\": [{\"NAME\": \"point_mass\", \"PROPOSITION\": \"the body is treated as a point mass\", \"REFS\": [\"m\"]}]}, \"BIND\": {\"VELOCITY\": [\"v_x\", \"v_z\"]}, \"VALUES\": {\"R_s\": {}}, \"ANSWERS\": {}}]}",
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it acts in this kernel only where one of your own laws states it.\", \"NO_LINE\": \"No buoyancy: the air's upthrust on the body is not included.\"}], \"TEST_BINDINGS\": [{\"NAME\": \"PROJECTILE_2D\", \"TPK\": {\"DOF\": [{\"NAME\": \"t\", \"DIMENSION\": \"T1\"}, {\"NAME\": \"x\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"z\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"v_x\", \"DIMENSION\": \"L1 T-1\"}, {\"NAME\": \"v_z\", \"DIMENSION\": \"L1 T-1\"}], \"CONSTANT\": [{\"NAME\": \"m\", \"DIMENSION\": \"M1\"}], \"LAW\": [{\"NAME\": \"KIN_X\", \"STATEMENT\": \"dx/dt = v_x\", \"REFS\": [\"t\", \"v_x\", \"x\"], \"ROLE\": \"EOM(x)\", \"EQUATION\": \"D(x,t)=v_x\"}, {\"NAME\": \"KIN_Z\", \"STATEMENT\": \"dz/dt = v_z\", \"REFS\": [\"t\", \"v_z\", \"z\"], \"ROLE\": \"EOM(z)\", \"EQUATION\": \"D(z,t)=v_z\"}, {\"NAME\": \"EOM_X\", \"STATEMENT\": \"m dv_x/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_x\"], \"ROLE\": \"EOM(v_x)\", \"EQUATION\": \"m*D(v_x,t)=0\"}, {\"NAME\": \"EOM_Z\", \"STATEMENT\": \"m dv_z/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_z\"], \"ROLE\": \"EOM(v_z)\", \"EQUATION\": \"m*D(v_z,t)=0\"}], \"ASSUMPTION\": [{\"NAME\": \"point_mass\", \"PROPOSITION\": \"the body is treated as a point mass\", \"REFS\": [\"m\"]}]}, \"BIND\": {\"HEIGHT\": [\"z\"], \"MASS\": [\"m\"], \"UP_VELOCITY\": [\"v_z\"]}, \"VALUES\": {\"h_max\": {\"VALUE\": \"100\", \"UNIT\": \"m\"}}, \"ANSWERS\": {}}, {\"NAME\": \"TABLE\", \"TPK\": {\"DOF\": [{\"NAME\": \"t\", \"DIMENSION\": \"T1\"}, {\"NAME\": \"x\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"z\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"v_x\", \"DIMENSION\": \"L1 T-1\"}, {\"NAME\": \"v_z\", \"DIMENSION\": \"L1 T-1\"}], \"CONSTANT\": [{\"NAME\": \"m\", \"DIMENSION\": \"M1\"}], \"LAW\": [{\"NAME\": \"KIN_X\", \"STATEMENT\": \"dx/dt = v_x\", \"REFS\": [\"t\", \"v_x\", \"x\"], \"ROLE\": \"EOM(x)\", \"EQUATION\": \"D(x,t)=v_x\"}, {\"NAME\": \"KIN_Z\", \"STATEMENT\": \"dz/dt = v_z\", \"REFS\": [\"t\", \"v_z\", \"z\"], \"ROLE\": \"CONSTRAINT\", \"EQUATION\": \"D(z,t)=v_z\"}, {\"NAME\": \"EOM_X\", \"STATEMENT\": \"m dv_x/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_x\"], \"ROLE\": \"EOM(v_x)\", \"EQUATION\": \"m*D(v_x,t)=0\"}], \"CONSTRAINT\": [{\"NAME\": \"C_Z\", \"TARGET\": \"z\", \"ACTION\": \"FIX\", \"VALUE\": \"0\", \"UNIT\": \"m\", \"STATEMENT\": \"the puck stays on the table top, z = 0\"}, {\"NAME\": \"C_VZ\", \"TARGET\": \"v_z\", \"ACTION\": \"FIX\", \"VALUE\": \"0\", \"UNIT\": \"m s-1\", \"STATEMENT\": \"the puck has no vertical velocity\"}]}, \"BIND\": {\"HEIGHT\": [\"z\"], \"MASS\": [\"m\"], \"UP_VELOCITY\": [\"v_z\"]}, \"VALUES\": {\"h_max\": {\"VALUE\": \"1\", \"UNIT\": \"m\"}}, \"ANSWERS\": {\"FIXED:v_z\": \"YES\"}}]}",
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{
"ACT": "MODULE ADD",
"DATE": "2026-10-01",
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"{\"ID\": \"AIR-LINEAR\", \"VERSION\": \"1.0.0\", \"TITLE\": \"Air resistance at sea level, linear in the speed (Stokes drag on a sphere)\", \"SOURCE\": \"ISO 2533:1975, Standard Atmosphere, sea-level values: density 1.225 kg m-3, dynamic viscosity 1.7894e-5 Pa s\", \"PREREQUISITES\": [{\"SLOT\": \"VELOCITY\", \"KIND\": \"DOF\", \"DIMENSION\": \"L1 T-1\", \"MIN\": 1, \"MAX\": 3, \"LABEL\": \"the velocity components of the body, one per axis\"}], \"PARAMETERS\": [{\"NAME\": \"rho_air\", \"DIMENSION\": \"L-3 M1\", \"SUPPLY\": \"DECLARED\", \"VALUE\": \"1.225\", \"UNIT\": \"kg m-3\", \"OVERRIDABLE\": \"NO\", \"LABEL\": \"the density of air at sea level\"}, {\"NAME\": \"mu_air\", \"DIMENSION\": \"L-1 M1 T-1\", \"SUPPLY\": \"DECLARED\", \"VALUE\": \"1.7894e-5\", \"UNIT\": \"Pa s\", \"OVERRIDABLE\": \"NO\", \"LABEL\": \"the dynamic viscosity of air at sea level\"}, {\"NAME\": \"pi_c\", \"DIMENSION\": \"1\", \"SUPPLY\": \"DECLARED\", \"VALUE\": \"3.141592653589793\", \"UNIT\": \"1\", \"OVERRIDABLE\": \"NO\", \"LABEL\": \"pi, to 16 significant digits\"}, {\"NAME\": \"R_s\", \"DIMENSION\": \"L1\", \"SUPPLY\": \"AUTHOR\", \"LABEL\": \"the radius of the sphere\"}], \"SUMS\": [{\"NAME\": \"SPEED2\", \"OVER\": \"VELOCITY\", \"EACH\": \"VELOCITY^2\"}], \"TERMS\": [{\"TARGET\": \"VELOCITY\", \"SIGN\": \"-\", \"EXPR\": \"6*pi_c*mu_air*R_s*VELOCITY\", \"LABEL\": \"the linear (Stokes) drag\"}], \"ASSUMPTIONS\": [{\"NAME\": \"air_still\", \"PROPOSITION\": \"the air is at rest in the frame of the body's velocity\", \"REFS\": [\"VELOCITY\"]}, {\"NAME\": \"air_uniform\", \"PROPOSITION\": \"the air density is uniform over the region of motion\", \"REFS\": [\"rho_air\"]}, {\"NAME\": \"drag_sphere\", \"PROPOSITION\": \"the body is a rigid sphere of radius R_s\", \"REFS\": [\"R_s\"]}], \"BOUNDARIES\": [{\"NAME\": \"drag_linear_regime\", \"PREDICATE\": \"2 rho_air |v| R_s / mu_air < 1: the regime of the linear law\", \"CONDITION\": \"mu_air != 0 and SPEED2 >= 0 and 2*rho_air*sqrt(SPEED2)*R_s/mu_air < 1\"}], \"NOT_CHOSEN\": \"No linear (Stokes) air resistance.\", \"NOT_INCLUDED\": [\"No wind: the air is at rest.\", \"No change of air density or viscosity with altitude or temperature.\", \"No drag outside the regime of the linear law.\"], \"EXCLUDES\": [], \"INTERACTS_WITH\": [], \"TEST_BINDINGS\": [{\"NAME\": \"PROJECTILE_2D\", \"TPK\": {\"DOF\": [{\"NAME\": \"t\", \"DIMENSION\": \"T1\"}, {\"NAME\": \"x\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"z\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"v_x\", \"DIMENSION\": \"L1 T-1\"}, {\"NAME\": \"v_z\", \"DIMENSION\": \"L1 T-1\"}], \"CONSTANT\": [{\"NAME\": \"m\", \"DIMENSION\": \"M1\"}], \"LAW\": [{\"NAME\": \"KIN_X\", \"STATEMENT\": \"dx/dt = v_x\", \"REFS\": [\"t\", \"v_x\", \"x\"], \"ROLE\": \"EOM(x)\", \"EQUATION\": \"D(x,t)=v_x\"}, {\"NAME\": \"KIN_Z\", \"STATEMENT\": \"dz/dt = v_z\", \"REFS\": [\"t\", \"v_z\", \"z\"], \"ROLE\": \"EOM(z)\", \"EQUATION\": \"D(z,t)=v_z\"}, {\"NAME\": \"EOM_X\", \"STATEMENT\": \"m dv_x/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_x\"], \"ROLE\": \"EOM(v_x)\", \"EQUATION\": \"m*D(v_x,t)=0\"}, {\"NAME\": \"EOM_Z\", \"STATEMENT\": \"m dv_z/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_z\"], \"ROLE\": \"EOM(v_z)\", \"EQUATION\": \"m*D(v_z,t)=0\"}], \"ASSUMPTION\": [{\"NAME\": \"point_mass\", \"PROPOSITION\": \"the body is treated as a point mass\", \"REFS\": [\"m\"]}]}, \"BIND\": {\"VELOCITY\": [\"v_x\", \"v_z\"]}, \"VALUES\": {\"R_s\": {}}, \"ANSWERS\": {}}]}",
"{\"ID\": \"AIR-QUADRATIC\", \"VERSION\": \"1.0.0\", \"TITLE\": \"Air resistance at sea level, quadratic in the speed\", \"SOURCE\": \"ISO 2533:1975, Standard Atmosphere, sea-level values: density 1.225 kg m-3, dynamic viscosity 1.7894e-5 Pa s\", \"PREREQUISITES\": [{\"SLOT\": \"VELOCITY\", \"KIND\": \"DOF\", \"DIMENSION\": \"L1 T-1\", \"MIN\": 1, \"MAX\": 3, \"LABEL\": \"the velocity components of the body, one per axis\"}], \"PARAMETERS\": [{\"NAME\": \"rho_air\", \"DIMENSION\": \"L-3 M1\", \"SUPPLY\": \"DECLARED\", \"VALUE\": \"1.225\", \"UNIT\": \"kg m-3\", \"OVERRIDABLE\": \"NO\", \"LABEL\": \"the density of air at sea level\"}, {\"NAME\": \"mu_air\", \"DIMENSION\": \"L-1 M1 T-1\", \"SUPPLY\": \"DECLARED\", \"VALUE\": \"1.7894e-5\", \"UNIT\": \"Pa s\", \"OVERRIDABLE\": \"NO\", \"LABEL\": \"the dynamic viscosity of air at sea level\"}, {\"NAME\": \"C_d\", \"DIMENSION\": \"1\", \"SUPPLY\": \"AUTHOR\", \"LABEL\": \"the drag coefficient of the body\"}, {\"NAME\": \"A_ref\", \"DIMENSION\": \"L2\", \"SUPPLY\": \"AUTHOR\", \"LABEL\": \"the reference area of the drag coefficient\"}, {\"NAME\": \"L_ref\", \"DIMENSION\": \"L1\", \"SUPPLY\": \"AUTHOR\", \"LABEL\": \"the reference length of the Reynolds number\"}], \"SUMS\": [{\"NAME\": \"SPEED2\", \"OVER\": \"VELOCITY\", \"EACH\": \"VELOCITY^2\"}], \"TERMS\": [{\"TARGET\": \"VELOCITY\", \"SIGN\": \"-\", \"EXPR\": \"0.5*rho_air*C_d*A_ref*sqrt(SPEED2)*VELOCITY\", \"LABEL\": \"the quadratic drag\"}], \"ASSUMPTIONS\": [{\"NAME\": \"air_still\", \"PROPOSITION\": \"the air is at rest in the frame of the body's velocity\", \"REFS\": [\"VELOCITY\"]}, {\"NAME\": \"air_uniform\", \"PROPOSITION\": \"the air density is uniform over the region of motion\", \"REFS\": [\"rho_air\"]}, {\"NAME\": \"drag_cd_constant\", \"PROPOSITION\": \"the drag coefficient C_d is constant over the motion\", \"REFS\": [\"C_d\"]}, {\"NAME\": \"drag_no_lift\", \"PROPOSITION\": \"the body experiences no lift force\", \"REFS\": [\"VELOCITY\"]}, {\"NAME\": \"drag_no_magnus\", \"PROPOSITION\": \"the body experiences no Magnus force\", \"REFS\": [\"VELOCITY\"]}], \"BOUNDARIES\": [{\"NAME\": \"drag_quadratic_regime\", \"PREDICATE\": \"1e3 < rho_air |v| L_ref / mu_air < 2e5: the Reynolds window of the quadratic law\", \"CONDITION\": \"mu_air != 0 and SPEED2 >= 0 and rho_air*sqrt(SPEED2)*L_ref/mu_air > 1000 and rho_air*sqrt(SPEED2)*L_ref/mu_air < 200000\"}], \"NOT_CHOSEN\": \"No quadratic air resistance.\", \"NOT_INCLUDED\": [\"No wind: the air is at rest.\", \"No change of air density or viscosity with altitude or temperature.\", \"No lift, Magnus or added-mass force.\", \"No drag outside the Reynolds window of the quadratic law.\"], \"EXCLUDES\": [\"AIR-LINEAR\"], \"INTERACTS_WITH\": [], \"TEST_BINDINGS\": [{\"NAME\": \"PROJECTILE_2D\", \"TPK\": {\"DOF\": [{\"NAME\": \"t\", \"DIMENSION\": \"T1\"}, {\"NAME\": \"x\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"z\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"v_x\", \"DIMENSION\": \"L1 T-1\"}, {\"NAME\": \"v_z\", \"DIMENSION\": \"L1 T-1\"}], \"CONSTANT\": [{\"NAME\": \"m\", \"DIMENSION\": \"M1\"}], \"LAW\": [{\"NAME\": \"KIN_X\", \"STATEMENT\": \"dx/dt = v_x\", \"REFS\": [\"t\", \"v_x\", \"x\"], \"ROLE\": \"EOM(x)\", \"EQUATION\": \"D(x,t)=v_x\"}, {\"NAME\": \"KIN_Z\", \"STATEMENT\": \"dz/dt = v_z\", \"REFS\": [\"t\", \"v_z\", \"z\"], \"ROLE\": \"EOM(z)\", \"EQUATION\": \"D(z,t)=v_z\"}, {\"NAME\": \"EOM_X\", \"STATEMENT\": \"m dv_x/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_x\"], \"ROLE\": \"EOM(v_x)\", \"EQUATION\": \"m*D(v_x,t)=0\"}, {\"NAME\": \"EOM_Z\", \"STATEMENT\": \"m dv_z/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_z\"], \"ROLE\": \"EOM(v_z)\", \"EQUATION\": \"m*D(v_z,t)=0\"}], \"ASSUMPTION\": [{\"NAME\": \"point_mass\", \"PROPOSITION\": \"the body is treated as a point mass\", \"REFS\": [\"m\"]}]}, \"BIND\": {\"VELOCITY\": [\"v_x\", \"v_z\"]}, \"VALUES\": {\"A_ref\": {}, \"C_d\": {}, \"L_ref\": {}}, \"ANSWERS\": {}}]}",
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it acts in this kernel only where one of your own laws states it.\", \"NO_LINE\": \"No buoyancy: the air's upthrust on the body is not included.\"}], \"TEST_BINDINGS\": [{\"NAME\": \"PROJECTILE_2D\", \"TPK\": {\"DOF\": [{\"NAME\": \"t\", \"DIMENSION\": \"T1\"}, {\"NAME\": \"x\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"z\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"v_x\", \"DIMENSION\": \"L1 T-1\"}, {\"NAME\": \"v_z\", \"DIMENSION\": \"L1 T-1\"}], \"CONSTANT\": [{\"NAME\": \"m\", \"DIMENSION\": \"M1\"}], \"LAW\": [{\"NAME\": \"KIN_X\", \"STATEMENT\": \"dx/dt = v_x\", \"REFS\": [\"t\", \"v_x\", \"x\"], \"ROLE\": \"EOM(x)\", \"EQUATION\": \"D(x,t)=v_x\"}, {\"NAME\": \"KIN_Z\", \"STATEMENT\": \"dz/dt = v_z\", \"REFS\": [\"t\", \"v_z\", \"z\"], \"ROLE\": \"EOM(z)\", \"EQUATION\": \"D(z,t)=v_z\"}, {\"NAME\": \"EOM_X\", \"STATEMENT\": \"m dv_x/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_x\"], \"ROLE\": \"EOM(v_x)\", \"EQUATION\": \"m*D(v_x,t)=0\"}, {\"NAME\": \"EOM_Z\", \"STATEMENT\": \"m dv_z/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_z\"], \"ROLE\": \"EOM(v_z)\", \"EQUATION\": \"m*D(v_z,t)=0\"}], \"ASSUMPTION\": [{\"NAME\": \"point_mass\", \"PROPOSITION\": \"the body is treated as a point mass\", \"REFS\": [\"m\"]}]}, \"BIND\": {\"HEIGHT\": [\"z\"], \"MASS\": [\"m\"], \"UP_VELOCITY\": [\"v_z\"]}, \"VALUES\": {\"h_max\": {\"VALUE\": \"100\", \"UNIT\": \"m\"}}, \"ANSWERS\": {}}, {\"NAME\": \"TABLE\", \"TPK\": {\"DOF\": [{\"NAME\": \"t\", \"DIMENSION\": \"T1\"}, {\"NAME\": \"x\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"z\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"v_x\", \"DIMENSION\": \"L1 T-1\"}, {\"NAME\": \"v_z\", \"DIMENSION\": \"L1 T-1\"}], \"CONSTANT\": [{\"NAME\": \"m\", \"DIMENSION\": \"M1\"}], \"LAW\": [{\"NAME\": \"KIN_X\", \"STATEMENT\": \"dx/dt = v_x\", \"REFS\": [\"t\", \"v_x\", \"x\"], \"ROLE\": \"EOM(x)\", \"EQUATION\": \"D(x,t)=v_x\"}, {\"NAME\": \"KIN_Z\", \"STATEMENT\": \"dz/dt = v_z\", \"REFS\": [\"t\", \"v_z\", \"z\"], \"ROLE\": \"CONSTRAINT\", \"EQUATION\": \"D(z,t)=v_z\"}, {\"NAME\": \"EOM_X\", \"STATEMENT\": \"m dv_x/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_x\"], \"ROLE\": \"EOM(v_x)\", \"EQUATION\": \"m*D(v_x,t)=0\"}], \"CONSTRAINT\": [{\"NAME\": \"C_Z\", \"TARGET\": \"z\", \"ACTION\": \"FIX\", \"VALUE\": \"0\", \"UNIT\": \"m\", \"STATEMENT\": \"the puck stays on the table top, z = 0\"}, {\"NAME\": \"C_VZ\", \"TARGET\": \"v_z\", \"ACTION\": \"FIX\", \"VALUE\": \"0\", \"UNIT\": \"m s-1\", \"STATEMENT\": \"the puck has no vertical velocity\"}]}, \"BIND\": {\"HEIGHT\": [\"z\"], \"MASS\": [\"m\"], \"UP_VELOCITY\": [\"v_z\"]}, \"VALUES\": {\"h_max\": {\"VALUE\": \"1\", \"UNIT\": \"m\"}}, \"ANSWERS\": {\"FIXED:v_z\": \"YES\"}}]}",
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"{\"ID\": \"AIR-LINEAR\", \"VERSION\": \"1.0.0\", \"TITLE\": \"Air resistance at sea level, linear in the speed (Stokes drag on a sphere)\", \"SOURCE\": \"ISO 2533:1975, Standard Atmosphere, sea-level values: density 1.225 kg m-3, dynamic viscosity 1.7894e-5 Pa s\", \"PREREQUISITES\": [{\"SLOT\": \"VELOCITY\", \"KIND\": \"DOF\", \"DIMENSION\": \"L1 T-1\", \"MIN\": 1, \"MAX\": 3, \"LABEL\": \"the velocity components of the body, one per axis\"}], \"PARAMETERS\": [{\"NAME\": \"rho_air\", \"DIMENSION\": \"L-3 M1\", \"SUPPLY\": \"DECLARED\", \"VALUE\": \"1.225\", \"UNIT\": \"kg m-3\", \"OVERRIDABLE\": \"NO\", \"LABEL\": \"the density of air at sea level\"}, {\"NAME\": \"mu_air\", \"DIMENSION\": \"L-1 M1 T-1\", \"SUPPLY\": \"DECLARED\", \"VALUE\": \"1.7894e-5\", \"UNIT\": \"Pa s\", \"OVERRIDABLE\": \"NO\", \"LABEL\": \"the dynamic viscosity of air at sea level\"}, {\"NAME\": \"pi_c\", \"DIMENSION\": \"1\", \"SUPPLY\": \"DECLARED\", \"VALUE\": \"3.141592653589793\", \"UNIT\": \"1\", \"OVERRIDABLE\": \"NO\", \"LABEL\": \"pi, to 16 significant digits\"}, {\"NAME\": \"R_s\", \"DIMENSION\": \"L1\", \"SUPPLY\": \"AUTHOR\", \"LABEL\": \"the radius of the sphere\"}], \"SUMS\": [{\"NAME\": \"SPEED2\", \"OVER\": \"VELOCITY\", \"EACH\": \"VELOCITY^2\"}], \"TERMS\": [{\"TARGET\": \"VELOCITY\", \"SIGN\": \"-\", \"EXPR\": \"6*pi_c*mu_air*R_s*VELOCITY\", \"LABEL\": \"the linear (Stokes) drag\"}], \"ASSUMPTIONS\": [{\"NAME\": \"air_still\", \"PROPOSITION\": \"the air is at rest in the frame of the body's velocity\", \"REFS\": [\"VELOCITY\"]}, {\"NAME\": \"air_uniform\", \"PROPOSITION\": \"the air density is uniform over the region of motion\", \"REFS\": [\"rho_air\"]}, {\"NAME\": \"drag_sphere\", \"PROPOSITION\": \"the body is a rigid sphere of radius R_s\", \"REFS\": [\"R_s\"]}], \"BOUNDARIES\": [{\"NAME\": \"drag_linear_regime\", \"PREDICATE\": \"2 rho_air |v| R_s / mu_air < 1: the regime of the linear law\", \"CONDITION\": \"mu_air != 0 and SPEED2 >= 0 and 2*rho_air*sqrt(SPEED2)*R_s/mu_air < 1\"}], \"NOT_CHOSEN\": \"No linear (Stokes) air resistance.\", \"NOT_INCLUDED\": [\"No wind: the air is at rest.\", \"No change of air density or viscosity with altitude or temperature.\", \"No drag outside the regime of the linear law.\"], \"EXCLUDES\": [], \"INTERACTS_WITH\": [], \"TEST_BINDINGS\": [{\"NAME\": \"PROJECTILE_2D\", \"TPK\": {\"DOF\": [{\"NAME\": \"t\", \"DIMENSION\": \"T1\"}, {\"NAME\": \"x\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"z\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"v_x\", \"DIMENSION\": \"L1 T-1\"}, {\"NAME\": \"v_z\", \"DIMENSION\": \"L1 T-1\"}], \"CONSTANT\": [{\"NAME\": \"m\", \"DIMENSION\": \"M1\"}], \"LAW\": [{\"NAME\": \"KIN_X\", \"STATEMENT\": \"dx/dt = v_x\", \"REFS\": [\"t\", \"v_x\", \"x\"], \"ROLE\": \"EOM(x)\", \"EQUATION\": \"D(x,t)=v_x\"}, {\"NAME\": \"KIN_Z\", \"STATEMENT\": \"dz/dt = v_z\", \"REFS\": [\"t\", \"v_z\", \"z\"], \"ROLE\": \"EOM(z)\", \"EQUATION\": \"D(z,t)=v_z\"}, {\"NAME\": \"EOM_X\", \"STATEMENT\": \"m dv_x/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_x\"], \"ROLE\": \"EOM(v_x)\", \"EQUATION\": \"m*D(v_x,t)=0\"}, {\"NAME\": \"EOM_Z\", \"STATEMENT\": \"m dv_z/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_z\"], \"ROLE\": \"EOM(v_z)\", \"EQUATION\": \"m*D(v_z,t)=0\"}], \"ASSUMPTION\": [{\"NAME\": \"point_mass\", \"PROPOSITION\": \"the body is treated as a point mass\", \"REFS\": [\"m\"]}]}, \"BIND\": {\"VELOCITY\": [\"v_x\", \"v_z\"]}, \"VALUES\": {\"R_s\": {}}, \"ANSWERS\": {}}]}",
"{\"ID\": \"AIR-QUADRATIC\", \"VERSION\": \"1.0.0\", \"TITLE\": \"Air resistance at sea level, quadratic in the speed\", \"SOURCE\": \"ISO 2533:1975, Standard Atmosphere, sea-level values: density 1.225 kg m-3, dynamic viscosity 1.7894e-5 Pa s\", \"PREREQUISITES\": [{\"SLOT\": \"VELOCITY\", \"KIND\": \"DOF\", \"DIMENSION\": \"L1 T-1\", \"MIN\": 1, \"MAX\": 3, \"LABEL\": \"the velocity components of the body, one per axis\"}], \"PARAMETERS\": [{\"NAME\": \"rho_air\", \"DIMENSION\": \"L-3 M1\", \"SUPPLY\": \"DECLARED\", \"VALUE\": \"1.225\", \"UNIT\": \"kg m-3\", \"OVERRIDABLE\": \"NO\", \"LABEL\": \"the density of air at sea level\"}, {\"NAME\": \"mu_air\", \"DIMENSION\": \"L-1 M1 T-1\", \"SUPPLY\": \"DECLARED\", \"VALUE\": \"1.7894e-5\", \"UNIT\": \"Pa s\", \"OVERRIDABLE\": \"NO\", \"LABEL\": \"the dynamic viscosity of air at sea level\"}, {\"NAME\": \"C_d\", \"DIMENSION\": \"1\", \"SUPPLY\": \"AUTHOR\", \"LABEL\": \"the drag coefficient of the body\"}, {\"NAME\": \"A_ref\", \"DIMENSION\": \"L2\", \"SUPPLY\": \"AUTHOR\", \"LABEL\": \"the reference area of the drag coefficient\"}, {\"NAME\": \"L_ref\", \"DIMENSION\": \"L1\", \"SUPPLY\": \"AUTHOR\", \"LABEL\": \"the reference length of the Reynolds number\"}], \"SUMS\": [{\"NAME\": \"SPEED2\", \"OVER\": \"VELOCITY\", \"EACH\": \"VELOCITY^2\"}], \"TERMS\": [{\"TARGET\": \"VELOCITY\", \"SIGN\": \"-\", \"EXPR\": \"0.5*rho_air*C_d*A_ref*sqrt(SPEED2)*VELOCITY\", \"LABEL\": \"the quadratic drag\"}], \"ASSUMPTIONS\": [{\"NAME\": \"air_still\", \"PROPOSITION\": \"the air is at rest in the frame of the body's velocity\", \"REFS\": [\"VELOCITY\"]}, {\"NAME\": \"air_uniform\", \"PROPOSITION\": \"the air density is uniform over the region of motion\", \"REFS\": [\"rho_air\"]}, {\"NAME\": \"drag_cd_constant\", \"PROPOSITION\": \"the drag coefficient C_d is constant over the motion\", \"REFS\": [\"C_d\"]}, {\"NAME\": \"drag_no_lift\", \"PROPOSITION\": \"the body experiences no lift force\", \"REFS\": [\"VELOCITY\"]}, {\"NAME\": \"drag_no_magnus\", \"PROPOSITION\": \"the body experiences no Magnus force\", \"REFS\": [\"VELOCITY\"]}], \"BOUNDARIES\": [{\"NAME\": \"drag_quadratic_regime\", \"PREDICATE\": \"1e3 < rho_air |v| L_ref / mu_air < 2e5: the Reynolds window of the quadratic law\", \"CONDITION\": \"mu_air != 0 and SPEED2 >= 0 and rho_air*sqrt(SPEED2)*L_ref/mu_air > 1000 and rho_air*sqrt(SPEED2)*L_ref/mu_air < 200000\"}], \"NOT_CHOSEN\": \"No quadratic air resistance.\", \"NOT_INCLUDED\": [\"No wind: the air is at rest.\", \"No change of air density or viscosity with altitude or temperature.\", \"No lift, Magnus or added-mass force.\", \"No drag outside the Reynolds window of the quadratic law.\"], \"EXCLUDES\": [\"AIR-LINEAR\"], \"INTERACTS_WITH\": [], \"TEST_BINDINGS\": [{\"NAME\": \"PROJECTILE_2D\", \"TPK\": {\"DOF\": [{\"NAME\": \"t\", \"DIMENSION\": \"T1\"}, {\"NAME\": \"x\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"z\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"v_x\", \"DIMENSION\": \"L1 T-1\"}, {\"NAME\": \"v_z\", \"DIMENSION\": \"L1 T-1\"}], \"CONSTANT\": [{\"NAME\": \"m\", \"DIMENSION\": \"M1\"}], \"LAW\": [{\"NAME\": \"KIN_X\", \"STATEMENT\": \"dx/dt = v_x\", \"REFS\": [\"t\", \"v_x\", \"x\"], \"ROLE\": \"EOM(x)\", \"EQUATION\": \"D(x,t)=v_x\"}, {\"NAME\": \"KIN_Z\", \"STATEMENT\": \"dz/dt = v_z\", \"REFS\": [\"t\", \"v_z\", \"z\"], \"ROLE\": \"EOM(z)\", \"EQUATION\": \"D(z,t)=v_z\"}, {\"NAME\": \"EOM_X\", \"STATEMENT\": \"m dv_x/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_x\"], \"ROLE\": \"EOM(v_x)\", \"EQUATION\": \"m*D(v_x,t)=0\"}, {\"NAME\": \"EOM_Z\", \"STATEMENT\": \"m dv_z/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_z\"], \"ROLE\": \"EOM(v_z)\", \"EQUATION\": \"m*D(v_z,t)=0\"}], \"ASSUMPTION\": [{\"NAME\": \"point_mass\", \"PROPOSITION\": \"the body is treated as a point mass\", \"REFS\": [\"m\"]}]}, \"BIND\": {\"VELOCITY\": [\"v_x\", \"v_z\"]}, \"VALUES\": {\"A_ref\": {}, \"C_d\": {}, \"L_ref\": {}}, \"ANSWERS\": {}}]}",
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it acts in this kernel only where one of your own laws states it.\", \"NO_LINE\": \"No buoyancy: the air's upthrust on the body is not included.\"}], \"TEST_BINDINGS\": [{\"NAME\": \"PROJECTILE_2D\", \"TPK\": {\"DOF\": [{\"NAME\": \"t\", \"DIMENSION\": \"T1\"}, {\"NAME\": \"x\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"z\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"v_x\", \"DIMENSION\": \"L1 T-1\"}, {\"NAME\": \"v_z\", \"DIMENSION\": \"L1 T-1\"}], \"CONSTANT\": [{\"NAME\": \"m\", \"DIMENSION\": \"M1\"}], \"LAW\": [{\"NAME\": \"KIN_X\", \"STATEMENT\": \"dx/dt = v_x\", \"REFS\": [\"t\", \"v_x\", \"x\"], \"ROLE\": \"EOM(x)\", \"EQUATION\": \"D(x,t)=v_x\"}, {\"NAME\": \"KIN_Z\", \"STATEMENT\": \"dz/dt = v_z\", \"REFS\": [\"t\", \"v_z\", \"z\"], \"ROLE\": \"EOM(z)\", \"EQUATION\": \"D(z,t)=v_z\"}, {\"NAME\": \"EOM_X\", \"STATEMENT\": \"m dv_x/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_x\"], \"ROLE\": \"EOM(v_x)\", \"EQUATION\": \"m*D(v_x,t)=0\"}, {\"NAME\": \"EOM_Z\", \"STATEMENT\": \"m dv_z/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_z\"], \"ROLE\": \"EOM(v_z)\", \"EQUATION\": \"m*D(v_z,t)=0\"}], \"ASSUMPTION\": [{\"NAME\": \"point_mass\", \"PROPOSITION\": \"the body is treated as a point mass\", \"REFS\": [\"m\"]}]}, \"BIND\": {\"HEIGHT\": [\"z\"], \"MASS\": [\"m\"], \"UP_VELOCITY\": [\"v_z\"]}, \"VALUES\": {\"h_max\": {\"VALUE\": \"100\", \"UNIT\": \"m\"}}, \"ANSWERS\": {}}, {\"NAME\": \"TABLE\", \"TPK\": {\"DOF\": [{\"NAME\": \"t\", \"DIMENSION\": \"T1\"}, {\"NAME\": \"x\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"z\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"v_x\", \"DIMENSION\": \"L1 T-1\"}, {\"NAME\": \"v_z\", \"DIMENSION\": \"L1 T-1\"}], \"CONSTANT\": [{\"NAME\": \"m\", \"DIMENSION\": \"M1\"}], \"LAW\": [{\"NAME\": \"KIN_X\", \"STATEMENT\": \"dx/dt = v_x\", \"REFS\": [\"t\", \"v_x\", \"x\"], \"ROLE\": \"EOM(x)\", \"EQUATION\": \"D(x,t)=v_x\"}, {\"NAME\": \"KIN_Z\", \"STATEMENT\": \"dz/dt = v_z\", \"REFS\": [\"t\", \"v_z\", \"z\"], \"ROLE\": \"CONSTRAINT\", \"EQUATION\": \"D(z,t)=v_z\"}, {\"NAME\": \"EOM_X\", \"STATEMENT\": \"m dv_x/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_x\"], \"ROLE\": \"EOM(v_x)\", \"EQUATION\": \"m*D(v_x,t)=0\"}], \"CONSTRAINT\": [{\"NAME\": \"C_Z\", \"TARGET\": \"z\", \"ACTION\": \"FIX\", \"VALUE\": \"0\", \"UNIT\": \"m\", \"STATEMENT\": \"the puck stays on the table top, z = 0\"}, {\"NAME\": \"C_VZ\", \"TARGET\": \"v_z\", \"ACTION\": \"FIX\", \"VALUE\": \"0\", \"UNIT\": \"m s-1\", \"STATEMENT\": \"the puck has no vertical velocity\"}]}, \"BIND\": {\"HEIGHT\": [\"z\"], \"MASS\": [\"m\"], \"UP_VELOCITY\": [\"v_z\"]}, \"VALUES\": {\"h_max\": {\"VALUE\": \"1\", \"UNIT\": \"m\"}}, \"ANSWERS\": {\"FIXED:v_z\": \"YES\"}}]}",
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"name": "I48 MODIFIED naming one module twice"
},
{
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"answer": [
{
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{
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{
"ACT": "MODULE ADD",
"DATE": "2026-10-01",
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"modules": [
"{\"ID\": \"AIR-LINEAR\", \"VERSION\": \"1.0.0\", \"TITLE\": \"Air resistance at sea level, linear in the speed (Stokes drag on a sphere)\", \"SOURCE\": \"ISO 2533:1975, Standard Atmosphere, sea-level values: density 1.225 kg m-3, dynamic viscosity 1.7894e-5 Pa s\", \"PREREQUISITES\": [{\"SLOT\": \"VELOCITY\", \"KIND\": \"DOF\", \"DIMENSION\": \"L1 T-1\", \"MIN\": 1, \"MAX\": 3, \"LABEL\": \"the velocity components of the body, one per axis\"}], \"PARAMETERS\": [{\"NAME\": \"rho_air\", \"DIMENSION\": \"L-3 M1\", \"SUPPLY\": \"DECLARED\", \"VALUE\": \"1.225\", \"UNIT\": \"kg m-3\", \"OVERRIDABLE\": \"NO\", \"LABEL\": \"the density of air at sea level\"}, {\"NAME\": \"mu_air\", \"DIMENSION\": \"L-1 M1 T-1\", \"SUPPLY\": \"DECLARED\", \"VALUE\": \"1.7894e-5\", \"UNIT\": \"Pa s\", \"OVERRIDABLE\": \"NO\", \"LABEL\": \"the dynamic viscosity of air at sea level\"}, {\"NAME\": \"pi_c\", \"DIMENSION\": \"1\", \"SUPPLY\": \"DECLARED\", \"VALUE\": \"3.141592653589793\", \"UNIT\": \"1\", \"OVERRIDABLE\": \"NO\", \"LABEL\": \"pi, to 16 significant digits\"}, {\"NAME\": \"R_s\", \"DIMENSION\": \"L1\", \"SUPPLY\": \"AUTHOR\", \"LABEL\": \"the radius of the sphere\"}], \"SUMS\": [{\"NAME\": \"SPEED2\", \"OVER\": \"VELOCITY\", \"EACH\": \"VELOCITY^2\"}], \"TERMS\": [{\"TARGET\": \"VELOCITY\", \"SIGN\": \"-\", \"EXPR\": \"6*pi_c*mu_air*R_s*VELOCITY\", \"LABEL\": \"the linear (Stokes) drag\"}], \"ASSUMPTIONS\": [{\"NAME\": \"air_still\", \"PROPOSITION\": \"the air is at rest in the frame of the body's velocity\", \"REFS\": [\"VELOCITY\"]}, {\"NAME\": \"air_uniform\", \"PROPOSITION\": \"the air density is uniform over the region of motion\", \"REFS\": [\"rho_air\"]}, {\"NAME\": \"drag_sphere\", \"PROPOSITION\": \"the body is a rigid sphere of radius R_s\", \"REFS\": [\"R_s\"]}], \"BOUNDARIES\": [{\"NAME\": \"drag_linear_regime\", \"PREDICATE\": \"2 rho_air |v| R_s / mu_air < 1: the regime of the linear law\", \"CONDITION\": \"mu_air != 0 and SPEED2 >= 0 and 2*rho_air*sqrt(SPEED2)*R_s/mu_air < 1\"}], \"NOT_CHOSEN\": \"No linear (Stokes) air resistance.\", \"NOT_INCLUDED\": [\"No wind: the air is at rest.\", \"No change of air density or viscosity with altitude or temperature.\", \"No drag outside the regime of the linear law.\"], \"EXCLUDES\": [], \"INTERACTS_WITH\": [], \"TEST_BINDINGS\": [{\"NAME\": \"PROJECTILE_2D\", \"TPK\": {\"DOF\": [{\"NAME\": \"t\", \"DIMENSION\": \"T1\"}, {\"NAME\": \"x\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"z\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"v_x\", \"DIMENSION\": \"L1 T-1\"}, {\"NAME\": \"v_z\", \"DIMENSION\": \"L1 T-1\"}], \"CONSTANT\": [{\"NAME\": \"m\", \"DIMENSION\": \"M1\"}], \"LAW\": [{\"NAME\": \"KIN_X\", \"STATEMENT\": \"dx/dt = v_x\", \"REFS\": [\"t\", \"v_x\", \"x\"], \"ROLE\": \"EOM(x)\", \"EQUATION\": \"D(x,t)=v_x\"}, {\"NAME\": \"KIN_Z\", \"STATEMENT\": \"dz/dt = v_z\", \"REFS\": [\"t\", \"v_z\", \"z\"], \"ROLE\": \"EOM(z)\", \"EQUATION\": \"D(z,t)=v_z\"}, {\"NAME\": \"EOM_X\", \"STATEMENT\": \"m dv_x/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_x\"], \"ROLE\": \"EOM(v_x)\", \"EQUATION\": \"m*D(v_x,t)=0\"}, {\"NAME\": \"EOM_Z\", \"STATEMENT\": \"m dv_z/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_z\"], \"ROLE\": \"EOM(v_z)\", \"EQUATION\": \"m*D(v_z,t)=0\"}], \"ASSUMPTION\": [{\"NAME\": \"point_mass\", \"PROPOSITION\": \"the body is treated as a point mass\", \"REFS\": [\"m\"]}]}, \"BIND\": {\"VELOCITY\": [\"v_x\", \"v_z\"]}, \"VALUES\": {\"R_s\": {}}, \"ANSWERS\": {}}]}",
"{\"ID\": \"AIR-QUADRATIC\", \"VERSION\": \"1.0.0\", \"TITLE\": \"Air resistance at sea level, quadratic in the speed\", \"SOURCE\": \"ISO 2533:1975, Standard Atmosphere, sea-level values: density 1.225 kg m-3, dynamic viscosity 1.7894e-5 Pa s\", \"PREREQUISITES\": [{\"SLOT\": \"VELOCITY\", \"KIND\": \"DOF\", \"DIMENSION\": \"L1 T-1\", \"MIN\": 1, \"MAX\": 3, \"LABEL\": \"the velocity components of the body, one per axis\"}], \"PARAMETERS\": [{\"NAME\": \"rho_air\", \"DIMENSION\": \"L-3 M1\", \"SUPPLY\": \"DECLARED\", \"VALUE\": \"1.225\", \"UNIT\": \"kg m-3\", \"OVERRIDABLE\": \"NO\", \"LABEL\": \"the density of air at sea level\"}, {\"NAME\": \"mu_air\", \"DIMENSION\": \"L-1 M1 T-1\", \"SUPPLY\": \"DECLARED\", \"VALUE\": \"1.7894e-5\", \"UNIT\": \"Pa s\", \"OVERRIDABLE\": \"NO\", \"LABEL\": \"the dynamic viscosity of air at sea level\"}, {\"NAME\": \"C_d\", \"DIMENSION\": \"1\", \"SUPPLY\": \"AUTHOR\", \"LABEL\": \"the drag coefficient of the body\"}, {\"NAME\": \"A_ref\", \"DIMENSION\": \"L2\", \"SUPPLY\": \"AUTHOR\", \"LABEL\": \"the reference area of the drag coefficient\"}, {\"NAME\": \"L_ref\", \"DIMENSION\": \"L1\", \"SUPPLY\": \"AUTHOR\", \"LABEL\": \"the reference length of the Reynolds number\"}], \"SUMS\": [{\"NAME\": \"SPEED2\", \"OVER\": \"VELOCITY\", \"EACH\": \"VELOCITY^2\"}], \"TERMS\": [{\"TARGET\": \"VELOCITY\", \"SIGN\": \"-\", \"EXPR\": \"0.5*rho_air*C_d*A_ref*sqrt(SPEED2)*VELOCITY\", \"LABEL\": \"the quadratic drag\"}], \"ASSUMPTIONS\": [{\"NAME\": \"air_still\", \"PROPOSITION\": \"the air is at rest in the frame of the body's velocity\", \"REFS\": [\"VELOCITY\"]}, {\"NAME\": \"air_uniform\", \"PROPOSITION\": \"the air density is uniform over the region of motion\", \"REFS\": [\"rho_air\"]}, {\"NAME\": \"drag_cd_constant\", \"PROPOSITION\": \"the drag coefficient C_d is constant over the motion\", \"REFS\": [\"C_d\"]}, {\"NAME\": \"drag_no_lift\", \"PROPOSITION\": \"the body experiences no lift force\", \"REFS\": [\"VELOCITY\"]}, {\"NAME\": \"drag_no_magnus\", \"PROPOSITION\": \"the body experiences no Magnus force\", \"REFS\": [\"VELOCITY\"]}], \"BOUNDARIES\": [{\"NAME\": \"drag_quadratic_regime\", \"PREDICATE\": \"1e3 < rho_air |v| L_ref / mu_air < 2e5: the Reynolds window of the quadratic law\", \"CONDITION\": \"mu_air != 0 and SPEED2 >= 0 and rho_air*sqrt(SPEED2)*L_ref/mu_air > 1000 and rho_air*sqrt(SPEED2)*L_ref/mu_air < 200000\"}], \"NOT_CHOSEN\": \"No quadratic air resistance.\", \"NOT_INCLUDED\": [\"No wind: the air is at rest.\", \"No change of air density or viscosity with altitude or temperature.\", \"No lift, Magnus or added-mass force.\", \"No drag outside the Reynolds window of the quadratic law.\"], \"EXCLUDES\": [\"AIR-LINEAR\"], \"INTERACTS_WITH\": [], \"TEST_BINDINGS\": [{\"NAME\": \"PROJECTILE_2D\", \"TPK\": {\"DOF\": [{\"NAME\": \"t\", \"DIMENSION\": \"T1\"}, {\"NAME\": \"x\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"z\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"v_x\", \"DIMENSION\": \"L1 T-1\"}, {\"NAME\": \"v_z\", \"DIMENSION\": \"L1 T-1\"}], \"CONSTANT\": [{\"NAME\": \"m\", \"DIMENSION\": \"M1\"}], \"LAW\": [{\"NAME\": \"KIN_X\", \"STATEMENT\": \"dx/dt = v_x\", \"REFS\": [\"t\", \"v_x\", \"x\"], \"ROLE\": \"EOM(x)\", \"EQUATION\": \"D(x,t)=v_x\"}, {\"NAME\": \"KIN_Z\", \"STATEMENT\": \"dz/dt = v_z\", \"REFS\": [\"t\", \"v_z\", \"z\"], \"ROLE\": \"EOM(z)\", \"EQUATION\": \"D(z,t)=v_z\"}, {\"NAME\": \"EOM_X\", \"STATEMENT\": \"m dv_x/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_x\"], \"ROLE\": \"EOM(v_x)\", \"EQUATION\": \"m*D(v_x,t)=0\"}, {\"NAME\": \"EOM_Z\", \"STATEMENT\": \"m dv_z/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_z\"], \"ROLE\": \"EOM(v_z)\", \"EQUATION\": \"m*D(v_z,t)=0\"}], \"ASSUMPTION\": [{\"NAME\": \"point_mass\", \"PROPOSITION\": \"the body is treated as a point mass\", \"REFS\": [\"m\"]}]}, \"BIND\": {\"VELOCITY\": [\"v_x\", \"v_z\"]}, \"VALUES\": {\"A_ref\": {}, \"C_d\": {}, \"L_ref\": {}}, \"ANSWERS\": {}}]}",
"{\"ID\": \"GRAV-UNIFORM\", \"VERSION\": \"1.0.0\", \"TITLE\": \"Uniform gravity at the standard value g_n\", \"SOURCE\": \"g_n = 9.80665 m s-2, exact by definition: 3rd CGPM (1901), declaration on the unit of mass and on the definition of weight\", \"PREREQUISITES\": [{\"SLOT\": \"MASS\", \"KIND\": \"CONSTANT\", \"DIMENSION\": \"M1\", \"MIN\": 1, \"MAX\": 1, \"LABEL\": \"the mass of the body\"}, {\"SLOT\": \"UP_VELOCITY\", \"KIND\": \"DOF\", \"DIMENSION\": \"L1 T-1\", \"MIN\": 1, \"MAX\": 1, \"LABEL\": \"the velocity component pointing up; its equation of motion receives the weight\"}, {\"SLOT\": \"HEIGHT\", \"KIND\": \"DOF\", \"DIMENSION\": \"L1\", \"MIN\": 1, \"MAX\": 1, \"LABEL\": \"the position along the same upward axis\"}], \"PARAMETERS\": [{\"NAME\": \"g_n\", \"DIMENSION\": \"L1 T-2\", \"SUPPLY\": \"DECLARED\", \"VALUE\": \"9.80665\", \"UNIT\": \"m s-2\", \"OVERRIDABLE\": \"NO\", \"LABEL\": \"the standard acceleration of gravity\"}, {\"NAME\": \"h_max\", \"DIMENSION\": \"L1\", \"SUPPLY\": \"AUTHOR\", \"LABEL\": \"the largest height, above or below the origin, over which the field is taken as uniform\"}], \"SUMS\": [], \"TERMS\": [{\"TARGET\": \"UP_VELOCITY\", \"SIGN\": \"-\", \"EXPR\": \"MASS*g_n\", \"LABEL\": \"the weight\"}], \"ASSUMPTIONS\": [{\"NAME\": \"gravity_uniform\", \"PROPOSITION\": \"the gravitational field is uniform over the region abs({HEIGHT}) < h_max\", \"REFS\": [\"HEIGHT\", \"h_max\"]}, {\"NAME\": \"gravity_standard\", \"PROPOSITION\": \"the local gravitational acceleration equals the conventional standard value g_n\", \"REFS\": [\"g_n\"]}, {\"NAME\": \"frame_inertial\", \"PROPOSITION\": \"the frame in which {HEIGHT} is measured is treated as inertial\", \"REFS\": [\"HEIGHT\"]}], \"BOUNDARIES\": [{\"NAME\": \"gravity_region\", \"PREDICATE\": \"abs({HEIGHT}) < h_max\", \"CONDITION\": \"abs(HEIGHT) < h_max\"}], \"NOT_CHOSEN\": \"No gravity: no weight acts on any DOF.\", \"NOT_INCLUDED\": [\"No variation of gravity with height or latitude beyond what g_n contains.\", \"No Earth rotation (Coriolis or centrifugal force) beyond what g_n contains.\", \"No gravity of bodies other than the Earth.\"], \"EXCLUDES\": [], \"INTERACTS_WITH\": [{\"WITH\": \"AIR-*\", \"QUESTION_ID\": \"BUOYANCY\", \"QUESTION\": \"Does the air's buoyancy (upthrust) act on the body in the system you mean?\", \"YES_LINE\": \"Buoyancy acts (your answer): no module adds it; it acts in this kernel only where one of your own laws states it.\", \"NO_LINE\": \"No buoyancy: the air's upthrust on the body is not included.\"}], \"TEST_BINDINGS\": [{\"NAME\": \"PROJECTILE_2D\", \"TPK\": {\"DOF\": [{\"NAME\": \"t\", \"DIMENSION\": \"T1\"}, {\"NAME\": \"x\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"z\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"v_x\", \"DIMENSION\": \"L1 T-1\"}, {\"NAME\": \"v_z\", \"DIMENSION\": \"L1 T-1\"}], \"CONSTANT\": [{\"NAME\": \"m\", \"DIMENSION\": \"M1\"}], \"LAW\": [{\"NAME\": \"KIN_X\", \"STATEMENT\": \"dx/dt = v_x\", \"REFS\": [\"t\", \"v_x\", \"x\"], \"ROLE\": \"EOM(x)\", \"EQUATION\": \"D(x,t)=v_x\"}, {\"NAME\": \"KIN_Z\", \"STATEMENT\": \"dz/dt = v_z\", \"REFS\": [\"t\", \"v_z\", \"z\"], \"ROLE\": \"EOM(z)\", \"EQUATION\": \"D(z,t)=v_z\"}, {\"NAME\": \"EOM_X\", \"STATEMENT\": \"m dv_x/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_x\"], \"ROLE\": \"EOM(v_x)\", \"EQUATION\": \"m*D(v_x,t)=0\"}, {\"NAME\": \"EOM_Z\", \"STATEMENT\": \"m dv_z/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_z\"], \"ROLE\": \"EOM(v_z)\", \"EQUATION\": \"m*D(v_z,t)=0\"}], \"ASSUMPTION\": [{\"NAME\": \"point_mass\", \"PROPOSITION\": \"the body is treated as a point mass\", \"REFS\": [\"m\"]}]}, \"BIND\": {\"HEIGHT\": [\"z\"], \"MASS\": [\"m\"], \"UP_VELOCITY\": [\"v_z\"]}, \"VALUES\": {\"h_max\": {\"VALUE\": \"100\", \"UNIT\": \"m\"}}, \"ANSWERS\": {}}, {\"NAME\": \"TABLE\", \"TPK\": {\"DOF\": [{\"NAME\": \"t\", \"DIMENSION\": \"T1\"}, {\"NAME\": \"x\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"z\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"v_x\", \"DIMENSION\": \"L1 T-1\"}, {\"NAME\": \"v_z\", \"DIMENSION\": \"L1 T-1\"}], \"CONSTANT\": [{\"NAME\": \"m\", \"DIMENSION\": \"M1\"}], \"LAW\": [{\"NAME\": \"KIN_X\", \"STATEMENT\": \"dx/dt = v_x\", \"REFS\": [\"t\", \"v_x\", \"x\"], \"ROLE\": \"EOM(x)\", \"EQUATION\": \"D(x,t)=v_x\"}, {\"NAME\": \"KIN_Z\", \"STATEMENT\": \"dz/dt = v_z\", \"REFS\": [\"t\", \"v_z\", \"z\"], \"ROLE\": \"CONSTRAINT\", \"EQUATION\": \"D(z,t)=v_z\"}, {\"NAME\": \"EOM_X\", \"STATEMENT\": \"m dv_x/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_x\"], \"ROLE\": \"EOM(v_x)\", \"EQUATION\": \"m*D(v_x,t)=0\"}], \"CONSTRAINT\": [{\"NAME\": \"C_Z\", \"TARGET\": \"z\", \"ACTION\": \"FIX\", \"VALUE\": \"0\", \"UNIT\": \"m\", \"STATEMENT\": \"the puck stays on the table top, z = 0\"}, {\"NAME\": \"C_VZ\", \"TARGET\": \"v_z\", \"ACTION\": \"FIX\", \"VALUE\": \"0\", \"UNIT\": \"m s-1\", \"STATEMENT\": \"the puck has no vertical velocity\"}]}, \"BIND\": {\"HEIGHT\": [\"z\"], \"MASS\": [\"m\"], \"UP_VELOCITY\": [\"v_z\"]}, \"VALUES\": {\"h_max\": {\"VALUE\": \"1\", \"UNIT\": \"m\"}}, \"ANSWERS\": {\"FIXED:v_z\": \"YES\"}}]}",
"{\"ID\": \"MATH\", \"VERSION\": \"1.0.0\", \"TITLE\": \"The mathematical constant pi, as the CONSTANT pi_c\", \"SOURCE\": \"pi to 16 significant digits, 3.141592653589793, the nearest IEEE 754 binary64 value\", \"PREREQUISITES\": [], \"PARAMETERS\": [{\"NAME\": \"pi_c\", \"DIMENSION\": \"1\", \"SUPPLY\": \"DECLARED\", \"VALUE\": \"3.141592653589793\", \"UNIT\": \"1\", \"OVERRIDABLE\": \"NO\", \"LABEL\": \"pi, to 16 significant digits\"}], \"SUMS\": [], \"TERMS\": [], \"ASSUMPTIONS\": [], \"BOUNDARIES\": [], \"NOT_CHOSEN\": \"No mathematical constant: pi exists only if you declare it.\", \"NOT_INCLUDED\": [\"pi_c is pi rounded to 16 significant digits; no other mathematical constant is declared.\"], \"EXCLUDES\": [], \"INTERACTS_WITH\": [], \"TEST_BINDINGS\": [{\"NAME\": \"PROJECTILE_2D\", \"TPK\": {\"DOF\": [{\"NAME\": \"t\", \"DIMENSION\": \"T1\"}, {\"NAME\": \"x\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"z\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"v_x\", \"DIMENSION\": \"L1 T-1\"}, {\"NAME\": \"v_z\", \"DIMENSION\": \"L1 T-1\"}], \"CONSTANT\": [{\"NAME\": \"m\", \"DIMENSION\": \"M1\"}], \"LAW\": [{\"NAME\": \"KIN_X\", \"STATEMENT\": \"dx/dt = v_x\", \"REFS\": [\"t\", \"v_x\", \"x\"], \"ROLE\": \"EOM(x)\", \"EQUATION\": \"D(x,t)=v_x\"}, {\"NAME\": \"KIN_Z\", \"STATEMENT\": \"dz/dt = v_z\", \"REFS\": [\"t\", \"v_z\", \"z\"], \"ROLE\": \"EOM(z)\", \"EQUATION\": \"D(z,t)=v_z\"}, {\"NAME\": \"EOM_X\", \"STATEMENT\": \"m dv_x/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_x\"], \"ROLE\": \"EOM(v_x)\", \"EQUATION\": \"m*D(v_x,t)=0\"}, {\"NAME\": \"EOM_Z\", \"STATEMENT\": \"m dv_z/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_z\"], \"ROLE\": \"EOM(v_z)\", \"EQUATION\": \"m*D(v_z,t)=0\"}], \"ASSUMPTION\": [{\"NAME\": \"point_mass\", \"PROPOSITION\": \"the body is treated as a point mass\", \"REFS\": [\"m\"]}]}, \"BIND\": {}, \"VALUES\": {}, \"ANSWERS\": {}}]}",
"{\"ID\": \"GRAV-UNIFORM\", \"VERSION\": \"1.1.0\", \"TITLE\": \"Uniform gravity at the standard value g_n (text revised)\", \"SOURCE\": \"g_n = 9.80665 m s-2, exact by definition: 3rd CGPM (1901), declaration on the unit of mass and on the definition of weight\", \"PREREQUISITES\": [{\"SLOT\": \"MASS\", \"KIND\": \"CONSTANT\", \"DIMENSION\": \"M1\", \"MIN\": 1, \"MAX\": 1, \"LABEL\": \"the mass of the body\"}, {\"SLOT\": \"UP_VELOCITY\", \"KIND\": \"DOF\", \"DIMENSION\": \"L1 T-1\", \"MIN\": 1, \"MAX\": 1, \"LABEL\": \"the velocity component pointing up; its equation of motion receives the weight\"}, {\"SLOT\": \"HEIGHT\", \"KIND\": \"DOF\", \"DIMENSION\": \"L1\", \"MIN\": 1, \"MAX\": 1, \"LABEL\": \"the position along the same upward axis\"}], \"PARAMETERS\": [{\"NAME\": \"g_n\", \"DIMENSION\": \"L1 T-2\", \"SUPPLY\": \"DECLARED\", \"VALUE\": \"9.80665\", \"UNIT\": \"m s-2\", \"OVERRIDABLE\": \"NO\", \"LABEL\": \"the standard acceleration of gravity\"}, {\"NAME\": \"h_max\", \"DIMENSION\": \"L1\", \"SUPPLY\": \"AUTHOR\", \"LABEL\": \"the largest height, above or below the origin, over which the field is taken as uniform\"}], \"SUMS\": [], \"TERMS\": [{\"TARGET\": \"UP_VELOCITY\", \"SIGN\": \"-\", \"EXPR\": \"MASS*g_n\", \"LABEL\": \"the weight\"}], \"ASSUMPTIONS\": [{\"NAME\": \"gravity_uniform\", \"PROPOSITION\": \"the gravitational field is uniform over the region abs({HEIGHT}) < h_max\", \"REFS\": [\"HEIGHT\", \"h_max\"]}, {\"NAME\": \"gravity_standard\", \"PROPOSITION\": \"the local gravitational acceleration equals the conventional standard value g_n\", \"REFS\": [\"g_n\"]}, {\"NAME\": \"frame_inertial\", \"PROPOSITION\": \"the frame in which {HEIGHT} is measured is treated as inertial\", \"REFS\": [\"HEIGHT\"]}], \"BOUNDARIES\": [{\"NAME\": \"gravity_region\", \"PREDICATE\": \"abs({HEIGHT}) < h_max\", \"CONDITION\": \"abs(HEIGHT) < h_max\"}], \"NOT_CHOSEN\": \"No gravity: no weight acts on any DOF.\", \"NOT_INCLUDED\": [\"No variation of gravity with height or latitude beyond what g_n contains.\", \"No Earth rotation (Coriolis or centrifugal force) beyond what g_n contains.\", \"No gravity of bodies other than the Earth.\"], \"EXCLUDES\": [], \"INTERACTS_WITH\": [{\"WITH\": \"AIR-*\", \"QUESTION_ID\": \"BUOYANCY\", \"QUESTION\": \"Does the air's buoyancy (upthrust) act on the body in the system you mean?\", \"YES_LINE\": \"Buoyancy acts (your answer): no module adds it; it acts in this kernel only where one of your own laws states it.\", \"NO_LINE\": \"No buoyancy: the air's upthrust on the body is not included.\"}], \"TEST_BINDINGS\": [{\"NAME\": \"PROJECTILE_2D\", \"TPK\": {\"DOF\": [{\"NAME\": \"t\", \"DIMENSION\": \"T1\"}, {\"NAME\": \"x\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"z\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"v_x\", \"DIMENSION\": \"L1 T-1\"}, {\"NAME\": \"v_z\", \"DIMENSION\": \"L1 T-1\"}], \"CONSTANT\": [{\"NAME\": \"m\", \"DIMENSION\": \"M1\"}], \"LAW\": [{\"NAME\": \"KIN_X\", \"STATEMENT\": \"dx/dt = v_x\", \"REFS\": [\"t\", \"v_x\", \"x\"], \"ROLE\": \"EOM(x)\", \"EQUATION\": \"D(x,t)=v_x\"}, {\"NAME\": \"KIN_Z\", \"STATEMENT\": \"dz/dt = v_z\", \"REFS\": [\"t\", \"v_z\", \"z\"], \"ROLE\": \"EOM(z)\", \"EQUATION\": \"D(z,t)=v_z\"}, {\"NAME\": \"EOM_X\", \"STATEMENT\": \"m dv_x/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_x\"], \"ROLE\": \"EOM(v_x)\", \"EQUATION\": \"m*D(v_x,t)=0\"}, {\"NAME\": \"EOM_Z\", \"STATEMENT\": \"m dv_z/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_z\"], \"ROLE\": \"EOM(v_z)\", \"EQUATION\": \"m*D(v_z,t)=0\"}], \"ASSUMPTION\": [{\"NAME\": \"point_mass\", \"PROPOSITION\": \"the body is treated as a point mass\", \"REFS\": [\"m\"]}]}, \"BIND\": {\"HEIGHT\": [\"z\"], \"MASS\": [\"m\"], \"UP_VELOCITY\": [\"v_z\"]}, \"VALUES\": {\"h_max\": {\"VALUE\": \"100\", \"UNIT\": \"m\"}}, \"ANSWERS\": {}}, {\"NAME\": \"TABLE\", \"TPK\": {\"DOF\": [{\"NAME\": \"t\", \"DIMENSION\": \"T1\"}, {\"NAME\": \"x\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"z\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"v_x\", \"DIMENSION\": \"L1 T-1\"}, {\"NAME\": \"v_z\", \"DIMENSION\": \"L1 T-1\"}], \"CONSTANT\": [{\"NAME\": \"m\", \"DIMENSION\": \"M1\"}], \"LAW\": [{\"NAME\": \"KIN_X\", \"STATEMENT\": \"dx/dt = v_x\", \"REFS\": [\"t\", \"v_x\", \"x\"], \"ROLE\": \"EOM(x)\", \"EQUATION\": \"D(x,t)=v_x\"}, {\"NAME\": \"KIN_Z\", \"STATEMENT\": \"dz/dt = v_z\", \"REFS\": [\"t\", \"v_z\", \"z\"], \"ROLE\": \"CONSTRAINT\", \"EQUATION\": \"D(z,t)=v_z\"}, {\"NAME\": \"EOM_X\", \"STATEMENT\": \"m dv_x/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_x\"], \"ROLE\": \"EOM(v_x)\", \"EQUATION\": \"m*D(v_x,t)=0\"}], \"CONSTRAINT\": [{\"NAME\": \"C_Z\", \"TARGET\": \"z\", \"ACTION\": \"FIX\", \"VALUE\": \"0\", \"UNIT\": \"m\", \"STATEMENT\": \"the puck stays on the table top, z = 0\"}, {\"NAME\": \"C_VZ\", \"TARGET\": \"v_z\", \"ACTION\": \"FIX\", \"VALUE\": \"0\", \"UNIT\": \"m s-1\", \"STATEMENT\": \"the puck has no vertical velocity\"}]}, \"BIND\": {\"HEIGHT\": [\"z\"], \"MASS\": [\"m\"], \"UP_VELOCITY\": [\"v_z\"]}, \"VALUES\": {\"h_max\": {\"VALUE\": \"1\", \"UNIT\": \"m\"}}, \"ANSWERS\": {\"FIXED:v_z\": \"YES\"}}]}"
]
},
"expected": "[\"REFUSED\",\"ANSWER ROUND 2: field RESELECT has the wrong type\"]",
"fn": "interview_check",
"hand_checked": true,
"name": "I49 RESELECT of the wrong type"
},
{
"args": {
"answer": [
{
"AT": 4,
"CHOSEN": "NONE",
"COVERED": [
[
"AIR-LINEAR",
"1.0.0",
"5f3fe27b42378bce0830b0d0959f892f4a8e73b12b540ae877e39e6439d08b4d"
],
[
"AIR-QUADRATIC",
"1.0.0",
"6fb53c3a6546151eead2bd6e72e9cf8334f3a2040ad0ee2f5b988ec96d6fc852"
],
[
"GRAV-UNIFORM",
"1.0.0",
"24877ccb5c8ec300d29ed82ce6650592f35cf8899a3d878ccce9c08d4c72c025"
],
[
"MATH",
"1.0.0",
"8f39a356f35527b901fcee012764590f0819c8ffdeccad4bc05195ce3d2e0bcf"
]
]
},
{
"AT": 5,
"CHOSEN": "NONE",
"COVERED": [
[
"AIR-LINEAR",
"1.0.0",
"5f3fe27b42378bce0830b0d0959f892f4a8e73b12b540ae877e39e6439d08b4d"
],
[
"AIR-QUADRATIC",
"1.0.0",
"6fb53c3a6546151eead2bd6e72e9cf8334f3a2040ad0ee2f5b988ec96d6fc852"
],
[
"GRAV-UNIFORM",
"1.1.0",
"5be3923c28dc8f8ff910b033c2d17154f267f2a20fdb32c74a07293a37dfe338"
],
[
"MATH",
"1.0.0",
"8f39a356f35527b901fcee012764590f0819c8ffdeccad4bc05195ce3d2e0bcf"
]
],
"RESELECT": [
"MATH",
"GRAV-UNIFORM"
]
}
],
"carried": [],
"claims": [],
"lines": [
{
"ACT": "MODULE ADD",
"DATE": "2026-10-01",
"DIGEST": "5f3fe27b42378bce0830b0d0959f892f4a8e73b12b540ae877e39e6439d08b4d",
"ID": "AIR-LINEAR",
"VERSION": "1.0.0"
},
{
"ACT": "MODULE ADD",
"DATE": "2026-10-01",
"DIGEST": "6fb53c3a6546151eead2bd6e72e9cf8334f3a2040ad0ee2f5b988ec96d6fc852",
"ID": "AIR-QUADRATIC",
"VERSION": "1.0.0"
},
{
"ACT": "MODULE ADD",
"DATE": "2026-10-01",
"DIGEST": "24877ccb5c8ec300d29ed82ce6650592f35cf8899a3d878ccce9c08d4c72c025",
"ID": "GRAV-UNIFORM",
"VERSION": "1.0.0"
},
{
"ACT": "MODULE ADD",
"DATE": "2026-10-01",
"DIGEST": "8f39a356f35527b901fcee012764590f0819c8ffdeccad4bc05195ce3d2e0bcf",
"ID": "MATH",
"VERSION": "1.0.0"
},
{
"ACT": "MODULE VERSION",
"DATE": "2026-10-02",
"DIGEST": "5be3923c28dc8f8ff910b033c2d17154f267f2a20fdb32c74a07293a37dfe338",
"ID": "GRAV-UNIFORM",
"VERSION": "1.1.0"
}
],
"modified": [],
"modules": [
"{\"ID\": \"AIR-LINEAR\", \"VERSION\": \"1.0.0\", \"TITLE\": \"Air resistance at sea level, linear in the speed (Stokes drag on a sphere)\", \"SOURCE\": \"ISO 2533:1975, Standard Atmosphere, sea-level values: density 1.225 kg m-3, dynamic viscosity 1.7894e-5 Pa s\", \"PREREQUISITES\": [{\"SLOT\": \"VELOCITY\", \"KIND\": \"DOF\", \"DIMENSION\": \"L1 T-1\", \"MIN\": 1, \"MAX\": 3, \"LABEL\": \"the velocity components of the body, one per axis\"}], \"PARAMETERS\": [{\"NAME\": \"rho_air\", \"DIMENSION\": \"L-3 M1\", \"SUPPLY\": \"DECLARED\", \"VALUE\": \"1.225\", \"UNIT\": \"kg m-3\", \"OVERRIDABLE\": \"NO\", \"LABEL\": \"the density of air at sea level\"}, {\"NAME\": \"mu_air\", \"DIMENSION\": \"L-1 M1 T-1\", \"SUPPLY\": \"DECLARED\", \"VALUE\": \"1.7894e-5\", \"UNIT\": \"Pa s\", \"OVERRIDABLE\": \"NO\", \"LABEL\": \"the dynamic viscosity of air at sea level\"}, {\"NAME\": \"pi_c\", \"DIMENSION\": \"1\", \"SUPPLY\": \"DECLARED\", \"VALUE\": \"3.141592653589793\", \"UNIT\": \"1\", \"OVERRIDABLE\": \"NO\", \"LABEL\": \"pi, to 16 significant digits\"}, {\"NAME\": \"R_s\", \"DIMENSION\": \"L1\", \"SUPPLY\": \"AUTHOR\", \"LABEL\": \"the radius of the sphere\"}], \"SUMS\": [{\"NAME\": \"SPEED2\", \"OVER\": \"VELOCITY\", \"EACH\": \"VELOCITY^2\"}], \"TERMS\": [{\"TARGET\": \"VELOCITY\", \"SIGN\": \"-\", \"EXPR\": \"6*pi_c*mu_air*R_s*VELOCITY\", \"LABEL\": \"the linear (Stokes) drag\"}], \"ASSUMPTIONS\": [{\"NAME\": \"air_still\", \"PROPOSITION\": \"the air is at rest in the frame of the body's velocity\", \"REFS\": [\"VELOCITY\"]}, {\"NAME\": \"air_uniform\", \"PROPOSITION\": \"the air density is uniform over the region of motion\", \"REFS\": [\"rho_air\"]}, {\"NAME\": \"drag_sphere\", \"PROPOSITION\": \"the body is a rigid sphere of radius R_s\", \"REFS\": [\"R_s\"]}], \"BOUNDARIES\": [{\"NAME\": \"drag_linear_regime\", \"PREDICATE\": \"2 rho_air |v| R_s / mu_air < 1: the regime of the linear law\", \"CONDITION\": \"mu_air != 0 and SPEED2 >= 0 and 2*rho_air*sqrt(SPEED2)*R_s/mu_air < 1\"}], \"NOT_CHOSEN\": \"No linear (Stokes) air resistance.\", \"NOT_INCLUDED\": [\"No wind: the air is at rest.\", \"No change of air density or viscosity with altitude or temperature.\", \"No drag outside the regime of the linear law.\"], \"EXCLUDES\": [], \"INTERACTS_WITH\": [], \"TEST_BINDINGS\": [{\"NAME\": \"PROJECTILE_2D\", \"TPK\": {\"DOF\": [{\"NAME\": \"t\", \"DIMENSION\": \"T1\"}, {\"NAME\": \"x\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"z\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"v_x\", \"DIMENSION\": \"L1 T-1\"}, {\"NAME\": \"v_z\", \"DIMENSION\": \"L1 T-1\"}], \"CONSTANT\": [{\"NAME\": \"m\", \"DIMENSION\": \"M1\"}], \"LAW\": [{\"NAME\": \"KIN_X\", \"STATEMENT\": \"dx/dt = v_x\", \"REFS\": [\"t\", \"v_x\", \"x\"], \"ROLE\": \"EOM(x)\", \"EQUATION\": \"D(x,t)=v_x\"}, {\"NAME\": \"KIN_Z\", \"STATEMENT\": \"dz/dt = v_z\", \"REFS\": [\"t\", \"v_z\", \"z\"], \"ROLE\": \"EOM(z)\", \"EQUATION\": \"D(z,t)=v_z\"}, {\"NAME\": \"EOM_X\", \"STATEMENT\": \"m dv_x/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_x\"], \"ROLE\": \"EOM(v_x)\", \"EQUATION\": \"m*D(v_x,t)=0\"}, {\"NAME\": \"EOM_Z\", \"STATEMENT\": \"m dv_z/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_z\"], \"ROLE\": \"EOM(v_z)\", \"EQUATION\": \"m*D(v_z,t)=0\"}], \"ASSUMPTION\": [{\"NAME\": \"point_mass\", \"PROPOSITION\": \"the body is treated as a point mass\", \"REFS\": [\"m\"]}]}, \"BIND\": {\"VELOCITY\": [\"v_x\", \"v_z\"]}, \"VALUES\": {\"R_s\": {}}, \"ANSWERS\": {}}]}",
"{\"ID\": \"AIR-QUADRATIC\", \"VERSION\": \"1.0.0\", \"TITLE\": \"Air resistance at sea level, quadratic in the speed\", \"SOURCE\": \"ISO 2533:1975, Standard Atmosphere, sea-level values: density 1.225 kg m-3, dynamic viscosity 1.7894e-5 Pa s\", \"PREREQUISITES\": [{\"SLOT\": \"VELOCITY\", \"KIND\": \"DOF\", \"DIMENSION\": \"L1 T-1\", \"MIN\": 1, \"MAX\": 3, \"LABEL\": \"the velocity components of the body, one per axis\"}], \"PARAMETERS\": [{\"NAME\": \"rho_air\", \"DIMENSION\": \"L-3 M1\", \"SUPPLY\": \"DECLARED\", \"VALUE\": \"1.225\", \"UNIT\": \"kg m-3\", \"OVERRIDABLE\": \"NO\", \"LABEL\": \"the density of air at sea level\"}, {\"NAME\": \"mu_air\", \"DIMENSION\": \"L-1 M1 T-1\", \"SUPPLY\": \"DECLARED\", \"VALUE\": \"1.7894e-5\", \"UNIT\": \"Pa s\", \"OVERRIDABLE\": \"NO\", \"LABEL\": \"the dynamic viscosity of air at sea level\"}, {\"NAME\": \"C_d\", \"DIMENSION\": \"1\", \"SUPPLY\": \"AUTHOR\", \"LABEL\": \"the drag coefficient of the body\"}, {\"NAME\": \"A_ref\", \"DIMENSION\": \"L2\", \"SUPPLY\": \"AUTHOR\", \"LABEL\": \"the reference area of the drag coefficient\"}, {\"NAME\": \"L_ref\", \"DIMENSION\": \"L1\", \"SUPPLY\": \"AUTHOR\", \"LABEL\": \"the reference length of the Reynolds number\"}], \"SUMS\": [{\"NAME\": \"SPEED2\", \"OVER\": \"VELOCITY\", \"EACH\": \"VELOCITY^2\"}], \"TERMS\": [{\"TARGET\": \"VELOCITY\", \"SIGN\": \"-\", \"EXPR\": \"0.5*rho_air*C_d*A_ref*sqrt(SPEED2)*VELOCITY\", \"LABEL\": \"the quadratic drag\"}], \"ASSUMPTIONS\": [{\"NAME\": \"air_still\", \"PROPOSITION\": \"the air is at rest in the frame of the body's velocity\", \"REFS\": [\"VELOCITY\"]}, {\"NAME\": \"air_uniform\", \"PROPOSITION\": \"the air density is uniform over the region of motion\", \"REFS\": [\"rho_air\"]}, {\"NAME\": \"drag_cd_constant\", \"PROPOSITION\": \"the drag coefficient C_d is constant over the motion\", \"REFS\": [\"C_d\"]}, {\"NAME\": \"drag_no_lift\", \"PROPOSITION\": \"the body experiences no lift force\", \"REFS\": [\"VELOCITY\"]}, {\"NAME\": \"drag_no_magnus\", \"PROPOSITION\": \"the body experiences no Magnus force\", \"REFS\": [\"VELOCITY\"]}], \"BOUNDARIES\": [{\"NAME\": \"drag_quadratic_regime\", \"PREDICATE\": \"1e3 < rho_air |v| L_ref / mu_air < 2e5: the Reynolds window of the quadratic law\", \"CONDITION\": \"mu_air != 0 and SPEED2 >= 0 and rho_air*sqrt(SPEED2)*L_ref/mu_air > 1000 and rho_air*sqrt(SPEED2)*L_ref/mu_air < 200000\"}], \"NOT_CHOSEN\": \"No quadratic air resistance.\", \"NOT_INCLUDED\": [\"No wind: the air is at rest.\", \"No change of air density or viscosity with altitude or temperature.\", \"No lift, Magnus or added-mass force.\", \"No drag outside the Reynolds window of the quadratic law.\"], \"EXCLUDES\": [\"AIR-LINEAR\"], \"INTERACTS_WITH\": [], \"TEST_BINDINGS\": [{\"NAME\": \"PROJECTILE_2D\", \"TPK\": {\"DOF\": [{\"NAME\": \"t\", \"DIMENSION\": \"T1\"}, {\"NAME\": \"x\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"z\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"v_x\", \"DIMENSION\": \"L1 T-1\"}, {\"NAME\": \"v_z\", \"DIMENSION\": \"L1 T-1\"}], \"CONSTANT\": [{\"NAME\": \"m\", \"DIMENSION\": \"M1\"}], \"LAW\": [{\"NAME\": \"KIN_X\", \"STATEMENT\": \"dx/dt = v_x\", \"REFS\": [\"t\", \"v_x\", \"x\"], \"ROLE\": \"EOM(x)\", \"EQUATION\": \"D(x,t)=v_x\"}, {\"NAME\": \"KIN_Z\", \"STATEMENT\": \"dz/dt = v_z\", \"REFS\": [\"t\", \"v_z\", \"z\"], \"ROLE\": \"EOM(z)\", \"EQUATION\": \"D(z,t)=v_z\"}, {\"NAME\": \"EOM_X\", \"STATEMENT\": \"m dv_x/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_x\"], \"ROLE\": \"EOM(v_x)\", \"EQUATION\": \"m*D(v_x,t)=0\"}, {\"NAME\": \"EOM_Z\", \"STATEMENT\": \"m dv_z/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_z\"], \"ROLE\": \"EOM(v_z)\", \"EQUATION\": \"m*D(v_z,t)=0\"}], \"ASSUMPTION\": [{\"NAME\": \"point_mass\", \"PROPOSITION\": \"the body is treated as a point mass\", \"REFS\": [\"m\"]}]}, \"BIND\": {\"VELOCITY\": [\"v_x\", \"v_z\"]}, \"VALUES\": {\"A_ref\": {}, \"C_d\": {}, \"L_ref\": {}}, \"ANSWERS\": {}}]}",
"{\"ID\": \"GRAV-UNIFORM\", \"VERSION\": \"1.0.0\", \"TITLE\": \"Uniform gravity at the standard value g_n\", \"SOURCE\": \"g_n = 9.80665 m s-2, exact by definition: 3rd CGPM (1901), declaration on the unit of mass and on the definition of weight\", \"PREREQUISITES\": [{\"SLOT\": \"MASS\", \"KIND\": \"CONSTANT\", \"DIMENSION\": \"M1\", \"MIN\": 1, \"MAX\": 1, \"LABEL\": \"the mass of the body\"}, {\"SLOT\": \"UP_VELOCITY\", \"KIND\": \"DOF\", \"DIMENSION\": \"L1 T-1\", \"MIN\": 1, \"MAX\": 1, \"LABEL\": \"the velocity component pointing up; its equation of motion receives the weight\"}, {\"SLOT\": \"HEIGHT\", \"KIND\": \"DOF\", \"DIMENSION\": \"L1\", \"MIN\": 1, \"MAX\": 1, \"LABEL\": \"the position along the same upward axis\"}], \"PARAMETERS\": [{\"NAME\": \"g_n\", \"DIMENSION\": \"L1 T-2\", \"SUPPLY\": \"DECLARED\", \"VALUE\": \"9.80665\", \"UNIT\": \"m s-2\", \"OVERRIDABLE\": \"NO\", \"LABEL\": \"the standard acceleration of gravity\"}, {\"NAME\": \"h_max\", \"DIMENSION\": \"L1\", \"SUPPLY\": \"AUTHOR\", \"LABEL\": \"the largest height, above or below the origin, over which the field is taken as uniform\"}], \"SUMS\": [], \"TERMS\": [{\"TARGET\": \"UP_VELOCITY\", \"SIGN\": \"-\", \"EXPR\": \"MASS*g_n\", \"LABEL\": \"the weight\"}], \"ASSUMPTIONS\": [{\"NAME\": \"gravity_uniform\", \"PROPOSITION\": \"the gravitational field is uniform over the region abs({HEIGHT}) < h_max\", \"REFS\": [\"HEIGHT\", \"h_max\"]}, {\"NAME\": \"gravity_standard\", \"PROPOSITION\": \"the local gravitational acceleration equals the conventional standard value g_n\", \"REFS\": [\"g_n\"]}, {\"NAME\": \"frame_inertial\", \"PROPOSITION\": \"the frame in which {HEIGHT} is measured is treated as inertial\", \"REFS\": [\"HEIGHT\"]}], \"BOUNDARIES\": [{\"NAME\": \"gravity_region\", \"PREDICATE\": \"abs({HEIGHT}) < h_max\", \"CONDITION\": \"abs(HEIGHT) < h_max\"}], \"NOT_CHOSEN\": \"No gravity: no weight acts on any DOF.\", \"NOT_INCLUDED\": [\"No variation of gravity with height or latitude beyond what g_n contains.\", \"No Earth rotation (Coriolis or centrifugal force) beyond what g_n contains.\", \"No gravity of bodies other than the Earth.\"], \"EXCLUDES\": [], \"INTERACTS_WITH\": [{\"WITH\": \"AIR-*\", \"QUESTION_ID\": \"BUOYANCY\", \"QUESTION\": \"Does the air's buoyancy (upthrust) act on the body in the system you mean?\", \"YES_LINE\": \"Buoyancy acts (your answer): no module adds it; it acts in this kernel only where one of your own laws states it.\", \"NO_LINE\": \"No buoyancy: the air's upthrust on the body is not included.\"}], \"TEST_BINDINGS\": [{\"NAME\": \"PROJECTILE_2D\", \"TPK\": {\"DOF\": [{\"NAME\": \"t\", \"DIMENSION\": \"T1\"}, {\"NAME\": \"x\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"z\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"v_x\", \"DIMENSION\": \"L1 T-1\"}, {\"NAME\": \"v_z\", \"DIMENSION\": \"L1 T-1\"}], \"CONSTANT\": [{\"NAME\": \"m\", \"DIMENSION\": \"M1\"}], \"LAW\": [{\"NAME\": \"KIN_X\", \"STATEMENT\": \"dx/dt = v_x\", \"REFS\": [\"t\", \"v_x\", \"x\"], \"ROLE\": \"EOM(x)\", \"EQUATION\": \"D(x,t)=v_x\"}, {\"NAME\": \"KIN_Z\", \"STATEMENT\": \"dz/dt = v_z\", \"REFS\": [\"t\", \"v_z\", \"z\"], \"ROLE\": \"EOM(z)\", \"EQUATION\": \"D(z,t)=v_z\"}, {\"NAME\": \"EOM_X\", \"STATEMENT\": \"m dv_x/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_x\"], \"ROLE\": \"EOM(v_x)\", \"EQUATION\": \"m*D(v_x,t)=0\"}, {\"NAME\": \"EOM_Z\", \"STATEMENT\": \"m dv_z/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_z\"], \"ROLE\": \"EOM(v_z)\", \"EQUATION\": \"m*D(v_z,t)=0\"}], \"ASSUMPTION\": [{\"NAME\": \"point_mass\", \"PROPOSITION\": \"the body is treated as a point mass\", \"REFS\": [\"m\"]}]}, \"BIND\": {\"HEIGHT\": [\"z\"], \"MASS\": [\"m\"], \"UP_VELOCITY\": [\"v_z\"]}, \"VALUES\": {\"h_max\": {\"VALUE\": \"100\", \"UNIT\": \"m\"}}, \"ANSWERS\": {}}, {\"NAME\": \"TABLE\", \"TPK\": {\"DOF\": [{\"NAME\": \"t\", \"DIMENSION\": \"T1\"}, {\"NAME\": \"x\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"z\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"v_x\", \"DIMENSION\": \"L1 T-1\"}, {\"NAME\": \"v_z\", \"DIMENSION\": \"L1 T-1\"}], \"CONSTANT\": [{\"NAME\": \"m\", \"DIMENSION\": \"M1\"}], \"LAW\": [{\"NAME\": \"KIN_X\", \"STATEMENT\": \"dx/dt = v_x\", \"REFS\": [\"t\", \"v_x\", \"x\"], \"ROLE\": \"EOM(x)\", \"EQUATION\": \"D(x,t)=v_x\"}, {\"NAME\": \"KIN_Z\", \"STATEMENT\": \"dz/dt = v_z\", \"REFS\": [\"t\", \"v_z\", \"z\"], \"ROLE\": \"CONSTRAINT\", \"EQUATION\": \"D(z,t)=v_z\"}, {\"NAME\": \"EOM_X\", \"STATEMENT\": \"m dv_x/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_x\"], \"ROLE\": \"EOM(v_x)\", \"EQUATION\": \"m*D(v_x,t)=0\"}], \"CONSTRAINT\": [{\"NAME\": \"C_Z\", \"TARGET\": \"z\", \"ACTION\": \"FIX\", \"VALUE\": \"0\", \"UNIT\": \"m\", \"STATEMENT\": \"the puck stays on the table top, z = 0\"}, {\"NAME\": \"C_VZ\", \"TARGET\": \"v_z\", \"ACTION\": \"FIX\", \"VALUE\": \"0\", \"UNIT\": \"m s-1\", \"STATEMENT\": \"the puck has no vertical velocity\"}]}, \"BIND\": {\"HEIGHT\": [\"z\"], \"MASS\": [\"m\"], \"UP_VELOCITY\": [\"v_z\"]}, \"VALUES\": {\"h_max\": {\"VALUE\": \"1\", \"UNIT\": \"m\"}}, \"ANSWERS\": {\"FIXED:v_z\": \"YES\"}}]}",
"{\"ID\": \"MATH\", \"VERSION\": \"1.0.0\", \"TITLE\": \"The mathematical constant pi, as the CONSTANT pi_c\", \"SOURCE\": \"pi to 16 significant digits, 3.141592653589793, the nearest IEEE 754 binary64 value\", \"PREREQUISITES\": [], \"PARAMETERS\": [{\"NAME\": \"pi_c\", \"DIMENSION\": \"1\", \"SUPPLY\": \"DECLARED\", \"VALUE\": \"3.141592653589793\", \"UNIT\": \"1\", \"OVERRIDABLE\": \"NO\", \"LABEL\": \"pi, to 16 significant digits\"}], \"SUMS\": [], \"TERMS\": [], \"ASSUMPTIONS\": [], \"BOUNDARIES\": [], \"NOT_CHOSEN\": \"No mathematical constant: pi exists only if you declare it.\", \"NOT_INCLUDED\": [\"pi_c is pi rounded to 16 significant digits; no other mathematical constant is declared.\"], \"EXCLUDES\": [], \"INTERACTS_WITH\": [], \"TEST_BINDINGS\": [{\"NAME\": \"PROJECTILE_2D\", \"TPK\": {\"DOF\": [{\"NAME\": \"t\", \"DIMENSION\": \"T1\"}, {\"NAME\": \"x\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"z\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"v_x\", \"DIMENSION\": \"L1 T-1\"}, {\"NAME\": \"v_z\", \"DIMENSION\": \"L1 T-1\"}], \"CONSTANT\": [{\"NAME\": \"m\", \"DIMENSION\": \"M1\"}], \"LAW\": [{\"NAME\": \"KIN_X\", \"STATEMENT\": \"dx/dt = v_x\", \"REFS\": [\"t\", \"v_x\", \"x\"], \"ROLE\": \"EOM(x)\", \"EQUATION\": \"D(x,t)=v_x\"}, {\"NAME\": \"KIN_Z\", \"STATEMENT\": \"dz/dt = v_z\", \"REFS\": [\"t\", \"v_z\", \"z\"], \"ROLE\": \"EOM(z)\", \"EQUATION\": \"D(z,t)=v_z\"}, {\"NAME\": \"EOM_X\", \"STATEMENT\": \"m dv_x/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_x\"], \"ROLE\": \"EOM(v_x)\", \"EQUATION\": \"m*D(v_x,t)=0\"}, {\"NAME\": \"EOM_Z\", \"STATEMENT\": \"m dv_z/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_z\"], \"ROLE\": \"EOM(v_z)\", \"EQUATION\": \"m*D(v_z,t)=0\"}], \"ASSUMPTION\": [{\"NAME\": \"point_mass\", \"PROPOSITION\": \"the body is treated as a point mass\", \"REFS\": [\"m\"]}]}, \"BIND\": {}, \"VALUES\": {}, \"ANSWERS\": {}}]}",
"{\"ID\": \"GRAV-UNIFORM\", \"VERSION\": \"1.1.0\", \"TITLE\": \"Uniform gravity at the standard value g_n (text revised)\", \"SOURCE\": \"g_n = 9.80665 m s-2, exact by definition: 3rd CGPM (1901), declaration on the unit of mass and on the definition of weight\", \"PREREQUISITES\": [{\"SLOT\": \"MASS\", \"KIND\": \"CONSTANT\", \"DIMENSION\": \"M1\", \"MIN\": 1, \"MAX\": 1, \"LABEL\": \"the mass of the body\"}, {\"SLOT\": \"UP_VELOCITY\", \"KIND\": \"DOF\", \"DIMENSION\": \"L1 T-1\", \"MIN\": 1, \"MAX\": 1, \"LABEL\": \"the velocity component pointing up; its equation of motion receives the weight\"}, {\"SLOT\": \"HEIGHT\", \"KIND\": \"DOF\", \"DIMENSION\": \"L1\", \"MIN\": 1, \"MAX\": 1, \"LABEL\": \"the position along the same upward axis\"}], \"PARAMETERS\": [{\"NAME\": \"g_n\", \"DIMENSION\": \"L1 T-2\", \"SUPPLY\": \"DECLARED\", \"VALUE\": \"9.80665\", \"UNIT\": \"m s-2\", \"OVERRIDABLE\": \"NO\", \"LABEL\": \"the standard acceleration of gravity\"}, {\"NAME\": \"h_max\", \"DIMENSION\": \"L1\", \"SUPPLY\": \"AUTHOR\", \"LABEL\": \"the largest height, above or below the origin, over which the field is taken as uniform\"}], \"SUMS\": [], \"TERMS\": [{\"TARGET\": \"UP_VELOCITY\", \"SIGN\": \"-\", \"EXPR\": \"MASS*g_n\", \"LABEL\": \"the weight\"}], \"ASSUMPTIONS\": [{\"NAME\": \"gravity_uniform\", \"PROPOSITION\": \"the gravitational field is uniform over the region abs({HEIGHT}) < h_max\", \"REFS\": [\"HEIGHT\", \"h_max\"]}, {\"NAME\": \"gravity_standard\", \"PROPOSITION\": \"the local gravitational acceleration equals the conventional standard value g_n\", \"REFS\": [\"g_n\"]}, {\"NAME\": \"frame_inertial\", \"PROPOSITION\": \"the frame in which {HEIGHT} is measured is treated as inertial\", \"REFS\": [\"HEIGHT\"]}], \"BOUNDARIES\": [{\"NAME\": \"gravity_region\", \"PREDICATE\": \"abs({HEIGHT}) < h_max\", \"CONDITION\": \"abs(HEIGHT) < h_max\"}], \"NOT_CHOSEN\": \"No gravity: no weight acts on any DOF.\", \"NOT_INCLUDED\": [\"No variation of gravity with height or latitude beyond what g_n contains.\", \"No Earth rotation (Coriolis or centrifugal force) beyond what g_n contains.\", \"No gravity of bodies other than the Earth.\"], \"EXCLUDES\": [], \"INTERACTS_WITH\": [{\"WITH\": \"AIR-*\", \"QUESTION_ID\": \"BUOYANCY\", \"QUESTION\": \"Does the air's buoyancy (upthrust) act on the body in the system you mean?\", \"YES_LINE\": \"Buoyancy acts (your answer): no module adds it; it acts in this kernel only where one of your own laws states it.\", \"NO_LINE\": \"No buoyancy: the air's upthrust on the body is not included.\"}], \"TEST_BINDINGS\": [{\"NAME\": \"PROJECTILE_2D\", \"TPK\": {\"DOF\": [{\"NAME\": \"t\", \"DIMENSION\": \"T1\"}, {\"NAME\": \"x\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"z\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"v_x\", \"DIMENSION\": \"L1 T-1\"}, {\"NAME\": \"v_z\", \"DIMENSION\": \"L1 T-1\"}], \"CONSTANT\": [{\"NAME\": \"m\", \"DIMENSION\": \"M1\"}], \"LAW\": [{\"NAME\": \"KIN_X\", \"STATEMENT\": \"dx/dt = v_x\", \"REFS\": [\"t\", \"v_x\", \"x\"], \"ROLE\": \"EOM(x)\", \"EQUATION\": \"D(x,t)=v_x\"}, {\"NAME\": \"KIN_Z\", \"STATEMENT\": \"dz/dt = v_z\", \"REFS\": [\"t\", \"v_z\", \"z\"], \"ROLE\": \"EOM(z)\", \"EQUATION\": \"D(z,t)=v_z\"}, {\"NAME\": \"EOM_X\", \"STATEMENT\": \"m dv_x/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_x\"], \"ROLE\": \"EOM(v_x)\", \"EQUATION\": \"m*D(v_x,t)=0\"}, {\"NAME\": \"EOM_Z\", \"STATEMENT\": \"m dv_z/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_z\"], \"ROLE\": \"EOM(v_z)\", \"EQUATION\": \"m*D(v_z,t)=0\"}], \"ASSUMPTION\": [{\"NAME\": \"point_mass\", \"PROPOSITION\": \"the body is treated as a point mass\", \"REFS\": [\"m\"]}]}, \"BIND\": {\"HEIGHT\": [\"z\"], \"MASS\": [\"m\"], \"UP_VELOCITY\": [\"v_z\"]}, \"VALUES\": {\"h_max\": {\"VALUE\": \"100\", \"UNIT\": \"m\"}}, \"ANSWERS\": {}}, {\"NAME\": \"TABLE\", \"TPK\": {\"DOF\": [{\"NAME\": \"t\", \"DIMENSION\": \"T1\"}, {\"NAME\": \"x\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"z\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"v_x\", \"DIMENSION\": \"L1 T-1\"}, {\"NAME\": \"v_z\", \"DIMENSION\": \"L1 T-1\"}], \"CONSTANT\": [{\"NAME\": \"m\", \"DIMENSION\": \"M1\"}], \"LAW\": [{\"NAME\": \"KIN_X\", \"STATEMENT\": \"dx/dt = v_x\", \"REFS\": [\"t\", \"v_x\", \"x\"], \"ROLE\": \"EOM(x)\", \"EQUATION\": \"D(x,t)=v_x\"}, {\"NAME\": \"KIN_Z\", \"STATEMENT\": \"dz/dt = v_z\", \"REFS\": [\"t\", \"v_z\", \"z\"], \"ROLE\": \"CONSTRAINT\", \"EQUATION\": \"D(z,t)=v_z\"}, {\"NAME\": \"EOM_X\", \"STATEMENT\": \"m dv_x/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_x\"], \"ROLE\": \"EOM(v_x)\", \"EQUATION\": \"m*D(v_x,t)=0\"}], \"CONSTRAINT\": [{\"NAME\": \"C_Z\", \"TARGET\": \"z\", \"ACTION\": \"FIX\", \"VALUE\": \"0\", \"UNIT\": \"m\", \"STATEMENT\": \"the puck stays on the table top, z = 0\"}, {\"NAME\": \"C_VZ\", \"TARGET\": \"v_z\", \"ACTION\": \"FIX\", \"VALUE\": \"0\", \"UNIT\": \"m s-1\", \"STATEMENT\": \"the puck has no vertical velocity\"}]}, \"BIND\": {\"HEIGHT\": [\"z\"], \"MASS\": [\"m\"], \"UP_VELOCITY\": [\"v_z\"]}, \"VALUES\": {\"h_max\": {\"VALUE\": \"1\", \"UNIT\": \"m\"}}, \"ANSWERS\": {\"FIXED:v_z\": \"YES\"}}]}"
]
},
"expected": "[\"REFUSED\",\"ANSWER ROUND 2: RESELECT is not in code point order without repeats\"]",
"fn": "interview_check",
"hand_checked": true,
"name": "I50 RESELECT out of order"
},
{
"args": {
"answer": [
{
"AT": 4,
"CHOSEN": [
"GRAV-UNIFORM"
],
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{
"AT": 6,
"CHOSEN": "NONE",
"COVERED": [],
"RESELECT": [
"GRAV-UNIFORM"
]
}
],
"carried": [],
"claims": [
{
"ANSWERS": {},
"BIND": {
"HEIGHT": [
"z"
],
"MASS": [
"m"
],
"UP_VELOCITY": [
"v_z"
]
},
"DIGEST": "24877ccb5c8ec300d29ed82ce6650592f35cf8899a3d878ccce9c08d4c72c025",
"ID": "GRAV-UNIFORM",
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"h_max": {
"UNIT": "m",
"VALUE": "100"
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},
"VERSION": "1.0.0"
}
],
"lines": [
{
"ACT": "MODULE ADD",
"DATE": "2026-10-01",
"DIGEST": "5f3fe27b42378bce0830b0d0959f892f4a8e73b12b540ae877e39e6439d08b4d",
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{
"ACT": "MODULE ADD",
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{
"ACT": "MODULE ADD",
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"ID": "GRAV-UNIFORM",
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{
"ACT": "MODULE ADD",
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{
"ACT": "MODULE WITHDRAW",
"DATE": "2026-10-03",
"ID": "GRAV-UNIFORM",
"REASON": "the weight's sign was reversed in the binding page's preview",
"VERSION": "1.1.0"
}
],
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"{\"ID\": \"AIR-LINEAR\", \"VERSION\": \"1.0.0\", \"TITLE\": \"Air resistance at sea level, linear in the speed (Stokes drag on a sphere)\", \"SOURCE\": \"ISO 2533:1975, Standard Atmosphere, sea-level values: density 1.225 kg m-3, dynamic viscosity 1.7894e-5 Pa s\", \"PREREQUISITES\": [{\"SLOT\": \"VELOCITY\", \"KIND\": \"DOF\", \"DIMENSION\": \"L1 T-1\", \"MIN\": 1, \"MAX\": 3, \"LABEL\": \"the velocity components of the body, one per axis\"}], \"PARAMETERS\": [{\"NAME\": \"rho_air\", \"DIMENSION\": \"L-3 M1\", \"SUPPLY\": \"DECLARED\", \"VALUE\": \"1.225\", \"UNIT\": \"kg m-3\", \"OVERRIDABLE\": \"NO\", \"LABEL\": \"the density of air at sea level\"}, {\"NAME\": \"mu_air\", \"DIMENSION\": \"L-1 M1 T-1\", \"SUPPLY\": \"DECLARED\", \"VALUE\": \"1.7894e-5\", \"UNIT\": \"Pa s\", \"OVERRIDABLE\": \"NO\", \"LABEL\": \"the dynamic viscosity of air at sea level\"}, {\"NAME\": \"pi_c\", \"DIMENSION\": \"1\", \"SUPPLY\": \"DECLARED\", \"VALUE\": \"3.141592653589793\", \"UNIT\": \"1\", \"OVERRIDABLE\": \"NO\", \"LABEL\": \"pi, to 16 significant digits\"}, {\"NAME\": \"R_s\", \"DIMENSION\": \"L1\", \"SUPPLY\": \"AUTHOR\", \"LABEL\": \"the radius of the sphere\"}], \"SUMS\": [{\"NAME\": \"SPEED2\", \"OVER\": \"VELOCITY\", \"EACH\": \"VELOCITY^2\"}], \"TERMS\": [{\"TARGET\": \"VELOCITY\", \"SIGN\": \"-\", \"EXPR\": \"6*pi_c*mu_air*R_s*VELOCITY\", \"LABEL\": \"the linear (Stokes) drag\"}], \"ASSUMPTIONS\": [{\"NAME\": \"air_still\", \"PROPOSITION\": \"the air is at rest in the frame of the body's velocity\", \"REFS\": [\"VELOCITY\"]}, {\"NAME\": \"air_uniform\", \"PROPOSITION\": \"the air density is uniform over the region of motion\", \"REFS\": [\"rho_air\"]}, {\"NAME\": \"drag_sphere\", \"PROPOSITION\": \"the body is a rigid sphere of radius R_s\", \"REFS\": [\"R_s\"]}], \"BOUNDARIES\": [{\"NAME\": \"drag_linear_regime\", \"PREDICATE\": \"2 rho_air |v| R_s / mu_air < 1: the regime of the linear law\", \"CONDITION\": \"mu_air != 0 and SPEED2 >= 0 and 2*rho_air*sqrt(SPEED2)*R_s/mu_air < 1\"}], \"NOT_CHOSEN\": \"No linear (Stokes) air resistance.\", \"NOT_INCLUDED\": [\"No wind: the air is at rest.\", \"No change of air density or viscosity with altitude or temperature.\", \"No drag outside the regime of the linear law.\"], \"EXCLUDES\": [], \"INTERACTS_WITH\": [], \"TEST_BINDINGS\": [{\"NAME\": \"PROJECTILE_2D\", \"TPK\": {\"DOF\": [{\"NAME\": \"t\", \"DIMENSION\": \"T1\"}, {\"NAME\": \"x\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"z\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"v_x\", \"DIMENSION\": \"L1 T-1\"}, {\"NAME\": \"v_z\", \"DIMENSION\": \"L1 T-1\"}], \"CONSTANT\": [{\"NAME\": \"m\", \"DIMENSION\": \"M1\"}], \"LAW\": [{\"NAME\": \"KIN_X\", \"STATEMENT\": \"dx/dt = v_x\", \"REFS\": [\"t\", \"v_x\", \"x\"], \"ROLE\": \"EOM(x)\", \"EQUATION\": \"D(x,t)=v_x\"}, {\"NAME\": \"KIN_Z\", \"STATEMENT\": \"dz/dt = v_z\", \"REFS\": [\"t\", \"v_z\", \"z\"], \"ROLE\": \"EOM(z)\", \"EQUATION\": \"D(z,t)=v_z\"}, {\"NAME\": \"EOM_X\", \"STATEMENT\": \"m dv_x/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_x\"], \"ROLE\": \"EOM(v_x)\", \"EQUATION\": \"m*D(v_x,t)=0\"}, {\"NAME\": \"EOM_Z\", \"STATEMENT\": \"m dv_z/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_z\"], \"ROLE\": \"EOM(v_z)\", \"EQUATION\": \"m*D(v_z,t)=0\"}], \"ASSUMPTION\": [{\"NAME\": \"point_mass\", \"PROPOSITION\": \"the body is treated as a point mass\", \"REFS\": [\"m\"]}]}, \"BIND\": {\"VELOCITY\": [\"v_x\", \"v_z\"]}, \"VALUES\": {\"R_s\": {}}, \"ANSWERS\": {}}]}",
"{\"ID\": \"AIR-QUADRATIC\", \"VERSION\": \"1.0.0\", \"TITLE\": \"Air resistance at sea level, quadratic in the speed\", \"SOURCE\": \"ISO 2533:1975, Standard Atmosphere, sea-level values: density 1.225 kg m-3, dynamic viscosity 1.7894e-5 Pa s\", \"PREREQUISITES\": [{\"SLOT\": \"VELOCITY\", \"KIND\": \"DOF\", \"DIMENSION\": \"L1 T-1\", \"MIN\": 1, \"MAX\": 3, \"LABEL\": \"the velocity components of the body, one per axis\"}], \"PARAMETERS\": [{\"NAME\": \"rho_air\", \"DIMENSION\": \"L-3 M1\", \"SUPPLY\": \"DECLARED\", \"VALUE\": \"1.225\", \"UNIT\": \"kg m-3\", \"OVERRIDABLE\": \"NO\", \"LABEL\": \"the density of air at sea level\"}, {\"NAME\": \"mu_air\", \"DIMENSION\": \"L-1 M1 T-1\", \"SUPPLY\": \"DECLARED\", \"VALUE\": \"1.7894e-5\", \"UNIT\": \"Pa s\", \"OVERRIDABLE\": \"NO\", \"LABEL\": \"the dynamic viscosity of air at sea level\"}, {\"NAME\": \"C_d\", \"DIMENSION\": \"1\", \"SUPPLY\": \"AUTHOR\", \"LABEL\": \"the drag coefficient of the body\"}, {\"NAME\": \"A_ref\", \"DIMENSION\": \"L2\", \"SUPPLY\": \"AUTHOR\", \"LABEL\": \"the reference area of the drag coefficient\"}, {\"NAME\": \"L_ref\", \"DIMENSION\": \"L1\", \"SUPPLY\": \"AUTHOR\", \"LABEL\": \"the reference length of the Reynolds number\"}], \"SUMS\": [{\"NAME\": \"SPEED2\", \"OVER\": \"VELOCITY\", \"EACH\": \"VELOCITY^2\"}], \"TERMS\": [{\"TARGET\": \"VELOCITY\", \"SIGN\": \"-\", \"EXPR\": \"0.5*rho_air*C_d*A_ref*sqrt(SPEED2)*VELOCITY\", \"LABEL\": \"the quadratic drag\"}], \"ASSUMPTIONS\": [{\"NAME\": \"air_still\", \"PROPOSITION\": \"the air is at rest in the frame of the body's velocity\", \"REFS\": [\"VELOCITY\"]}, {\"NAME\": \"air_uniform\", \"PROPOSITION\": \"the air density is uniform over the region of motion\", \"REFS\": [\"rho_air\"]}, {\"NAME\": \"drag_cd_constant\", \"PROPOSITION\": \"the drag coefficient C_d is constant over the motion\", \"REFS\": [\"C_d\"]}, {\"NAME\": \"drag_no_lift\", \"PROPOSITION\": \"the body experiences no lift force\", \"REFS\": [\"VELOCITY\"]}, {\"NAME\": \"drag_no_magnus\", \"PROPOSITION\": \"the body experiences no Magnus force\", \"REFS\": [\"VELOCITY\"]}], \"BOUNDARIES\": [{\"NAME\": \"drag_quadratic_regime\", \"PREDICATE\": \"1e3 < rho_air |v| L_ref / mu_air < 2e5: the Reynolds window of the quadratic law\", \"CONDITION\": \"mu_air != 0 and SPEED2 >= 0 and rho_air*sqrt(SPEED2)*L_ref/mu_air > 1000 and rho_air*sqrt(SPEED2)*L_ref/mu_air < 200000\"}], \"NOT_CHOSEN\": \"No quadratic air resistance.\", \"NOT_INCLUDED\": [\"No wind: the air is at rest.\", \"No change of air density or viscosity with altitude or temperature.\", \"No lift, Magnus or added-mass force.\", \"No drag outside the Reynolds window of the quadratic law.\"], \"EXCLUDES\": [\"AIR-LINEAR\"], \"INTERACTS_WITH\": [], \"TEST_BINDINGS\": [{\"NAME\": \"PROJECTILE_2D\", \"TPK\": {\"DOF\": [{\"NAME\": \"t\", \"DIMENSION\": \"T1\"}, {\"NAME\": \"x\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"z\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"v_x\", \"DIMENSION\": \"L1 T-1\"}, {\"NAME\": \"v_z\", \"DIMENSION\": \"L1 T-1\"}], \"CONSTANT\": [{\"NAME\": \"m\", \"DIMENSION\": \"M1\"}], \"LAW\": [{\"NAME\": \"KIN_X\", \"STATEMENT\": \"dx/dt = v_x\", \"REFS\": [\"t\", \"v_x\", \"x\"], \"ROLE\": \"EOM(x)\", \"EQUATION\": \"D(x,t)=v_x\"}, {\"NAME\": \"KIN_Z\", \"STATEMENT\": \"dz/dt = v_z\", \"REFS\": [\"t\", \"v_z\", \"z\"], \"ROLE\": \"EOM(z)\", \"EQUATION\": \"D(z,t)=v_z\"}, {\"NAME\": \"EOM_X\", \"STATEMENT\": \"m dv_x/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_x\"], \"ROLE\": \"EOM(v_x)\", \"EQUATION\": \"m*D(v_x,t)=0\"}, {\"NAME\": \"EOM_Z\", \"STATEMENT\": \"m dv_z/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_z\"], \"ROLE\": \"EOM(v_z)\", \"EQUATION\": \"m*D(v_z,t)=0\"}], \"ASSUMPTION\": [{\"NAME\": \"point_mass\", \"PROPOSITION\": \"the body is treated as a point mass\", \"REFS\": [\"m\"]}]}, \"BIND\": {\"VELOCITY\": [\"v_x\", \"v_z\"]}, \"VALUES\": {\"A_ref\": {}, \"C_d\": {}, \"L_ref\": {}}, \"ANSWERS\": {}}]}",
"{\"ID\": \"GRAV-UNIFORM\", \"VERSION\": \"1.0.0\", \"TITLE\": \"Uniform gravity at the standard value g_n\", \"SOURCE\": \"g_n = 9.80665 m s-2, exact by definition: 3rd CGPM (1901), declaration on the unit of mass and on the definition of weight\", \"PREREQUISITES\": [{\"SLOT\": \"MASS\", \"KIND\": \"CONSTANT\", \"DIMENSION\": \"M1\", \"MIN\": 1, \"MAX\": 1, \"LABEL\": \"the mass of the body\"}, {\"SLOT\": \"UP_VELOCITY\", \"KIND\": \"DOF\", \"DIMENSION\": \"L1 T-1\", \"MIN\": 1, \"MAX\": 1, \"LABEL\": \"the velocity component pointing up; its equation of motion receives the weight\"}, {\"SLOT\": \"HEIGHT\", \"KIND\": \"DOF\", \"DIMENSION\": \"L1\", \"MIN\": 1, \"MAX\": 1, \"LABEL\": \"the position along the same upward axis\"}], \"PARAMETERS\": [{\"NAME\": \"g_n\", \"DIMENSION\": \"L1 T-2\", \"SUPPLY\": \"DECLARED\", \"VALUE\": \"9.80665\", \"UNIT\": \"m s-2\", \"OVERRIDABLE\": \"NO\", \"LABEL\": \"the standard acceleration of gravity\"}, {\"NAME\": \"h_max\", \"DIMENSION\": \"L1\", \"SUPPLY\": \"AUTHOR\", \"LABEL\": \"the largest height, above or below the origin, over which the field is taken as uniform\"}], \"SUMS\": [], \"TERMS\": [{\"TARGET\": \"UP_VELOCITY\", \"SIGN\": \"-\", \"EXPR\": \"MASS*g_n\", \"LABEL\": \"the weight\"}], \"ASSUMPTIONS\": [{\"NAME\": \"gravity_uniform\", \"PROPOSITION\": \"the gravitational field is uniform over the region abs({HEIGHT}) < h_max\", \"REFS\": [\"HEIGHT\", \"h_max\"]}, {\"NAME\": \"gravity_standard\", \"PROPOSITION\": \"the local gravitational acceleration equals the conventional standard value g_n\", \"REFS\": [\"g_n\"]}, {\"NAME\": \"frame_inertial\", \"PROPOSITION\": \"the frame in which {HEIGHT} is measured is treated as inertial\", \"REFS\": [\"HEIGHT\"]}], \"BOUNDARIES\": [{\"NAME\": \"gravity_region\", \"PREDICATE\": \"abs({HEIGHT}) < h_max\", \"CONDITION\": \"abs(HEIGHT) < h_max\"}], \"NOT_CHOSEN\": \"No gravity: no weight acts on any DOF.\", \"NOT_INCLUDED\": [\"No variation of gravity with height or latitude beyond what g_n contains.\", \"No Earth rotation (Coriolis or centrifugal force) beyond what g_n contains.\", \"No gravity of bodies other than the Earth.\"], \"EXCLUDES\": [], \"INTERACTS_WITH\": [{\"WITH\": \"AIR-*\", \"QUESTION_ID\": \"BUOYANCY\", \"QUESTION\": \"Does the air's buoyancy (upthrust) act on the body in the system you mean?\", \"YES_LINE\": \"Buoyancy acts (your answer): no module adds it; it acts in this kernel only where one of your own laws states it.\", \"NO_LINE\": \"No buoyancy: the air's upthrust on the body is not included.\"}], \"TEST_BINDINGS\": [{\"NAME\": \"PROJECTILE_2D\", \"TPK\": {\"DOF\": [{\"NAME\": \"t\", \"DIMENSION\": \"T1\"}, {\"NAME\": \"x\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"z\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"v_x\", \"DIMENSION\": \"L1 T-1\"}, {\"NAME\": \"v_z\", \"DIMENSION\": \"L1 T-1\"}], \"CONSTANT\": [{\"NAME\": \"m\", \"DIMENSION\": \"M1\"}], \"LAW\": [{\"NAME\": \"KIN_X\", \"STATEMENT\": \"dx/dt = v_x\", \"REFS\": [\"t\", \"v_x\", \"x\"], \"ROLE\": \"EOM(x)\", \"EQUATION\": \"D(x,t)=v_x\"}, {\"NAME\": \"KIN_Z\", \"STATEMENT\": \"dz/dt = v_z\", \"REFS\": [\"t\", \"v_z\", \"z\"], \"ROLE\": \"EOM(z)\", \"EQUATION\": \"D(z,t)=v_z\"}, {\"NAME\": \"EOM_X\", \"STATEMENT\": \"m dv_x/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_x\"], \"ROLE\": \"EOM(v_x)\", \"EQUATION\": \"m*D(v_x,t)=0\"}, {\"NAME\": \"EOM_Z\", \"STATEMENT\": \"m dv_z/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_z\"], \"ROLE\": \"EOM(v_z)\", \"EQUATION\": \"m*D(v_z,t)=0\"}], \"ASSUMPTION\": [{\"NAME\": \"point_mass\", \"PROPOSITION\": \"the body is treated as a point mass\", \"REFS\": [\"m\"]}]}, \"BIND\": {\"HEIGHT\": [\"z\"], \"MASS\": [\"m\"], \"UP_VELOCITY\": [\"v_z\"]}, \"VALUES\": {\"h_max\": {\"VALUE\": \"100\", \"UNIT\": \"m\"}}, \"ANSWERS\": {}}, {\"NAME\": \"TABLE\", \"TPK\": {\"DOF\": [{\"NAME\": \"t\", \"DIMENSION\": \"T1\"}, {\"NAME\": \"x\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"z\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"v_x\", \"DIMENSION\": \"L1 T-1\"}, {\"NAME\": \"v_z\", \"DIMENSION\": \"L1 T-1\"}], \"CONSTANT\": [{\"NAME\": \"m\", \"DIMENSION\": \"M1\"}], \"LAW\": [{\"NAME\": \"KIN_X\", \"STATEMENT\": \"dx/dt = v_x\", \"REFS\": [\"t\", \"v_x\", \"x\"], \"ROLE\": \"EOM(x)\", \"EQUATION\": \"D(x,t)=v_x\"}, {\"NAME\": \"KIN_Z\", \"STATEMENT\": \"dz/dt = v_z\", \"REFS\": [\"t\", \"v_z\", \"z\"], \"ROLE\": \"CONSTRAINT\", \"EQUATION\": \"D(z,t)=v_z\"}, {\"NAME\": \"EOM_X\", \"STATEMENT\": \"m dv_x/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_x\"], \"ROLE\": \"EOM(v_x)\", \"EQUATION\": \"m*D(v_x,t)=0\"}], \"CONSTRAINT\": [{\"NAME\": \"C_Z\", \"TARGET\": \"z\", \"ACTION\": \"FIX\", \"VALUE\": \"0\", \"UNIT\": \"m\", \"STATEMENT\": \"the puck stays on the table top, z = 0\"}, {\"NAME\": \"C_VZ\", \"TARGET\": \"v_z\", \"ACTION\": \"FIX\", \"VALUE\": \"0\", \"UNIT\": \"m s-1\", \"STATEMENT\": \"the puck has no vertical velocity\"}]}, \"BIND\": {\"HEIGHT\": [\"z\"], \"MASS\": [\"m\"], \"UP_VELOCITY\": [\"v_z\"]}, \"VALUES\": {\"h_max\": {\"VALUE\": \"1\", \"UNIT\": \"m\"}}, \"ANSWERS\": {\"FIXED:v_z\": \"YES\"}}]}",
"{\"ID\": \"MATH\", \"VERSION\": \"1.0.0\", \"TITLE\": \"The mathematical constant pi, as the CONSTANT pi_c\", \"SOURCE\": \"pi to 16 significant digits, 3.141592653589793, the nearest IEEE 754 binary64 value\", \"PREREQUISITES\": [], \"PARAMETERS\": [{\"NAME\": \"pi_c\", \"DIMENSION\": \"1\", \"SUPPLY\": \"DECLARED\", \"VALUE\": \"3.141592653589793\", \"UNIT\": \"1\", \"OVERRIDABLE\": \"NO\", \"LABEL\": \"pi, to 16 significant digits\"}], \"SUMS\": [], \"TERMS\": [], \"ASSUMPTIONS\": [], \"BOUNDARIES\": [], \"NOT_CHOSEN\": \"No mathematical constant: pi exists only if you declare it.\", \"NOT_INCLUDED\": [\"pi_c is pi rounded to 16 significant digits; no other mathematical constant is declared.\"], \"EXCLUDES\": [], \"INTERACTS_WITH\": [], \"TEST_BINDINGS\": [{\"NAME\": \"PROJECTILE_2D\", \"TPK\": {\"DOF\": [{\"NAME\": \"t\", \"DIMENSION\": \"T1\"}, {\"NAME\": \"x\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"z\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"v_x\", \"DIMENSION\": \"L1 T-1\"}, {\"NAME\": \"v_z\", \"DIMENSION\": \"L1 T-1\"}], \"CONSTANT\": [{\"NAME\": \"m\", \"DIMENSION\": \"M1\"}], \"LAW\": [{\"NAME\": \"KIN_X\", \"STATEMENT\": \"dx/dt = v_x\", \"REFS\": [\"t\", \"v_x\", \"x\"], \"ROLE\": \"EOM(x)\", \"EQUATION\": \"D(x,t)=v_x\"}, {\"NAME\": \"KIN_Z\", \"STATEMENT\": \"dz/dt = v_z\", \"REFS\": [\"t\", \"v_z\", \"z\"], \"ROLE\": \"EOM(z)\", \"EQUATION\": \"D(z,t)=v_z\"}, {\"NAME\": \"EOM_X\", \"STATEMENT\": \"m dv_x/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_x\"], \"ROLE\": \"EOM(v_x)\", \"EQUATION\": \"m*D(v_x,t)=0\"}, {\"NAME\": \"EOM_Z\", \"STATEMENT\": \"m dv_z/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_z\"], \"ROLE\": \"EOM(v_z)\", \"EQUATION\": \"m*D(v_z,t)=0\"}], \"ASSUMPTION\": [{\"NAME\": \"point_mass\", \"PROPOSITION\": \"the body is treated as a point mass\", \"REFS\": [\"m\"]}]}, \"BIND\": {}, \"VALUES\": {}, \"ANSWERS\": {}}]}",
"{\"ID\": \"GRAV-UNIFORM\", \"VERSION\": \"1.1.0\", \"TITLE\": \"Uniform gravity at the standard value g_n (text revised)\", \"SOURCE\": \"g_n = 9.80665 m s-2, exact by definition: 3rd CGPM (1901), declaration on the unit of mass and on the definition of weight\", \"PREREQUISITES\": [{\"SLOT\": \"MASS\", \"KIND\": \"CONSTANT\", \"DIMENSION\": \"M1\", \"MIN\": 1, \"MAX\": 1, \"LABEL\": \"the mass of the body\"}, {\"SLOT\": \"UP_VELOCITY\", \"KIND\": \"DOF\", \"DIMENSION\": \"L1 T-1\", \"MIN\": 1, \"MAX\": 1, \"LABEL\": \"the velocity component pointing up; its equation of motion receives the weight\"}, {\"SLOT\": \"HEIGHT\", \"KIND\": \"DOF\", \"DIMENSION\": \"L1\", \"MIN\": 1, \"MAX\": 1, \"LABEL\": \"the position along the same upward axis\"}], \"PARAMETERS\": [{\"NAME\": \"g_n\", \"DIMENSION\": \"L1 T-2\", \"SUPPLY\": \"DECLARED\", \"VALUE\": \"9.80665\", \"UNIT\": \"m s-2\", \"OVERRIDABLE\": \"NO\", \"LABEL\": \"the standard acceleration of gravity\"}, {\"NAME\": \"h_max\", \"DIMENSION\": \"L1\", \"SUPPLY\": \"AUTHOR\", \"LABEL\": \"the largest height, above or below the origin, over which the field is taken as uniform\"}], \"SUMS\": [], \"TERMS\": [{\"TARGET\": \"UP_VELOCITY\", \"SIGN\": \"-\", \"EXPR\": \"MASS*g_n\", \"LABEL\": \"the weight\"}], \"ASSUMPTIONS\": [{\"NAME\": \"gravity_uniform\", \"PROPOSITION\": \"the gravitational field is uniform over the region abs({HEIGHT}) < h_max\", \"REFS\": [\"HEIGHT\", \"h_max\"]}, {\"NAME\": \"gravity_standard\", \"PROPOSITION\": \"the local gravitational acceleration equals the conventional standard value g_n\", \"REFS\": [\"g_n\"]}, {\"NAME\": \"frame_inertial\", \"PROPOSITION\": \"the frame in which {HEIGHT} is measured is treated as inertial\", \"REFS\": [\"HEIGHT\"]}], \"BOUNDARIES\": [{\"NAME\": \"gravity_region\", \"PREDICATE\": \"abs({HEIGHT}) < h_max\", \"CONDITION\": \"abs(HEIGHT) < h_max\"}], \"NOT_CHOSEN\": \"No gravity: no weight acts on any DOF.\", \"NOT_INCLUDED\": [\"No variation of gravity with height or latitude beyond what g_n contains.\", \"No Earth rotation (Coriolis or centrifugal force) beyond what g_n contains.\", \"No gravity of bodies other than the Earth.\"], \"EXCLUDES\": [], \"INTERACTS_WITH\": [{\"WITH\": \"AIR-*\", \"QUESTION_ID\": \"BUOYANCY\", \"QUESTION\": \"Does the air's buoyancy (upthrust) act on the body in the system you mean?\", \"YES_LINE\": \"Buoyancy acts (your answer): no module adds it; it acts in this kernel only where one of your own laws states it.\", \"NO_LINE\": \"No buoyancy: the air's upthrust on the body is not included.\"}], \"TEST_BINDINGS\": [{\"NAME\": \"PROJECTILE_2D\", \"TPK\": {\"DOF\": [{\"NAME\": \"t\", \"DIMENSION\": \"T1\"}, {\"NAME\": \"x\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"z\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"v_x\", \"DIMENSION\": \"L1 T-1\"}, {\"NAME\": \"v_z\", \"DIMENSION\": \"L1 T-1\"}], \"CONSTANT\": [{\"NAME\": \"m\", \"DIMENSION\": \"M1\"}], \"LAW\": [{\"NAME\": \"KIN_X\", \"STATEMENT\": \"dx/dt = v_x\", \"REFS\": [\"t\", \"v_x\", \"x\"], \"ROLE\": \"EOM(x)\", \"EQUATION\": \"D(x,t)=v_x\"}, {\"NAME\": \"KIN_Z\", \"STATEMENT\": \"dz/dt = v_z\", \"REFS\": [\"t\", \"v_z\", \"z\"], \"ROLE\": \"EOM(z)\", \"EQUATION\": \"D(z,t)=v_z\"}, {\"NAME\": \"EOM_X\", \"STATEMENT\": \"m dv_x/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_x\"], \"ROLE\": \"EOM(v_x)\", \"EQUATION\": \"m*D(v_x,t)=0\"}, {\"NAME\": \"EOM_Z\", \"STATEMENT\": \"m dv_z/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_z\"], \"ROLE\": \"EOM(v_z)\", \"EQUATION\": \"m*D(v_z,t)=0\"}], \"ASSUMPTION\": [{\"NAME\": \"point_mass\", \"PROPOSITION\": \"the body is treated as a point mass\", \"REFS\": [\"m\"]}]}, \"BIND\": {\"HEIGHT\": [\"z\"], \"MASS\": [\"m\"], \"UP_VELOCITY\": [\"v_z\"]}, \"VALUES\": {\"h_max\": {\"VALUE\": \"100\", \"UNIT\": \"m\"}}, \"ANSWERS\": {}}, {\"NAME\": \"TABLE\", \"TPK\": {\"DOF\": [{\"NAME\": \"t\", \"DIMENSION\": \"T1\"}, {\"NAME\": \"x\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"z\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"v_x\", \"DIMENSION\": \"L1 T-1\"}, {\"NAME\": \"v_z\", \"DIMENSION\": \"L1 T-1\"}], \"CONSTANT\": [{\"NAME\": \"m\", \"DIMENSION\": \"M1\"}], \"LAW\": [{\"NAME\": \"KIN_X\", \"STATEMENT\": \"dx/dt = v_x\", \"REFS\": [\"t\", \"v_x\", \"x\"], \"ROLE\": \"EOM(x)\", \"EQUATION\": \"D(x,t)=v_x\"}, {\"NAME\": \"KIN_Z\", \"STATEMENT\": \"dz/dt = v_z\", \"REFS\": [\"t\", \"v_z\", \"z\"], \"ROLE\": \"CONSTRAINT\", \"EQUATION\": \"D(z,t)=v_z\"}, {\"NAME\": \"EOM_X\", \"STATEMENT\": \"m dv_x/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_x\"], \"ROLE\": \"EOM(v_x)\", \"EQUATION\": \"m*D(v_x,t)=0\"}], \"CONSTRAINT\": [{\"NAME\": \"C_Z\", \"TARGET\": \"z\", \"ACTION\": \"FIX\", \"VALUE\": \"0\", \"UNIT\": \"m\", \"STATEMENT\": \"the puck stays on the table top, z = 0\"}, {\"NAME\": \"C_VZ\", \"TARGET\": \"v_z\", \"ACTION\": \"FIX\", \"VALUE\": \"0\", \"UNIT\": \"m s-1\", \"STATEMENT\": \"the puck has no vertical velocity\"}]}, \"BIND\": {\"HEIGHT\": [\"z\"], \"MASS\": [\"m\"], \"UP_VELOCITY\": [\"v_z\"]}, \"VALUES\": {\"h_max\": {\"VALUE\": \"1\", \"UNIT\": \"m\"}}, \"ANSWERS\": {\"FIXED:v_z\": \"YES\"}}]}"
]
},
"expected": "[\"REFUSED\",\"ANSWER ROUND 2: RESELECT GRAV-UNIFORM is not offered at AT\"]",
"fn": "interview_check",
"hand_checked": true,
"name": "I51 RESELECT of an ID no longer offered"
},
{
"args": {
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[
[
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]
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"claims": [],
"lines": [
{
"ACT": "MODULE ADD",
"DATE": "2026-10-01",
"DIGEST": "5f3fe27b42378bce0830b0d0959f892f4a8e73b12b540ae877e39e6439d08b4d",
"ID": "AIR-LINEAR",
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{
"ACT": "MODULE ADD",
"DATE": "2026-10-01",
"DIGEST": "6fb53c3a6546151eead2bd6e72e9cf8334f3a2040ad0ee2f5b988ec96d6fc852",
"ID": "AIR-QUADRATIC",
"VERSION": "1.0.0"
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{
"ACT": "MODULE ADD",
"DATE": "2026-10-01",
"DIGEST": "24877ccb5c8ec300d29ed82ce6650592f35cf8899a3d878ccce9c08d4c72c025",
"ID": "GRAV-UNIFORM",
"VERSION": "1.0.0"
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{
"ACT": "MODULE ADD",
"DATE": "2026-10-01",
"DIGEST": "8f39a356f35527b901fcee012764590f0819c8ffdeccad4bc05195ce3d2e0bcf",
"ID": "MATH",
"VERSION": "1.0.0"
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"{\"ID\": \"AIR-LINEAR\", \"VERSION\": \"1.0.0\", \"TITLE\": \"Air resistance at sea level, linear in the speed (Stokes drag on a sphere)\", \"SOURCE\": \"ISO 2533:1975, Standard Atmosphere, sea-level values: density 1.225 kg m-3, dynamic viscosity 1.7894e-5 Pa s\", \"PREREQUISITES\": [{\"SLOT\": \"VELOCITY\", \"KIND\": \"DOF\", \"DIMENSION\": \"L1 T-1\", \"MIN\": 1, \"MAX\": 3, \"LABEL\": \"the velocity components of the body, one per axis\"}], \"PARAMETERS\": [{\"NAME\": \"rho_air\", \"DIMENSION\": \"L-3 M1\", \"SUPPLY\": \"DECLARED\", \"VALUE\": \"1.225\", \"UNIT\": \"kg m-3\", \"OVERRIDABLE\": \"NO\", \"LABEL\": \"the density of air at sea level\"}, {\"NAME\": \"mu_air\", \"DIMENSION\": \"L-1 M1 T-1\", \"SUPPLY\": \"DECLARED\", \"VALUE\": \"1.7894e-5\", \"UNIT\": \"Pa s\", \"OVERRIDABLE\": \"NO\", \"LABEL\": \"the dynamic viscosity of air at sea level\"}, {\"NAME\": \"pi_c\", \"DIMENSION\": \"1\", \"SUPPLY\": \"DECLARED\", \"VALUE\": \"3.141592653589793\", \"UNIT\": \"1\", \"OVERRIDABLE\": \"NO\", \"LABEL\": \"pi, to 16 significant digits\"}, {\"NAME\": \"R_s\", \"DIMENSION\": \"L1\", \"SUPPLY\": \"AUTHOR\", \"LABEL\": \"the radius of the sphere\"}], \"SUMS\": [{\"NAME\": \"SPEED2\", \"OVER\": \"VELOCITY\", \"EACH\": \"VELOCITY^2\"}], \"TERMS\": [{\"TARGET\": \"VELOCITY\", \"SIGN\": \"-\", \"EXPR\": \"6*pi_c*mu_air*R_s*VELOCITY\", \"LABEL\": \"the linear (Stokes) drag\"}], \"ASSUMPTIONS\": [{\"NAME\": \"air_still\", \"PROPOSITION\": \"the air is at rest in the frame of the body's velocity\", \"REFS\": [\"VELOCITY\"]}, {\"NAME\": \"air_uniform\", \"PROPOSITION\": \"the air density is uniform over the region of motion\", \"REFS\": [\"rho_air\"]}, {\"NAME\": \"drag_sphere\", \"PROPOSITION\": \"the body is a rigid sphere of radius R_s\", \"REFS\": [\"R_s\"]}], \"BOUNDARIES\": [{\"NAME\": \"drag_linear_regime\", \"PREDICATE\": \"2 rho_air |v| R_s / mu_air < 1: the regime of the linear law\", \"CONDITION\": \"mu_air != 0 and SPEED2 >= 0 and 2*rho_air*sqrt(SPEED2)*R_s/mu_air < 1\"}], \"NOT_CHOSEN\": \"No linear (Stokes) air resistance.\", \"NOT_INCLUDED\": [\"No wind: the air is at rest.\", \"No change of air density or viscosity with altitude or temperature.\", \"No drag outside the regime of the linear law.\"], \"EXCLUDES\": [], \"INTERACTS_WITH\": [], \"TEST_BINDINGS\": [{\"NAME\": \"PROJECTILE_2D\", \"TPK\": {\"DOF\": [{\"NAME\": \"t\", \"DIMENSION\": \"T1\"}, {\"NAME\": \"x\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"z\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"v_x\", \"DIMENSION\": \"L1 T-1\"}, {\"NAME\": \"v_z\", \"DIMENSION\": \"L1 T-1\"}], \"CONSTANT\": [{\"NAME\": \"m\", \"DIMENSION\": \"M1\"}], \"LAW\": [{\"NAME\": \"KIN_X\", \"STATEMENT\": \"dx/dt = v_x\", \"REFS\": [\"t\", \"v_x\", \"x\"], \"ROLE\": \"EOM(x)\", \"EQUATION\": \"D(x,t)=v_x\"}, {\"NAME\": \"KIN_Z\", \"STATEMENT\": \"dz/dt = v_z\", \"REFS\": [\"t\", \"v_z\", \"z\"], \"ROLE\": \"EOM(z)\", \"EQUATION\": \"D(z,t)=v_z\"}, {\"NAME\": \"EOM_X\", \"STATEMENT\": \"m dv_x/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_x\"], \"ROLE\": \"EOM(v_x)\", \"EQUATION\": \"m*D(v_x,t)=0\"}, {\"NAME\": \"EOM_Z\", \"STATEMENT\": \"m dv_z/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_z\"], \"ROLE\": \"EOM(v_z)\", \"EQUATION\": \"m*D(v_z,t)=0\"}], \"ASSUMPTION\": [{\"NAME\": \"point_mass\", \"PROPOSITION\": \"the body is treated as a point mass\", \"REFS\": [\"m\"]}]}, \"BIND\": {\"VELOCITY\": [\"v_x\", \"v_z\"]}, \"VALUES\": {\"R_s\": {}}, \"ANSWERS\": {}}]}",
"{\"ID\": \"AIR-QUADRATIC\", \"VERSION\": \"1.0.0\", \"TITLE\": \"Air resistance at sea level, quadratic in the speed\", \"SOURCE\": \"ISO 2533:1975, Standard Atmosphere, sea-level values: density 1.225 kg m-3, dynamic viscosity 1.7894e-5 Pa s\", \"PREREQUISITES\": [{\"SLOT\": \"VELOCITY\", \"KIND\": \"DOF\", \"DIMENSION\": \"L1 T-1\", \"MIN\": 1, \"MAX\": 3, \"LABEL\": \"the velocity components of the body, one per axis\"}], \"PARAMETERS\": [{\"NAME\": \"rho_air\", \"DIMENSION\": \"L-3 M1\", \"SUPPLY\": \"DECLARED\", \"VALUE\": \"1.225\", \"UNIT\": \"kg m-3\", \"OVERRIDABLE\": \"NO\", \"LABEL\": \"the density of air at sea level\"}, {\"NAME\": \"mu_air\", \"DIMENSION\": \"L-1 M1 T-1\", \"SUPPLY\": \"DECLARED\", \"VALUE\": \"1.7894e-5\", \"UNIT\": \"Pa s\", \"OVERRIDABLE\": \"NO\", \"LABEL\": \"the dynamic viscosity of air at sea level\"}, {\"NAME\": \"C_d\", \"DIMENSION\": \"1\", \"SUPPLY\": \"AUTHOR\", \"LABEL\": \"the drag coefficient of the body\"}, {\"NAME\": \"A_ref\", \"DIMENSION\": \"L2\", \"SUPPLY\": \"AUTHOR\", \"LABEL\": \"the reference area of the drag coefficient\"}, {\"NAME\": \"L_ref\", \"DIMENSION\": \"L1\", \"SUPPLY\": \"AUTHOR\", \"LABEL\": \"the reference length of the Reynolds number\"}], \"SUMS\": [{\"NAME\": \"SPEED2\", \"OVER\": \"VELOCITY\", \"EACH\": \"VELOCITY^2\"}], \"TERMS\": [{\"TARGET\": \"VELOCITY\", \"SIGN\": \"-\", \"EXPR\": \"0.5*rho_air*C_d*A_ref*sqrt(SPEED2)*VELOCITY\", \"LABEL\": \"the quadratic drag\"}], \"ASSUMPTIONS\": [{\"NAME\": \"air_still\", \"PROPOSITION\": \"the air is at rest in the frame of the body's velocity\", \"REFS\": [\"VELOCITY\"]}, {\"NAME\": \"air_uniform\", \"PROPOSITION\": \"the air density is uniform over the region of motion\", \"REFS\": [\"rho_air\"]}, {\"NAME\": \"drag_cd_constant\", \"PROPOSITION\": \"the drag coefficient C_d is constant over the motion\", \"REFS\": [\"C_d\"]}, {\"NAME\": \"drag_no_lift\", \"PROPOSITION\": \"the body experiences no lift force\", \"REFS\": [\"VELOCITY\"]}, {\"NAME\": \"drag_no_magnus\", \"PROPOSITION\": \"the body experiences no Magnus force\", \"REFS\": [\"VELOCITY\"]}], \"BOUNDARIES\": [{\"NAME\": \"drag_quadratic_regime\", \"PREDICATE\": \"1e3 < rho_air |v| L_ref / mu_air < 2e5: the Reynolds window of the quadratic law\", \"CONDITION\": \"mu_air != 0 and SPEED2 >= 0 and rho_air*sqrt(SPEED2)*L_ref/mu_air > 1000 and rho_air*sqrt(SPEED2)*L_ref/mu_air < 200000\"}], \"NOT_CHOSEN\": \"No quadratic air resistance.\", \"NOT_INCLUDED\": [\"No wind: the air is at rest.\", \"No change of air density or viscosity with altitude or temperature.\", \"No lift, Magnus or added-mass force.\", \"No drag outside the Reynolds window of the quadratic law.\"], \"EXCLUDES\": [\"AIR-LINEAR\"], \"INTERACTS_WITH\": [], \"TEST_BINDINGS\": [{\"NAME\": \"PROJECTILE_2D\", \"TPK\": {\"DOF\": [{\"NAME\": \"t\", \"DIMENSION\": \"T1\"}, {\"NAME\": \"x\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"z\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"v_x\", \"DIMENSION\": \"L1 T-1\"}, {\"NAME\": \"v_z\", \"DIMENSION\": \"L1 T-1\"}], \"CONSTANT\": [{\"NAME\": \"m\", \"DIMENSION\": \"M1\"}], \"LAW\": [{\"NAME\": \"KIN_X\", \"STATEMENT\": \"dx/dt = v_x\", \"REFS\": [\"t\", \"v_x\", \"x\"], \"ROLE\": \"EOM(x)\", \"EQUATION\": \"D(x,t)=v_x\"}, {\"NAME\": \"KIN_Z\", \"STATEMENT\": \"dz/dt = v_z\", \"REFS\": [\"t\", \"v_z\", \"z\"], \"ROLE\": \"EOM(z)\", \"EQUATION\": \"D(z,t)=v_z\"}, {\"NAME\": \"EOM_X\", \"STATEMENT\": \"m dv_x/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_x\"], \"ROLE\": \"EOM(v_x)\", \"EQUATION\": \"m*D(v_x,t)=0\"}, {\"NAME\": \"EOM_Z\", \"STATEMENT\": \"m dv_z/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_z\"], \"ROLE\": \"EOM(v_z)\", \"EQUATION\": \"m*D(v_z,t)=0\"}], \"ASSUMPTION\": [{\"NAME\": \"point_mass\", \"PROPOSITION\": \"the body is treated as a point mass\", \"REFS\": [\"m\"]}]}, \"BIND\": {\"VELOCITY\": [\"v_x\", \"v_z\"]}, \"VALUES\": {\"A_ref\": {}, \"C_d\": {}, \"L_ref\": {}}, \"ANSWERS\": {}}]}",
"{\"ID\": \"GRAV-UNIFORM\", \"VERSION\": \"1.0.0\", \"TITLE\": \"Uniform gravity at the standard value g_n\", \"SOURCE\": \"g_n = 9.80665 m s-2, exact by definition: 3rd CGPM (1901), declaration on the unit of mass and on the definition of weight\", \"PREREQUISITES\": [{\"SLOT\": \"MASS\", \"KIND\": \"CONSTANT\", \"DIMENSION\": \"M1\", \"MIN\": 1, \"MAX\": 1, \"LABEL\": \"the mass of the body\"}, {\"SLOT\": \"UP_VELOCITY\", \"KIND\": \"DOF\", \"DIMENSION\": \"L1 T-1\", \"MIN\": 1, \"MAX\": 1, \"LABEL\": \"the velocity component pointing up; its equation of motion receives the weight\"}, {\"SLOT\": \"HEIGHT\", \"KIND\": \"DOF\", \"DIMENSION\": \"L1\", \"MIN\": 1, \"MAX\": 1, \"LABEL\": \"the position along the same upward axis\"}], \"PARAMETERS\": [{\"NAME\": \"g_n\", \"DIMENSION\": \"L1 T-2\", \"SUPPLY\": \"DECLARED\", \"VALUE\": \"9.80665\", \"UNIT\": \"m s-2\", \"OVERRIDABLE\": \"NO\", \"LABEL\": \"the standard acceleration of gravity\"}, {\"NAME\": \"h_max\", \"DIMENSION\": \"L1\", \"SUPPLY\": \"AUTHOR\", \"LABEL\": \"the largest height, above or below the origin, over which the field is taken as uniform\"}], \"SUMS\": [], \"TERMS\": [{\"TARGET\": \"UP_VELOCITY\", \"SIGN\": \"-\", \"EXPR\": \"MASS*g_n\", \"LABEL\": \"the weight\"}], \"ASSUMPTIONS\": [{\"NAME\": \"gravity_uniform\", \"PROPOSITION\": \"the gravitational field is uniform over the region abs({HEIGHT}) < h_max\", \"REFS\": [\"HEIGHT\", \"h_max\"]}, {\"NAME\": \"gravity_standard\", \"PROPOSITION\": \"the local gravitational acceleration equals the conventional standard value g_n\", \"REFS\": [\"g_n\"]}, {\"NAME\": \"frame_inertial\", \"PROPOSITION\": \"the frame in which {HEIGHT} is measured is treated as inertial\", \"REFS\": [\"HEIGHT\"]}], \"BOUNDARIES\": [{\"NAME\": \"gravity_region\", \"PREDICATE\": \"abs({HEIGHT}) < h_max\", \"CONDITION\": \"abs(HEIGHT) < h_max\"}], \"NOT_CHOSEN\": \"No gravity: no weight acts on any DOF.\", \"NOT_INCLUDED\": [\"No variation of gravity with height or latitude beyond what g_n contains.\", \"No Earth rotation (Coriolis or centrifugal force) beyond what g_n contains.\", \"No gravity of bodies other than the Earth.\"], \"EXCLUDES\": [], \"INTERACTS_WITH\": [{\"WITH\": \"AIR-*\", \"QUESTION_ID\": \"BUOYANCY\", \"QUESTION\": \"Does the air's buoyancy (upthrust) act on the body in the system you mean?\", \"YES_LINE\": \"Buoyancy acts (your answer): no module adds it; it acts in this kernel only where one of your own laws states it.\", \"NO_LINE\": \"No buoyancy: the air's upthrust on the body is not included.\"}], \"TEST_BINDINGS\": [{\"NAME\": \"PROJECTILE_2D\", \"TPK\": {\"DOF\": [{\"NAME\": \"t\", \"DIMENSION\": \"T1\"}, {\"NAME\": \"x\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"z\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"v_x\", \"DIMENSION\": \"L1 T-1\"}, {\"NAME\": \"v_z\", \"DIMENSION\": \"L1 T-1\"}], \"CONSTANT\": [{\"NAME\": \"m\", \"DIMENSION\": \"M1\"}], \"LAW\": [{\"NAME\": \"KIN_X\", \"STATEMENT\": \"dx/dt = v_x\", \"REFS\": [\"t\", \"v_x\", \"x\"], \"ROLE\": \"EOM(x)\", \"EQUATION\": \"D(x,t)=v_x\"}, {\"NAME\": \"KIN_Z\", \"STATEMENT\": \"dz/dt = v_z\", \"REFS\": [\"t\", \"v_z\", \"z\"], \"ROLE\": \"EOM(z)\", \"EQUATION\": \"D(z,t)=v_z\"}, {\"NAME\": \"EOM_X\", \"STATEMENT\": \"m dv_x/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_x\"], \"ROLE\": \"EOM(v_x)\", \"EQUATION\": \"m*D(v_x,t)=0\"}, {\"NAME\": \"EOM_Z\", \"STATEMENT\": \"m dv_z/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_z\"], \"ROLE\": \"EOM(v_z)\", \"EQUATION\": \"m*D(v_z,t)=0\"}], \"ASSUMPTION\": [{\"NAME\": \"point_mass\", \"PROPOSITION\": \"the body is treated as a point mass\", \"REFS\": [\"m\"]}]}, \"BIND\": {\"HEIGHT\": [\"z\"], \"MASS\": [\"m\"], \"UP_VELOCITY\": [\"v_z\"]}, \"VALUES\": {\"h_max\": {\"VALUE\": \"100\", \"UNIT\": \"m\"}}, \"ANSWERS\": {}}, {\"NAME\": \"TABLE\", \"TPK\": {\"DOF\": [{\"NAME\": \"t\", \"DIMENSION\": \"T1\"}, {\"NAME\": \"x\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"z\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"v_x\", \"DIMENSION\": \"L1 T-1\"}, {\"NAME\": \"v_z\", \"DIMENSION\": \"L1 T-1\"}], \"CONSTANT\": [{\"NAME\": \"m\", \"DIMENSION\": \"M1\"}], \"LAW\": [{\"NAME\": \"KIN_X\", \"STATEMENT\": \"dx/dt = v_x\", \"REFS\": [\"t\", \"v_x\", \"x\"], \"ROLE\": \"EOM(x)\", \"EQUATION\": \"D(x,t)=v_x\"}, {\"NAME\": \"KIN_Z\", \"STATEMENT\": \"dz/dt = v_z\", \"REFS\": [\"t\", \"v_z\", \"z\"], \"ROLE\": \"CONSTRAINT\", \"EQUATION\": \"D(z,t)=v_z\"}, {\"NAME\": \"EOM_X\", \"STATEMENT\": \"m dv_x/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_x\"], \"ROLE\": \"EOM(v_x)\", \"EQUATION\": \"m*D(v_x,t)=0\"}], \"CONSTRAINT\": [{\"NAME\": \"C_Z\", \"TARGET\": \"z\", \"ACTION\": \"FIX\", \"VALUE\": \"0\", \"UNIT\": \"m\", \"STATEMENT\": \"the puck stays on the table top, z = 0\"}, {\"NAME\": \"C_VZ\", \"TARGET\": \"v_z\", \"ACTION\": \"FIX\", \"VALUE\": \"0\", \"UNIT\": \"m s-1\", \"STATEMENT\": \"the puck has no vertical velocity\"}]}, \"BIND\": {\"HEIGHT\": [\"z\"], \"MASS\": [\"m\"], \"UP_VELOCITY\": [\"v_z\"]}, \"VALUES\": {\"h_max\": {\"VALUE\": \"1\", \"UNIT\": \"m\"}}, \"ANSWERS\": {\"FIXED:v_z\": \"YES\"}}]}",
"{\"ID\": \"MATH\", \"VERSION\": \"1.0.0\", \"TITLE\": \"The mathematical constant pi, as the CONSTANT pi_c\", \"SOURCE\": \"pi to 16 significant digits, 3.141592653589793, the nearest IEEE 754 binary64 value\", \"PREREQUISITES\": [], \"PARAMETERS\": [{\"NAME\": \"pi_c\", \"DIMENSION\": \"1\", \"SUPPLY\": \"DECLARED\", \"VALUE\": \"3.141592653589793\", \"UNIT\": \"1\", \"OVERRIDABLE\": \"NO\", \"LABEL\": \"pi, to 16 significant digits\"}], \"SUMS\": [], \"TERMS\": [], \"ASSUMPTIONS\": [], \"BOUNDARIES\": [], \"NOT_CHOSEN\": \"No mathematical constant: pi exists only if you declare it.\", \"NOT_INCLUDED\": [\"pi_c is pi rounded to 16 significant digits; no other mathematical constant is declared.\"], \"EXCLUDES\": [], \"INTERACTS_WITH\": [], \"TEST_BINDINGS\": [{\"NAME\": \"PROJECTILE_2D\", \"TPK\": {\"DOF\": [{\"NAME\": \"t\", \"DIMENSION\": \"T1\"}, {\"NAME\": \"x\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"z\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"v_x\", \"DIMENSION\": \"L1 T-1\"}, {\"NAME\": \"v_z\", \"DIMENSION\": \"L1 T-1\"}], \"CONSTANT\": [{\"NAME\": \"m\", \"DIMENSION\": \"M1\"}], \"LAW\": [{\"NAME\": \"KIN_X\", \"STATEMENT\": \"dx/dt = v_x\", \"REFS\": [\"t\", \"v_x\", \"x\"], \"ROLE\": \"EOM(x)\", \"EQUATION\": \"D(x,t)=v_x\"}, {\"NAME\": \"KIN_Z\", \"STATEMENT\": \"dz/dt = v_z\", \"REFS\": [\"t\", \"v_z\", \"z\"], \"ROLE\": \"EOM(z)\", \"EQUATION\": \"D(z,t)=v_z\"}, {\"NAME\": \"EOM_X\", \"STATEMENT\": \"m dv_x/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_x\"], \"ROLE\": \"EOM(v_x)\", \"EQUATION\": \"m*D(v_x,t)=0\"}, {\"NAME\": \"EOM_Z\", \"STATEMENT\": \"m dv_z/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_z\"], \"ROLE\": \"EOM(v_z)\", \"EQUATION\": \"m*D(v_z,t)=0\"}], \"ASSUMPTION\": [{\"NAME\": \"point_mass\", \"PROPOSITION\": \"the body is treated as a point mass\", \"REFS\": [\"m\"]}]}, \"BIND\": {}, \"VALUES\": {}, \"ANSWERS\": {}}]}"
]
},
"expected": "[\"REFUSED\",\"ANSWER ROUND 1: not an object\"]",
"fn": "interview_check",
"hand_checked": true,
"name": "I52 a round that is not an object"
},
{
"args": {
"answer": [
{
"AT": 4,
"CHOSEN": "NONE",
"COVERED": [
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[
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],
"NOTE": "x"
}
],
"carried": [],
"claims": [],
"lines": [
{
"ACT": "MODULE ADD",
"DATE": "2026-10-01",
"DIGEST": "5f3fe27b42378bce0830b0d0959f892f4a8e73b12b540ae877e39e6439d08b4d",
"ID": "AIR-LINEAR",
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{
"ACT": "MODULE ADD",
"DATE": "2026-10-01",
"DIGEST": "6fb53c3a6546151eead2bd6e72e9cf8334f3a2040ad0ee2f5b988ec96d6fc852",
"ID": "AIR-QUADRATIC",
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{
"ACT": "MODULE ADD",
"DATE": "2026-10-01",
"DIGEST": "24877ccb5c8ec300d29ed82ce6650592f35cf8899a3d878ccce9c08d4c72c025",
"ID": "GRAV-UNIFORM",
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{
"ACT": "MODULE ADD",
"DATE": "2026-10-01",
"DIGEST": "8f39a356f35527b901fcee012764590f0819c8ffdeccad4bc05195ce3d2e0bcf",
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"{\"ID\": \"AIR-LINEAR\", \"VERSION\": \"1.0.0\", \"TITLE\": \"Air resistance at sea level, linear in the speed (Stokes drag on a sphere)\", \"SOURCE\": \"ISO 2533:1975, Standard Atmosphere, sea-level values: density 1.225 kg m-3, dynamic viscosity 1.7894e-5 Pa s\", \"PREREQUISITES\": [{\"SLOT\": \"VELOCITY\", \"KIND\": \"DOF\", \"DIMENSION\": \"L1 T-1\", \"MIN\": 1, \"MAX\": 3, \"LABEL\": \"the velocity components of the body, one per axis\"}], \"PARAMETERS\": [{\"NAME\": \"rho_air\", \"DIMENSION\": \"L-3 M1\", \"SUPPLY\": \"DECLARED\", \"VALUE\": \"1.225\", \"UNIT\": \"kg m-3\", \"OVERRIDABLE\": \"NO\", \"LABEL\": \"the density of air at sea level\"}, {\"NAME\": \"mu_air\", \"DIMENSION\": \"L-1 M1 T-1\", \"SUPPLY\": \"DECLARED\", \"VALUE\": \"1.7894e-5\", \"UNIT\": \"Pa s\", \"OVERRIDABLE\": \"NO\", \"LABEL\": \"the dynamic viscosity of air at sea level\"}, {\"NAME\": \"pi_c\", \"DIMENSION\": \"1\", \"SUPPLY\": \"DECLARED\", \"VALUE\": \"3.141592653589793\", \"UNIT\": \"1\", \"OVERRIDABLE\": \"NO\", \"LABEL\": \"pi, to 16 significant digits\"}, {\"NAME\": \"R_s\", \"DIMENSION\": \"L1\", \"SUPPLY\": \"AUTHOR\", \"LABEL\": \"the radius of the sphere\"}], \"SUMS\": [{\"NAME\": \"SPEED2\", \"OVER\": \"VELOCITY\", \"EACH\": \"VELOCITY^2\"}], \"TERMS\": [{\"TARGET\": \"VELOCITY\", \"SIGN\": \"-\", \"EXPR\": \"6*pi_c*mu_air*R_s*VELOCITY\", \"LABEL\": \"the linear (Stokes) drag\"}], \"ASSUMPTIONS\": [{\"NAME\": \"air_still\", \"PROPOSITION\": \"the air is at rest in the frame of the body's velocity\", \"REFS\": [\"VELOCITY\"]}, {\"NAME\": \"air_uniform\", \"PROPOSITION\": \"the air density is uniform over the region of motion\", \"REFS\": [\"rho_air\"]}, {\"NAME\": \"drag_sphere\", \"PROPOSITION\": \"the body is a rigid sphere of radius R_s\", \"REFS\": [\"R_s\"]}], \"BOUNDARIES\": [{\"NAME\": \"drag_linear_regime\", \"PREDICATE\": \"2 rho_air |v| R_s / mu_air < 1: the regime of the linear law\", \"CONDITION\": \"mu_air != 0 and SPEED2 >= 0 and 2*rho_air*sqrt(SPEED2)*R_s/mu_air < 1\"}], \"NOT_CHOSEN\": \"No linear (Stokes) air resistance.\", \"NOT_INCLUDED\": [\"No wind: the air is at rest.\", \"No change of air density or viscosity with altitude or temperature.\", \"No drag outside the regime of the linear law.\"], \"EXCLUDES\": [], \"INTERACTS_WITH\": [], \"TEST_BINDINGS\": [{\"NAME\": \"PROJECTILE_2D\", \"TPK\": {\"DOF\": [{\"NAME\": \"t\", \"DIMENSION\": \"T1\"}, {\"NAME\": \"x\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"z\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"v_x\", \"DIMENSION\": \"L1 T-1\"}, {\"NAME\": \"v_z\", \"DIMENSION\": \"L1 T-1\"}], \"CONSTANT\": [{\"NAME\": \"m\", \"DIMENSION\": \"M1\"}], \"LAW\": [{\"NAME\": \"KIN_X\", \"STATEMENT\": \"dx/dt = v_x\", \"REFS\": [\"t\", \"v_x\", \"x\"], \"ROLE\": \"EOM(x)\", \"EQUATION\": \"D(x,t)=v_x\"}, {\"NAME\": \"KIN_Z\", \"STATEMENT\": \"dz/dt = v_z\", \"REFS\": [\"t\", \"v_z\", \"z\"], \"ROLE\": \"EOM(z)\", \"EQUATION\": \"D(z,t)=v_z\"}, {\"NAME\": \"EOM_X\", \"STATEMENT\": \"m dv_x/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_x\"], \"ROLE\": \"EOM(v_x)\", \"EQUATION\": \"m*D(v_x,t)=0\"}, {\"NAME\": \"EOM_Z\", \"STATEMENT\": \"m dv_z/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_z\"], \"ROLE\": \"EOM(v_z)\", \"EQUATION\": \"m*D(v_z,t)=0\"}], \"ASSUMPTION\": [{\"NAME\": \"point_mass\", \"PROPOSITION\": \"the body is treated as a point mass\", \"REFS\": [\"m\"]}]}, \"BIND\": {\"VELOCITY\": [\"v_x\", \"v_z\"]}, \"VALUES\": {\"R_s\": {}}, \"ANSWERS\": {}}]}",
"{\"ID\": \"AIR-QUADRATIC\", \"VERSION\": \"1.0.0\", \"TITLE\": \"Air resistance at sea level, quadratic in the speed\", \"SOURCE\": \"ISO 2533:1975, Standard Atmosphere, sea-level values: density 1.225 kg m-3, dynamic viscosity 1.7894e-5 Pa s\", \"PREREQUISITES\": [{\"SLOT\": \"VELOCITY\", \"KIND\": \"DOF\", \"DIMENSION\": \"L1 T-1\", \"MIN\": 1, \"MAX\": 3, \"LABEL\": \"the velocity components of the body, one per axis\"}], \"PARAMETERS\": [{\"NAME\": \"rho_air\", \"DIMENSION\": \"L-3 M1\", \"SUPPLY\": \"DECLARED\", \"VALUE\": \"1.225\", \"UNIT\": \"kg m-3\", \"OVERRIDABLE\": \"NO\", \"LABEL\": \"the density of air at sea level\"}, {\"NAME\": \"mu_air\", \"DIMENSION\": \"L-1 M1 T-1\", \"SUPPLY\": \"DECLARED\", \"VALUE\": \"1.7894e-5\", \"UNIT\": \"Pa s\", \"OVERRIDABLE\": \"NO\", \"LABEL\": \"the dynamic viscosity of air at sea level\"}, {\"NAME\": \"C_d\", \"DIMENSION\": \"1\", \"SUPPLY\": \"AUTHOR\", \"LABEL\": \"the drag coefficient of the body\"}, {\"NAME\": \"A_ref\", \"DIMENSION\": \"L2\", \"SUPPLY\": \"AUTHOR\", \"LABEL\": \"the reference area of the drag coefficient\"}, {\"NAME\": \"L_ref\", \"DIMENSION\": \"L1\", \"SUPPLY\": \"AUTHOR\", \"LABEL\": \"the reference length of the Reynolds number\"}], \"SUMS\": [{\"NAME\": \"SPEED2\", \"OVER\": \"VELOCITY\", \"EACH\": \"VELOCITY^2\"}], \"TERMS\": [{\"TARGET\": \"VELOCITY\", \"SIGN\": \"-\", \"EXPR\": \"0.5*rho_air*C_d*A_ref*sqrt(SPEED2)*VELOCITY\", \"LABEL\": \"the quadratic drag\"}], \"ASSUMPTIONS\": [{\"NAME\": \"air_still\", \"PROPOSITION\": \"the air is at rest in the frame of the body's velocity\", \"REFS\": [\"VELOCITY\"]}, {\"NAME\": \"air_uniform\", \"PROPOSITION\": \"the air density is uniform over the region of motion\", \"REFS\": [\"rho_air\"]}, {\"NAME\": \"drag_cd_constant\", \"PROPOSITION\": \"the drag coefficient C_d is constant over the motion\", \"REFS\": [\"C_d\"]}, {\"NAME\": \"drag_no_lift\", \"PROPOSITION\": \"the body experiences no lift force\", \"REFS\": [\"VELOCITY\"]}, {\"NAME\": \"drag_no_magnus\", \"PROPOSITION\": \"the body experiences no Magnus force\", \"REFS\": [\"VELOCITY\"]}], \"BOUNDARIES\": [{\"NAME\": \"drag_quadratic_regime\", \"PREDICATE\": \"1e3 < rho_air |v| L_ref / mu_air < 2e5: the Reynolds window of the quadratic law\", \"CONDITION\": \"mu_air != 0 and SPEED2 >= 0 and rho_air*sqrt(SPEED2)*L_ref/mu_air > 1000 and rho_air*sqrt(SPEED2)*L_ref/mu_air < 200000\"}], \"NOT_CHOSEN\": \"No quadratic air resistance.\", \"NOT_INCLUDED\": [\"No wind: the air is at rest.\", \"No change of air density or viscosity with altitude or temperature.\", \"No lift, Magnus or added-mass force.\", \"No drag outside the Reynolds window of the quadratic law.\"], \"EXCLUDES\": [\"AIR-LINEAR\"], \"INTERACTS_WITH\": [], \"TEST_BINDINGS\": [{\"NAME\": \"PROJECTILE_2D\", \"TPK\": {\"DOF\": [{\"NAME\": \"t\", \"DIMENSION\": \"T1\"}, {\"NAME\": \"x\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"z\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"v_x\", \"DIMENSION\": \"L1 T-1\"}, {\"NAME\": \"v_z\", \"DIMENSION\": \"L1 T-1\"}], \"CONSTANT\": [{\"NAME\": \"m\", \"DIMENSION\": \"M1\"}], \"LAW\": [{\"NAME\": \"KIN_X\", \"STATEMENT\": \"dx/dt = v_x\", \"REFS\": [\"t\", \"v_x\", \"x\"], \"ROLE\": \"EOM(x)\", \"EQUATION\": \"D(x,t)=v_x\"}, {\"NAME\": \"KIN_Z\", \"STATEMENT\": \"dz/dt = v_z\", \"REFS\": [\"t\", \"v_z\", \"z\"], \"ROLE\": \"EOM(z)\", \"EQUATION\": \"D(z,t)=v_z\"}, {\"NAME\": \"EOM_X\", \"STATEMENT\": \"m dv_x/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_x\"], \"ROLE\": \"EOM(v_x)\", \"EQUATION\": \"m*D(v_x,t)=0\"}, {\"NAME\": \"EOM_Z\", \"STATEMENT\": \"m dv_z/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_z\"], \"ROLE\": \"EOM(v_z)\", \"EQUATION\": \"m*D(v_z,t)=0\"}], \"ASSUMPTION\": [{\"NAME\": \"point_mass\", \"PROPOSITION\": \"the body is treated as a point mass\", \"REFS\": [\"m\"]}]}, \"BIND\": {\"VELOCITY\": [\"v_x\", \"v_z\"]}, \"VALUES\": {\"A_ref\": {}, \"C_d\": {}, \"L_ref\": {}}, \"ANSWERS\": {}}]}",
"{\"ID\": \"GRAV-UNIFORM\", \"VERSION\": \"1.0.0\", \"TITLE\": \"Uniform gravity at the standard value g_n\", \"SOURCE\": \"g_n = 9.80665 m s-2, exact by definition: 3rd CGPM (1901), declaration on the unit of mass and on the definition of weight\", \"PREREQUISITES\": [{\"SLOT\": \"MASS\", \"KIND\": \"CONSTANT\", \"DIMENSION\": \"M1\", \"MIN\": 1, \"MAX\": 1, \"LABEL\": \"the mass of the body\"}, {\"SLOT\": \"UP_VELOCITY\", \"KIND\": \"DOF\", \"DIMENSION\": \"L1 T-1\", \"MIN\": 1, \"MAX\": 1, \"LABEL\": \"the velocity component pointing up; its equation of motion receives the weight\"}, {\"SLOT\": \"HEIGHT\", \"KIND\": \"DOF\", \"DIMENSION\": \"L1\", \"MIN\": 1, \"MAX\": 1, \"LABEL\": \"the position along the same upward axis\"}], \"PARAMETERS\": [{\"NAME\": \"g_n\", \"DIMENSION\": \"L1 T-2\", \"SUPPLY\": \"DECLARED\", \"VALUE\": \"9.80665\", \"UNIT\": \"m s-2\", \"OVERRIDABLE\": \"NO\", \"LABEL\": \"the standard acceleration of gravity\"}, {\"NAME\": \"h_max\", \"DIMENSION\": \"L1\", \"SUPPLY\": \"AUTHOR\", \"LABEL\": \"the largest height, above or below the origin, over which the field is taken as uniform\"}], \"SUMS\": [], \"TERMS\": [{\"TARGET\": \"UP_VELOCITY\", \"SIGN\": \"-\", \"EXPR\": \"MASS*g_n\", \"LABEL\": \"the weight\"}], \"ASSUMPTIONS\": [{\"NAME\": \"gravity_uniform\", \"PROPOSITION\": \"the gravitational field is uniform over the region abs({HEIGHT}) < h_max\", \"REFS\": [\"HEIGHT\", \"h_max\"]}, {\"NAME\": \"gravity_standard\", \"PROPOSITION\": \"the local gravitational acceleration equals the conventional standard value g_n\", \"REFS\": [\"g_n\"]}, {\"NAME\": \"frame_inertial\", \"PROPOSITION\": \"the frame in which {HEIGHT} is measured is treated as inertial\", \"REFS\": [\"HEIGHT\"]}], \"BOUNDARIES\": [{\"NAME\": \"gravity_region\", \"PREDICATE\": \"abs({HEIGHT}) < h_max\", \"CONDITION\": \"abs(HEIGHT) < h_max\"}], \"NOT_CHOSEN\": \"No gravity: no weight acts on any DOF.\", \"NOT_INCLUDED\": [\"No variation of gravity with height or latitude beyond what g_n contains.\", \"No Earth rotation (Coriolis or centrifugal force) beyond what g_n contains.\", \"No gravity of bodies other than the Earth.\"], \"EXCLUDES\": [], \"INTERACTS_WITH\": [{\"WITH\": \"AIR-*\", \"QUESTION_ID\": \"BUOYANCY\", \"QUESTION\": \"Does the air's buoyancy (upthrust) act on the body in the system you mean?\", \"YES_LINE\": \"Buoyancy acts (your answer): no module adds it; it acts in this kernel only where one of your own laws states it.\", \"NO_LINE\": \"No buoyancy: the air's upthrust on the body is not included.\"}], \"TEST_BINDINGS\": [{\"NAME\": \"PROJECTILE_2D\", \"TPK\": {\"DOF\": [{\"NAME\": \"t\", \"DIMENSION\": \"T1\"}, {\"NAME\": \"x\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"z\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"v_x\", \"DIMENSION\": \"L1 T-1\"}, {\"NAME\": \"v_z\", \"DIMENSION\": \"L1 T-1\"}], \"CONSTANT\": [{\"NAME\": \"m\", \"DIMENSION\": \"M1\"}], \"LAW\": [{\"NAME\": \"KIN_X\", \"STATEMENT\": \"dx/dt = v_x\", \"REFS\": [\"t\", \"v_x\", \"x\"], \"ROLE\": \"EOM(x)\", \"EQUATION\": \"D(x,t)=v_x\"}, {\"NAME\": \"KIN_Z\", \"STATEMENT\": \"dz/dt = v_z\", \"REFS\": [\"t\", \"v_z\", \"z\"], \"ROLE\": \"EOM(z)\", \"EQUATION\": \"D(z,t)=v_z\"}, {\"NAME\": \"EOM_X\", \"STATEMENT\": \"m dv_x/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_x\"], \"ROLE\": \"EOM(v_x)\", \"EQUATION\": \"m*D(v_x,t)=0\"}, {\"NAME\": \"EOM_Z\", \"STATEMENT\": \"m dv_z/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_z\"], \"ROLE\": \"EOM(v_z)\", \"EQUATION\": \"m*D(v_z,t)=0\"}], \"ASSUMPTION\": [{\"NAME\": \"point_mass\", \"PROPOSITION\": \"the body is treated as a point mass\", \"REFS\": [\"m\"]}]}, \"BIND\": {\"HEIGHT\": [\"z\"], \"MASS\": [\"m\"], \"UP_VELOCITY\": [\"v_z\"]}, \"VALUES\": {\"h_max\": {\"VALUE\": \"100\", \"UNIT\": \"m\"}}, \"ANSWERS\": {}}, {\"NAME\": \"TABLE\", \"TPK\": {\"DOF\": [{\"NAME\": \"t\", \"DIMENSION\": \"T1\"}, {\"NAME\": \"x\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"z\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"v_x\", \"DIMENSION\": \"L1 T-1\"}, {\"NAME\": \"v_z\", \"DIMENSION\": \"L1 T-1\"}], \"CONSTANT\": [{\"NAME\": \"m\", \"DIMENSION\": \"M1\"}], \"LAW\": [{\"NAME\": \"KIN_X\", \"STATEMENT\": \"dx/dt = v_x\", \"REFS\": [\"t\", \"v_x\", \"x\"], \"ROLE\": \"EOM(x)\", \"EQUATION\": \"D(x,t)=v_x\"}, {\"NAME\": \"KIN_Z\", \"STATEMENT\": \"dz/dt = v_z\", \"REFS\": [\"t\", \"v_z\", \"z\"], \"ROLE\": \"CONSTRAINT\", \"EQUATION\": \"D(z,t)=v_z\"}, {\"NAME\": \"EOM_X\", \"STATEMENT\": \"m dv_x/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_x\"], \"ROLE\": \"EOM(v_x)\", \"EQUATION\": \"m*D(v_x,t)=0\"}], \"CONSTRAINT\": [{\"NAME\": \"C_Z\", \"TARGET\": \"z\", \"ACTION\": \"FIX\", \"VALUE\": \"0\", \"UNIT\": \"m\", \"STATEMENT\": \"the puck stays on the table top, z = 0\"}, {\"NAME\": \"C_VZ\", \"TARGET\": \"v_z\", \"ACTION\": \"FIX\", \"VALUE\": \"0\", \"UNIT\": \"m s-1\", \"STATEMENT\": \"the puck has no vertical velocity\"}]}, \"BIND\": {\"HEIGHT\": [\"z\"], \"MASS\": [\"m\"], \"UP_VELOCITY\": [\"v_z\"]}, \"VALUES\": {\"h_max\": {\"VALUE\": \"1\", \"UNIT\": \"m\"}}, \"ANSWERS\": {\"FIXED:v_z\": \"YES\"}}]}",
"{\"ID\": \"MATH\", \"VERSION\": \"1.0.0\", \"TITLE\": \"The mathematical constant pi, as the CONSTANT pi_c\", \"SOURCE\": \"pi to 16 significant digits, 3.141592653589793, the nearest IEEE 754 binary64 value\", \"PREREQUISITES\": [], \"PARAMETERS\": [{\"NAME\": \"pi_c\", \"DIMENSION\": \"1\", \"SUPPLY\": \"DECLARED\", \"VALUE\": \"3.141592653589793\", \"UNIT\": \"1\", \"OVERRIDABLE\": \"NO\", \"LABEL\": \"pi, to 16 significant digits\"}], \"SUMS\": [], \"TERMS\": [], \"ASSUMPTIONS\": [], \"BOUNDARIES\": [], \"NOT_CHOSEN\": \"No mathematical constant: pi exists only if you declare it.\", \"NOT_INCLUDED\": [\"pi_c is pi rounded to 16 significant digits; no other mathematical constant is declared.\"], \"EXCLUDES\": [], \"INTERACTS_WITH\": [], \"TEST_BINDINGS\": [{\"NAME\": \"PROJECTILE_2D\", \"TPK\": {\"DOF\": [{\"NAME\": \"t\", \"DIMENSION\": \"T1\"}, {\"NAME\": \"x\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"z\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"v_x\", \"DIMENSION\": \"L1 T-1\"}, {\"NAME\": \"v_z\", \"DIMENSION\": \"L1 T-1\"}], \"CONSTANT\": [{\"NAME\": \"m\", \"DIMENSION\": \"M1\"}], \"LAW\": [{\"NAME\": \"KIN_X\", \"STATEMENT\": \"dx/dt = v_x\", \"REFS\": [\"t\", \"v_x\", \"x\"], \"ROLE\": \"EOM(x)\", \"EQUATION\": \"D(x,t)=v_x\"}, {\"NAME\": \"KIN_Z\", \"STATEMENT\": \"dz/dt = v_z\", \"REFS\": [\"t\", \"v_z\", \"z\"], \"ROLE\": \"EOM(z)\", \"EQUATION\": \"D(z,t)=v_z\"}, {\"NAME\": \"EOM_X\", \"STATEMENT\": \"m dv_x/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_x\"], \"ROLE\": \"EOM(v_x)\", \"EQUATION\": \"m*D(v_x,t)=0\"}, {\"NAME\": \"EOM_Z\", \"STATEMENT\": \"m dv_z/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_z\"], \"ROLE\": \"EOM(v_z)\", \"EQUATION\": \"m*D(v_z,t)=0\"}], \"ASSUMPTION\": [{\"NAME\": \"point_mass\", \"PROPOSITION\": \"the body is treated as a point mass\", \"REFS\": [\"m\"]}]}, \"BIND\": {}, \"VALUES\": {}, \"ANSWERS\": {}}]}"
]
},
"expected": "[\"REFUSED\",\"ANSWER ROUND 1: unknown field NOTE\"]",
"fn": "interview_check",
"hand_checked": true,
"name": "I53 a round with an unknown field"
},
{
"args": {
"answer": [
{
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"claims": [],
"lines": [
{
"ACT": "MODULE ADD",
"DATE": "2026-10-01",
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"ID": "AIR-LINEAR",
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"modules": [
"{\"ID\": \"AIR-LINEAR\", \"VERSION\": \"1.0.0\", \"TITLE\": \"Air resistance at sea level, linear in the speed (Stokes drag on a sphere)\", \"SOURCE\": \"ISO 2533:1975, Standard Atmosphere, sea-level values: density 1.225 kg m-3, dynamic viscosity 1.7894e-5 Pa s\", \"PREREQUISITES\": [{\"SLOT\": \"VELOCITY\", \"KIND\": \"DOF\", \"DIMENSION\": \"L1 T-1\", \"MIN\": 1, \"MAX\": 3, \"LABEL\": \"the velocity components of the body, one per axis\"}], \"PARAMETERS\": [{\"NAME\": \"rho_air\", \"DIMENSION\": \"L-3 M1\", \"SUPPLY\": \"DECLARED\", \"VALUE\": \"1.225\", \"UNIT\": \"kg m-3\", \"OVERRIDABLE\": \"NO\", \"LABEL\": \"the density of air at sea level\"}, {\"NAME\": \"mu_air\", \"DIMENSION\": \"L-1 M1 T-1\", \"SUPPLY\": \"DECLARED\", \"VALUE\": \"1.7894e-5\", \"UNIT\": \"Pa s\", \"OVERRIDABLE\": \"NO\", \"LABEL\": \"the dynamic viscosity of air at sea level\"}, {\"NAME\": \"pi_c\", \"DIMENSION\": \"1\", \"SUPPLY\": \"DECLARED\", \"VALUE\": \"3.141592653589793\", \"UNIT\": \"1\", \"OVERRIDABLE\": \"NO\", \"LABEL\": \"pi, to 16 significant digits\"}, {\"NAME\": \"R_s\", \"DIMENSION\": \"L1\", \"SUPPLY\": \"AUTHOR\", \"LABEL\": \"the radius of the sphere\"}], \"SUMS\": [{\"NAME\": \"SPEED2\", \"OVER\": \"VELOCITY\", \"EACH\": \"VELOCITY^2\"}], \"TERMS\": [{\"TARGET\": \"VELOCITY\", \"SIGN\": \"-\", \"EXPR\": \"6*pi_c*mu_air*R_s*VELOCITY\", \"LABEL\": \"the linear (Stokes) drag\"}], \"ASSUMPTIONS\": [{\"NAME\": \"air_still\", \"PROPOSITION\": \"the air is at rest in the frame of the body's velocity\", \"REFS\": [\"VELOCITY\"]}, {\"NAME\": \"air_uniform\", \"PROPOSITION\": \"the air density is uniform over the region of motion\", \"REFS\": [\"rho_air\"]}, {\"NAME\": \"drag_sphere\", \"PROPOSITION\": \"the body is a rigid sphere of radius R_s\", \"REFS\": [\"R_s\"]}], \"BOUNDARIES\": [{\"NAME\": \"drag_linear_regime\", \"PREDICATE\": \"2 rho_air |v| R_s / mu_air < 1: the regime of the linear law\", \"CONDITION\": \"mu_air != 0 and SPEED2 >= 0 and 2*rho_air*sqrt(SPEED2)*R_s/mu_air < 1\"}], \"NOT_CHOSEN\": \"No linear (Stokes) air resistance.\", \"NOT_INCLUDED\": [\"No wind: the air is at rest.\", \"No change of air density or viscosity with altitude or temperature.\", \"No drag outside the regime of the linear law.\"], \"EXCLUDES\": [], \"INTERACTS_WITH\": [], \"TEST_BINDINGS\": [{\"NAME\": \"PROJECTILE_2D\", \"TPK\": {\"DOF\": [{\"NAME\": \"t\", \"DIMENSION\": \"T1\"}, {\"NAME\": \"x\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"z\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"v_x\", \"DIMENSION\": \"L1 T-1\"}, {\"NAME\": \"v_z\", \"DIMENSION\": \"L1 T-1\"}], \"CONSTANT\": [{\"NAME\": \"m\", \"DIMENSION\": \"M1\"}], \"LAW\": [{\"NAME\": \"KIN_X\", \"STATEMENT\": \"dx/dt = v_x\", \"REFS\": [\"t\", \"v_x\", \"x\"], \"ROLE\": \"EOM(x)\", \"EQUATION\": \"D(x,t)=v_x\"}, {\"NAME\": \"KIN_Z\", \"STATEMENT\": \"dz/dt = v_z\", \"REFS\": [\"t\", \"v_z\", \"z\"], \"ROLE\": \"EOM(z)\", \"EQUATION\": \"D(z,t)=v_z\"}, {\"NAME\": \"EOM_X\", \"STATEMENT\": \"m dv_x/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_x\"], \"ROLE\": \"EOM(v_x)\", \"EQUATION\": \"m*D(v_x,t)=0\"}, {\"NAME\": \"EOM_Z\", \"STATEMENT\": \"m dv_z/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_z\"], \"ROLE\": \"EOM(v_z)\", \"EQUATION\": \"m*D(v_z,t)=0\"}], \"ASSUMPTION\": [{\"NAME\": \"point_mass\", \"PROPOSITION\": \"the body is treated as a point mass\", \"REFS\": [\"m\"]}]}, \"BIND\": {\"VELOCITY\": [\"v_x\", \"v_z\"]}, \"VALUES\": {\"R_s\": {}}, \"ANSWERS\": {}}]}",
"{\"ID\": \"AIR-QUADRATIC\", \"VERSION\": \"1.0.0\", \"TITLE\": \"Air resistance at sea level, quadratic in the speed\", \"SOURCE\": \"ISO 2533:1975, Standard Atmosphere, sea-level values: density 1.225 kg m-3, dynamic viscosity 1.7894e-5 Pa s\", \"PREREQUISITES\": [{\"SLOT\": \"VELOCITY\", \"KIND\": \"DOF\", \"DIMENSION\": \"L1 T-1\", \"MIN\": 1, \"MAX\": 3, \"LABEL\": \"the velocity components of the body, one per axis\"}], \"PARAMETERS\": [{\"NAME\": \"rho_air\", \"DIMENSION\": \"L-3 M1\", \"SUPPLY\": \"DECLARED\", \"VALUE\": \"1.225\", \"UNIT\": \"kg m-3\", \"OVERRIDABLE\": \"NO\", \"LABEL\": \"the density of air at sea level\"}, {\"NAME\": \"mu_air\", \"DIMENSION\": \"L-1 M1 T-1\", \"SUPPLY\": \"DECLARED\", \"VALUE\": \"1.7894e-5\", \"UNIT\": \"Pa s\", \"OVERRIDABLE\": \"NO\", \"LABEL\": \"the dynamic viscosity of air at sea level\"}, {\"NAME\": \"C_d\", \"DIMENSION\": \"1\", \"SUPPLY\": \"AUTHOR\", \"LABEL\": \"the drag coefficient of the body\"}, {\"NAME\": \"A_ref\", \"DIMENSION\": \"L2\", \"SUPPLY\": \"AUTHOR\", \"LABEL\": \"the reference area of the drag coefficient\"}, {\"NAME\": \"L_ref\", \"DIMENSION\": \"L1\", \"SUPPLY\": \"AUTHOR\", \"LABEL\": \"the reference length of the Reynolds number\"}], \"SUMS\": [{\"NAME\": \"SPEED2\", \"OVER\": \"VELOCITY\", \"EACH\": \"VELOCITY^2\"}], \"TERMS\": [{\"TARGET\": \"VELOCITY\", \"SIGN\": \"-\", \"EXPR\": \"0.5*rho_air*C_d*A_ref*sqrt(SPEED2)*VELOCITY\", \"LABEL\": \"the quadratic drag\"}], \"ASSUMPTIONS\": [{\"NAME\": \"air_still\", \"PROPOSITION\": \"the air is at rest in the frame of the body's velocity\", \"REFS\": [\"VELOCITY\"]}, {\"NAME\": \"air_uniform\", \"PROPOSITION\": \"the air density is uniform over the region of motion\", \"REFS\": [\"rho_air\"]}, {\"NAME\": \"drag_cd_constant\", \"PROPOSITION\": \"the drag coefficient C_d is constant over the motion\", \"REFS\": [\"C_d\"]}, {\"NAME\": \"drag_no_lift\", \"PROPOSITION\": \"the body experiences no lift force\", \"REFS\": [\"VELOCITY\"]}, {\"NAME\": \"drag_no_magnus\", \"PROPOSITION\": \"the body experiences no Magnus force\", \"REFS\": [\"VELOCITY\"]}], \"BOUNDARIES\": [{\"NAME\": \"drag_quadratic_regime\", \"PREDICATE\": \"1e3 < rho_air |v| L_ref / mu_air < 2e5: the Reynolds window of the quadratic law\", \"CONDITION\": \"mu_air != 0 and SPEED2 >= 0 and rho_air*sqrt(SPEED2)*L_ref/mu_air > 1000 and rho_air*sqrt(SPEED2)*L_ref/mu_air < 200000\"}], \"NOT_CHOSEN\": \"No quadratic air resistance.\", \"NOT_INCLUDED\": [\"No wind: the air is at rest.\", \"No change of air density or viscosity with altitude or temperature.\", \"No lift, Magnus or added-mass force.\", \"No drag outside the Reynolds window of the quadratic law.\"], \"EXCLUDES\": [\"AIR-LINEAR\"], \"INTERACTS_WITH\": [], \"TEST_BINDINGS\": [{\"NAME\": \"PROJECTILE_2D\", \"TPK\": {\"DOF\": [{\"NAME\": \"t\", \"DIMENSION\": \"T1\"}, {\"NAME\": \"x\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"z\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"v_x\", \"DIMENSION\": \"L1 T-1\"}, {\"NAME\": \"v_z\", \"DIMENSION\": \"L1 T-1\"}], \"CONSTANT\": [{\"NAME\": \"m\", \"DIMENSION\": \"M1\"}], \"LAW\": [{\"NAME\": \"KIN_X\", \"STATEMENT\": \"dx/dt = v_x\", \"REFS\": [\"t\", \"v_x\", \"x\"], \"ROLE\": \"EOM(x)\", \"EQUATION\": \"D(x,t)=v_x\"}, {\"NAME\": \"KIN_Z\", \"STATEMENT\": \"dz/dt = v_z\", \"REFS\": [\"t\", \"v_z\", \"z\"], \"ROLE\": \"EOM(z)\", \"EQUATION\": \"D(z,t)=v_z\"}, {\"NAME\": \"EOM_X\", \"STATEMENT\": \"m dv_x/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_x\"], \"ROLE\": \"EOM(v_x)\", \"EQUATION\": \"m*D(v_x,t)=0\"}, {\"NAME\": \"EOM_Z\", \"STATEMENT\": \"m dv_z/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_z\"], \"ROLE\": \"EOM(v_z)\", \"EQUATION\": \"m*D(v_z,t)=0\"}], \"ASSUMPTION\": [{\"NAME\": \"point_mass\", \"PROPOSITION\": \"the body is treated as a point mass\", \"REFS\": [\"m\"]}]}, \"BIND\": {\"VELOCITY\": [\"v_x\", \"v_z\"]}, \"VALUES\": {\"A_ref\": {}, \"C_d\": {}, \"L_ref\": {}}, \"ANSWERS\": {}}]}",
"{\"ID\": \"GRAV-UNIFORM\", \"VERSION\": \"1.0.0\", \"TITLE\": \"Uniform gravity at the standard value g_n\", \"SOURCE\": \"g_n = 9.80665 m s-2, exact by definition: 3rd CGPM (1901), declaration on the unit of mass and on the definition of weight\", \"PREREQUISITES\": [{\"SLOT\": \"MASS\", \"KIND\": \"CONSTANT\", \"DIMENSION\": \"M1\", \"MIN\": 1, \"MAX\": 1, \"LABEL\": \"the mass of the body\"}, {\"SLOT\": \"UP_VELOCITY\", \"KIND\": \"DOF\", \"DIMENSION\": \"L1 T-1\", \"MIN\": 1, \"MAX\": 1, \"LABEL\": \"the velocity component pointing up; its equation of motion receives the weight\"}, {\"SLOT\": \"HEIGHT\", \"KIND\": \"DOF\", \"DIMENSION\": \"L1\", \"MIN\": 1, \"MAX\": 1, \"LABEL\": \"the position along the same upward axis\"}], \"PARAMETERS\": [{\"NAME\": \"g_n\", \"DIMENSION\": \"L1 T-2\", \"SUPPLY\": \"DECLARED\", \"VALUE\": \"9.80665\", \"UNIT\": \"m s-2\", \"OVERRIDABLE\": \"NO\", \"LABEL\": \"the standard acceleration of gravity\"}, {\"NAME\": \"h_max\", \"DIMENSION\": \"L1\", \"SUPPLY\": \"AUTHOR\", \"LABEL\": \"the largest height, above or below the origin, over which the field is taken as uniform\"}], \"SUMS\": [], \"TERMS\": [{\"TARGET\": \"UP_VELOCITY\", \"SIGN\": \"-\", \"EXPR\": \"MASS*g_n\", \"LABEL\": \"the weight\"}], \"ASSUMPTIONS\": [{\"NAME\": \"gravity_uniform\", \"PROPOSITION\": \"the gravitational field is uniform over the region abs({HEIGHT}) < h_max\", \"REFS\": [\"HEIGHT\", \"h_max\"]}, {\"NAME\": \"gravity_standard\", \"PROPOSITION\": \"the local gravitational acceleration equals the conventional standard value g_n\", \"REFS\": [\"g_n\"]}, {\"NAME\": \"frame_inertial\", \"PROPOSITION\": \"the frame in which {HEIGHT} is measured is treated as inertial\", \"REFS\": [\"HEIGHT\"]}], \"BOUNDARIES\": [{\"NAME\": \"gravity_region\", \"PREDICATE\": \"abs({HEIGHT}) < h_max\", \"CONDITION\": \"abs(HEIGHT) < h_max\"}], \"NOT_CHOSEN\": \"No gravity: no weight acts on any DOF.\", \"NOT_INCLUDED\": [\"No variation of gravity with height or latitude beyond what g_n contains.\", \"No Earth rotation (Coriolis or centrifugal force) beyond what g_n contains.\", \"No gravity of bodies other than the Earth.\"], \"EXCLUDES\": [], \"INTERACTS_WITH\": [{\"WITH\": \"AIR-*\", \"QUESTION_ID\": \"BUOYANCY\", \"QUESTION\": \"Does the air's buoyancy (upthrust) act on the body in the system you mean?\", \"YES_LINE\": \"Buoyancy acts (your answer): no module adds it; it acts in this kernel only where one of your own laws states it.\", \"NO_LINE\": \"No buoyancy: the air's upthrust on the body is not included.\"}], \"TEST_BINDINGS\": [{\"NAME\": \"PROJECTILE_2D\", \"TPK\": {\"DOF\": [{\"NAME\": \"t\", \"DIMENSION\": \"T1\"}, {\"NAME\": \"x\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"z\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"v_x\", \"DIMENSION\": \"L1 T-1\"}, {\"NAME\": \"v_z\", \"DIMENSION\": \"L1 T-1\"}], \"CONSTANT\": [{\"NAME\": \"m\", \"DIMENSION\": \"M1\"}], \"LAW\": [{\"NAME\": \"KIN_X\", \"STATEMENT\": \"dx/dt = v_x\", \"REFS\": [\"t\", \"v_x\", \"x\"], \"ROLE\": \"EOM(x)\", \"EQUATION\": \"D(x,t)=v_x\"}, {\"NAME\": \"KIN_Z\", \"STATEMENT\": \"dz/dt = v_z\", \"REFS\": [\"t\", \"v_z\", \"z\"], \"ROLE\": \"EOM(z)\", \"EQUATION\": \"D(z,t)=v_z\"}, {\"NAME\": \"EOM_X\", \"STATEMENT\": \"m dv_x/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_x\"], \"ROLE\": \"EOM(v_x)\", \"EQUATION\": \"m*D(v_x,t)=0\"}, {\"NAME\": \"EOM_Z\", \"STATEMENT\": \"m dv_z/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_z\"], \"ROLE\": \"EOM(v_z)\", \"EQUATION\": \"m*D(v_z,t)=0\"}], \"ASSUMPTION\": [{\"NAME\": \"point_mass\", \"PROPOSITION\": \"the body is treated as a point mass\", \"REFS\": [\"m\"]}]}, \"BIND\": {\"HEIGHT\": [\"z\"], \"MASS\": [\"m\"], \"UP_VELOCITY\": [\"v_z\"]}, \"VALUES\": {\"h_max\": {\"VALUE\": \"100\", \"UNIT\": \"m\"}}, \"ANSWERS\": {}}, {\"NAME\": \"TABLE\", \"TPK\": {\"DOF\": [{\"NAME\": \"t\", \"DIMENSION\": \"T1\"}, {\"NAME\": \"x\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"z\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"v_x\", \"DIMENSION\": \"L1 T-1\"}, {\"NAME\": \"v_z\", \"DIMENSION\": \"L1 T-1\"}], \"CONSTANT\": [{\"NAME\": \"m\", \"DIMENSION\": \"M1\"}], \"LAW\": [{\"NAME\": \"KIN_X\", \"STATEMENT\": \"dx/dt = v_x\", \"REFS\": [\"t\", \"v_x\", \"x\"], \"ROLE\": \"EOM(x)\", \"EQUATION\": \"D(x,t)=v_x\"}, {\"NAME\": \"KIN_Z\", \"STATEMENT\": \"dz/dt = v_z\", \"REFS\": [\"t\", \"v_z\", \"z\"], \"ROLE\": \"CONSTRAINT\", \"EQUATION\": \"D(z,t)=v_z\"}, {\"NAME\": \"EOM_X\", \"STATEMENT\": \"m dv_x/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_x\"], \"ROLE\": \"EOM(v_x)\", \"EQUATION\": \"m*D(v_x,t)=0\"}], \"CONSTRAINT\": [{\"NAME\": \"C_Z\", \"TARGET\": \"z\", \"ACTION\": \"FIX\", \"VALUE\": \"0\", \"UNIT\": \"m\", \"STATEMENT\": \"the puck stays on the table top, z = 0\"}, {\"NAME\": \"C_VZ\", \"TARGET\": \"v_z\", \"ACTION\": \"FIX\", \"VALUE\": \"0\", \"UNIT\": \"m s-1\", \"STATEMENT\": \"the puck has no vertical velocity\"}]}, \"BIND\": {\"HEIGHT\": [\"z\"], \"MASS\": [\"m\"], \"UP_VELOCITY\": [\"v_z\"]}, \"VALUES\": {\"h_max\": {\"VALUE\": \"1\", \"UNIT\": \"m\"}}, \"ANSWERS\": {\"FIXED:v_z\": \"YES\"}}]}",
"{\"ID\": \"MATH\", \"VERSION\": \"1.0.0\", \"TITLE\": \"The mathematical constant pi, as the CONSTANT pi_c\", \"SOURCE\": \"pi to 16 significant digits, 3.141592653589793, the nearest IEEE 754 binary64 value\", \"PREREQUISITES\": [], \"PARAMETERS\": [{\"NAME\": \"pi_c\", \"DIMENSION\": \"1\", \"SUPPLY\": \"DECLARED\", \"VALUE\": \"3.141592653589793\", \"UNIT\": \"1\", \"OVERRIDABLE\": \"NO\", \"LABEL\": \"pi, to 16 significant digits\"}], \"SUMS\": [], \"TERMS\": [], \"ASSUMPTIONS\": [], \"BOUNDARIES\": [], \"NOT_CHOSEN\": \"No mathematical constant: pi exists only if you declare it.\", \"NOT_INCLUDED\": [\"pi_c is pi rounded to 16 significant digits; no other mathematical constant is declared.\"], \"EXCLUDES\": [], \"INTERACTS_WITH\": [], \"TEST_BINDINGS\": [{\"NAME\": \"PROJECTILE_2D\", \"TPK\": {\"DOF\": [{\"NAME\": \"t\", \"DIMENSION\": \"T1\"}, {\"NAME\": \"x\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"z\", \"DIMENSION\": \"L1\"}, {\"NAME\": \"v_x\", \"DIMENSION\": \"L1 T-1\"}, {\"NAME\": \"v_z\", \"DIMENSION\": \"L1 T-1\"}], \"CONSTANT\": [{\"NAME\": \"m\", \"DIMENSION\": \"M1\"}], \"LAW\": [{\"NAME\": \"KIN_X\", \"STATEMENT\": \"dx/dt = v_x\", \"REFS\": [\"t\", \"v_x\", \"x\"], \"ROLE\": \"EOM(x)\", \"EQUATION\": \"D(x,t)=v_x\"}, {\"NAME\": \"KIN_Z\", \"STATEMENT\": \"dz/dt = v_z\", \"REFS\": [\"t\", \"v_z\", \"z\"], \"ROLE\": \"EOM(z)\", \"EQUATION\": \"D(z,t)=v_z\"}, {\"NAME\": \"EOM_X\", \"STATEMENT\": \"m dv_x/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_x\"], \"ROLE\": \"EOM(v_x)\", \"EQUATION\": \"m*D(v_x,t)=0\"}, {\"NAME\": \"EOM_Z\", \"STATEMENT\": \"m dv_z/dt = 0\", \"REFS\": [\"m\", \"t\", \"v_z\"], \"ROLE\": \"EOM(v_z)\", \"EQUATION\": \"m*D(v_z,t)=0\"}], \"ASSUMPTION\": [{\"NAME\": \"point_mass\", \"PROPOSITION\": \"the body is treated as a point mass\", \"REFS\": [\"m\"]}]}, \"BIND\": {}, \"VALUES\": {}, \"ANSWERS\": {}}]}"
]
},
"expected": "[\"REFUSED\",\"ANSWER ROUND 1: missing field CHOSEN\"]",
"fn": "interview_check",
"hand_checked": true,
"name": "I54 a round without CHOSEN"
},
{
"args": {
"answer": [