The Principia Machina/Inputs/Translation Manifold - Revision history

BFP Rauch: 1 revision imported

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DeltaS Zero: G-1 (outside AI session 2): the lead's last sentence now says where the agent-facing page is and addresses no one (base revision 4629)

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	{{TPM map}}		{{TPM map}}
	{{DISPLAYTITLE:Inputs: the Translation Manifold (TrM)}}		{{DISPLAYTITLE:Inputs: the Translation Manifold (TrM)}}
	''Public Recorder inputs: a help set for the people who put things into The Principia Machina - authors of a new UWC, operators, and the declaring authority. It explains; the specification governs. Start at [[The Principia Machina/Inputs\|the index]]; for a guided walk from a blank file to a declared UWC, follow [[The Principia Machina/Tutorial\|the tutorial]]. ~~Agents read~~ [[The Principia Machina/Agent/Inputs\|the agent-facing page]] ~~instead~~.''		''Public Recorder inputs: a help set for the people who put things into The Principia Machina - authors of a new UWC, operators, and the declaring authority. It explains; the specification governs. Start at [[The Principia Machina/Inputs\|the index]]; for a guided walk from a blank file to a declared UWC, follow [[The Principia Machina/Tutorial\|the tutorial]]. Its counterpart for agents is [[The Principia Machina/Agent/Inputs\|the agent-facing page]].''

	== Purpose ==		== Purpose ==

DeltaS Zero: Post-TPC-PY page batch (S70): HF; S61 FIXUP

2026-09-29T02:11:00Z

Post-TPC-PY page batch (S70): HF; S61 FIXUP

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	What you write in the second zone: the header, then the entries that tie each degree of freedom (DOF) to a quantity of the environment.		What you write in the second zone: the header, then the entries that tie each degree of freedom (DOF) to a quantity of the environment.

	''Explains: ~~TPS revision 6 (proposed as~~ TPS 0.3.0 ~~until the declaring authority declares it~~; it follows TPS 0.1.1, declared final on 2026-09-26), whose sections 2.2 to 2.5 carry the zone schemas with the optional declared form, the ROLE field, the D variable and the structure check (records D92.1, D98.1, D99.1, D100.1, D103.1-D105.1, D106.1-D108.1, D132.1, D176.1, D177.1, D179.1 and D186.1); TPC-PY ~~as built at increment 10~~ (tpc_zone 0.5.0, tpc_units 0.1.1, tpc_tests 0.2.0, tpc_form 0.2.0, tpc_eom 0.1.0; schema 0.5.0~~; no TPC-PY version is declared yet~~) with check_draft 0.5.0; Generic Specification Guide 0.1.0, sections 4.2 to 4.6 and C4. Where this page and the specification differ, the specification governs.''		''Explains: TPS 0.3.0 (declared final on 2026-09-28 at revision 6; it follows TPS 0.1.1, declared final on 2026-09-26), whose sections 2.2 to 2.5 carry the zone schemas with the optional declared form, the ROLE field, the D variable and the structure check (records D92.1, D98.1, D99.1, D100.1, D103.1-D105.1, D106.1-D108.1, D132.1, D176.1, D177.1, D179.1 and D186.1); [[The Principia Machina/TPC-PY\|TPC-PY 0.1.0]] (declared on 2026-09-28, tree digest a00161c1b321fd66abc591209007d46a7fa6290097835060e50f381426259043, conformed TPS 0.3.0; tpc_zone 0.5.0, tpc_units 0.1.1, tpc_tests 0.2.0, tpc_form 0.2.0, tpc_eom 0.1.0; schema 0.5.0) with check_draft 0.5.0; Generic Specification Guide 0.1.0, sections 4.2 to 4.6 and C4. Where this page and the specification differ, the specification governs.''

	== What the Translation Manifold is ==		== What the Translation Manifold is ==
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	== The checks ==		== The checks ==
	The '''~~structure~~ check''' runs first: parts present, fields present and of the right type, every DOF in an entry or a SIGNATURE is a kernel DOF, every ENVIRONMENT_QUANTITY is in the inventory, every BEARS name is a kernel LAW or CONSTRAINT, no duplicate names, and a SIGNATURE's FORM and IMAGE_FORM, where present, both present and parsed.		The '''structural check''' runs first: parts present, fields present and of the right type, every DOF in an entry or a SIGNATURE is a kernel DOF, every ENVIRONMENT_QUANTITY is in the inventory, every BEARS name is a kernel LAW or CONSTRAINT, no duplicate names, and a SIGNATURE's FORM and IMAGE_FORM, where present, both present and parsed.

	If the manifold and the kernel both pass their ~~structure~~ checks, the isomorphism checks run as the zone is entered ([[The Principia Machina/TPS/2.3 The Translation Manifold\|TPS 2.3]]). They map onto '''the kernel's DOF less those a REMOVE constraint takes out''' (record D107.1). A DOF that a FIX constraint pins stays in: it still needs an entry, and that entry may bear the constraint. A removed DOF must have no entry. The time t, declared as a DOF, needs an entry like any other.		If the manifold and the kernel both pass their structural checks, the isomorphism checks run as the zone is entered ([[The Principia Machina/TPS/2.3 The Translation Manifold\|TPS 2.3]]). They map onto '''the kernel's DOF less those a REMOVE constraint takes out''' (record D107.1). A DOF that a FIX constraint pins stays in: it still needs an entry, and that entry may bear the constraint. A removed DOF must have no entry. The time t, declared as a DOF, needs an entry like any other.
	* '''IC1 TOTAL''': every environment quantity is identified by some entry. Failure refuses the manifold.		* '''IC1 TOTAL''': every environment quantity is identified by some entry. Failure refuses the manifold.
	* '''IC2 SURJECTIVE''': every DOF, counted as above, is some entry's DOF. A DOF no entry reaches is an '''untied DOF'''. It is held as a named gap, and at the final pass the Measure Set's IC2_POLICY decides: GAP, the default, admits the manifold with the gap named; REJECT refuses it.		* '''IC2 SURJECTIVE''': every DOF, counted as above, is some entry's DOF. A DOF no entry reaches is an '''untied DOF'''. It is held as a named gap, and at the final pass the Measure Set's IC2_POLICY decides: GAP, the default, admits the manifold with the gap named; REJECT refuses it.

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DeltaS Zero: Second help pass (HELP-PASS-2): agent D's draft: its PENDING lines closed and D176.1-D190.1 applied; every quoted output re-printed from the increment-10 tree (S10)

2026-09-28T03:55:00Z

Second help pass (HELP-PASS-2): agent D's draft: its PENDING lines closed and D176.1-D190.1 applied; every quoted output re-printed from the increment-10 tree (S10)

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	What you write in the second zone: the header, then the entries that tie each degree of freedom (DOF) to a quantity of the environment.		What you write in the second zone: the header, then the entries that tie each degree of freedom (DOF) to a quantity of the environment.

	''Explains: TPS 0.2.0 ~~(proposed; revision 5 of~~ the ~~tree, imported 2026-09-26, not yet declared~~; TPS 0.1.~~0 was~~ declared final on 2026-09-22), whose sections 2.2 to 2.5 ~~now~~ carry the zone schemas ~~at schema 0.4.0~~ with the optional declared form (records D92.1, D98.1, D99.1, D100.1, D103.1-D105.1, D106.1-D108.1 and ~~D132~~.1); TPC-PY as built at increment 9 (tpc_zone 0.4.0, tpc_units 0.1.0, tpc_tests 0.2.0, tpc_form 0.1.0; no TPC-PY version is declared yet) with check_draft 0.4.0; Generic Specification Guide 0.1.0, sections 4.2 to 4.6 and C4. Where this page and the specification differ, the specification governs.''		''Explains: TPS revision 6 (proposed as TPS 0.3.0 until the declaring authority declares it; it follows TPS 0.1.1, declared final on 2026-09-26), whose sections 2.2 to 2.5 carry the zone schemas with the optional declared form, the ROLE field, the D variable and the structure check (records D92.1, D98.1, D99.1, D100.1, D103.1-D105.1, D106.1-D108.1, D132.1, D176.1, D177.1, D179.1 and D186.1); TPC-PY as built at increment 10 (tpc_zone 0.5.0, tpc_units 0.1.1, tpc_tests 0.2.0, tpc_form 0.2.0, tpc_eom 0.1.0; schema 0.5.0; no TPC-PY version is declared yet) with check_draft 0.5.0; Generic Specification Guide 0.1.0, sections 4.2 to 4.6 and C4. Where this page and the specification differ, the specification governs.''

	== What the Translation Manifold is ==		== What the Translation Manifold is ==

DeltaS Zero: Help batch (D185.1 (d)): the tutorial and inputs redraft of 2026-09-26 with its PENDING lines (items D176-D181 open); abbreviations expanded at first use (the user's directive, 2026-09-26)

2026-09-27T01:00:22Z

Help batch (D185.1 (d)): the tutorial and inputs redraft of 2026-09-26 with its PENDING lines (items D176-D181 open); abbreviations expanded at first use (the user's directive, 2026-09-26)

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BFP Rauch: help set: TrM input, schema 0.3.0

2026-09-23T01:06:19Z

help set: TrM input, schema 0.3.0

New page

{{TPM map}}
{{DISPLAYTITLE:Inputs: the Translation Manifold (TrM)}}
''Public Recorder inputs: a help set for the people who put things into The Principia Machina - authors of a new UWC, operators, and the declaring authority. It explains; the specification governs. Start at [[The Principia Machina/Inputs|the index]]; for a guided walk from a blank file to a declared UWC, follow [[The Principia Machina/Tutorial|the tutorial]]. Agents read [[The Principia Machina/Agent/Inputs|the agent-facing page]] instead.''

== Purpose ==
What you write in the second zone: the header, then the entries that tie each degree of freedom to a quantity of the environment.

''Explains: TPS 0.1.0, revision 4 (declared final 2026-09-22); the zone schemas the declaring authority selected on 2026-09-22 (records D92.1, D98.1, D99.1, D100.1, and for units D103.1, D104.1, D105.1; schema 0.3.0), whose text enters TPS at revision 5, and the kernel tests and isomorphism checks selected the same day (D106.1, D107.1, D108.1; tpm_kernel_tests 0.2.0), whose text follows at the next TPS revision; TPC-PY as built 2026-09-22 (tpc_zone 0.3.0, tpc_units 0.1.0, tpc_tests 0.1.0; no TPC-PY version is declared yet) with check_draft 0.3.0; Generic Specification Guide 0.1.0, sections 4.2 to 4.6 and C4. Where this page and the specification differ, the specification governs.''

== What the Translation Manifold is ==
The Translation Manifold (TrM) says what each DOF of the kernel ''is'' in the environment the kernel describes - which measurable quantity x is, for example. Every entry must be an isomorphism: nothing lost, nothing merged, structure kept. Its header and every entry are immutable once declared ([[The Principia Machina/TPS/2.1 The Full Kernel and immutability|TPS 2.1]] and [[The Principia Machina/TPS/2.3 The Translation Manifold|2.3]]).

== Two parts: HEADER and ENTRIES ==
Both are required. The header is entered first.

=== The header ===
; ENVIRONMENT_INVENTORY
: The quantities of the environment, each an object with <code>ENVIRONMENT_QUANTITY</code> (an identifier, unique in the inventory) and <code>DIMENSION</code>.
; SIGNATURE
: The relations and operations on the DOF that the map must carry, each with <code>NAME</code>, <code>OVER</code> (the list of DOF it acts on) and <code>IMAGE</code> (prose: what it becomes in the environment).
; TRANSFORMATIONS
: The re-representations under which an identification stays the same identification - a change of units, a shift of the time origin - each with <code>NAME</code> and <code>STATEMENT</code>. Two identifications related by a transformation count as one.

=== Each entry ===
All nine fields are required.
{| class="wikitable"
! Field !! What it holds
|-
| NAME || an identifier, unique among entries. A measured register record names this entry as its QUANTITY.
|-
| DOF || the kernel DOF this entry identifies
|-
| DOMAIN || prose: where the identification holds. Not blank.
|-
| ENVIRONMENT_QUANTITY || the inventory quantity the DOF is
|-
| IDENTIFICATION || prose: the identification itself
|-
| FALSIFIER || prose: what observation or derivation would show the identification false. Not blank.
|-
| FALSIFIER_CLASS || how severe that falsifier is: F1, F2 or F3 (below)
|-
| BEARS || the kernel LAW and CONSTRAINT names the entry carries into the environment
|-
| DIMENSION || the dimension of the identified quantity
|}
The field is called ENVIRONMENT_QUANTITY, not QUANTITY, because in TPM "QUANTITY" already names something else: the TrM entry a measured record's value belongs to. One word, one meaning.

== Falsifier classes ==
From the Generic Specification Guide, C4:
* '''F0''', no falsifier: not admitted. The entry is malformed.
* '''F1''', nominal: shown false only by an error in the author's own computation. Re-derivation is the test.
* '''F2''', independent: a second party can evaluate it from the record's fields alone, without the author's steps. Independent reproduction is the test.
* '''F3''', external: it names an external quantity with stated uncertainty that a measurement or an outside source could contradict.
The class also matters later: a result is promoted only when its falsifier reaches the UWC's promotion floor, which the Measure Set declares ([[The Principia Machina/Inputs/Measure Set|Measure Set]]).

== The checks ==
The '''structure check''' runs first: parts present, fields present and of the right type, every DOF in an entry or a SIGNATURE is a kernel DOF, every ENVIRONMENT_QUANTITY is in the inventory, every BEARS name is a kernel LAW or CONSTRAINT, no duplicate names.

If the manifold and the kernel both pass their structure checks, the four isomorphism checks run as the zone is entered ([[The Principia Machina/TPS/2.3 The Translation Manifold|TPS 2.3]]; tpm_kernel_tests 0.2.0). They map onto '''the kernel's DOF less those a REMOVE constraint takes out''' (record D107.1). A DOF that a FIX constraint pins stays in: it still needs an entry, and that entry may bear the constraint. A removed DOF must have no entry.
* '''IC1 TOTAL''': every environment quantity is identified by some entry. Failure refuses the manifold.
* '''IC2 SURJECTIVE''': every DOF, counted as above, is some entry's DOF. A DOF no entry reaches is an '''untied DOF'''. It is held as a named gap, and at the final pass the Measure Set's IC2_POLICY decides: GAP, the default, admits the manifold with the gap named; REJECT refuses it.
* '''IC3 INJECTIVE''': no DOF is identified with two environment quantities, and no environment quantity with two DOF. Failure refuses.
* '''IC4 STRUCTURE-PRESERVING''', the parts a machine can read: each entry's DIMENSION equals its DOF's and its environment quantity's; and every DOF named by a law an entry bears, and the TARGET of every constraint it bears, is identified by some entry. Failure refuses.
* '''CODOMAIN''': an entry on a removed DOF is refused.
The checks take environment quantities by name: two names are two quantities, even where a transformation relates them. This can refuse too much, never admit too much.

What stays with the declaring authority, by inspection ([[The Principia Machina/TPS/2.3 The Translation Manifold|TPS 2.3]]):
* whether two names are the same quantity under one of the TRANSFORMATIONS;
* '''IC4''', the rest: whether each SIGNATURE relation is carried to its image, and whether each borne law can in fact be expressed in the environment;
* '''IC5 falsifier invariance''': no transformation changes what would falsify an entry.
The Generic Specification Guide describes the inventory as what the laws, minus the constraints, leave free. TPM keeps fixed DOF in it, so that a fixed DOF is still tied to something measurable; that difference is recorded as a divergence against the guide.

== Non-goals ==
The manifold has no exclusions field and no per-entry ceiling. To restrict a kernel, add a CONSTRAINT to the TPK ([[The Principia Machina/TPS/2.3 The Translation Manifold|TPS 2.3]]).

== Worked example ==
The spring manifold: three environment quantities, one signature relation (the time derivative takes position to velocity), one transformation (a shift of the time origin), and one entry per DOF.
<pre>
{
"TrM": {
"HEADER": {
"ENVIRONMENT_INVENTORY": [
{"ENVIRONMENT_QUANTITY": "position", "DIMENSION": "L1"},
{"ENVIRONMENT_QUANTITY": "velocity", "DIMENSION": "L1 T-1"},
{"ENVIRONMENT_QUANTITY": "height", "DIMENSION": "L1"}
],
"SIGNATURE": [
{
"NAME": "time_derivative",
"OVER": ["x", "v"],
"IMAGE": "d/dt maps position to velocity"
}
],
"TRANSFORMATIONS": [
{"NAME": "time_translation", "STATEMENT": "t -> t + t0"}
]
},
"ENTRIES": [
{
"NAME": "E_x",
"DOF": "x",
"DOMAIN": "|x| < x_max",
"ENVIRONMENT_QUANTITY": "position",
"IDENTIFICATION": "x is the displacement from equilibrium along the spring axis",
"FALSIFIER": "a measured restoring force not proportional to x inside the domain",
"FALSIFIER_CLASS": "F3",
"BEARS": ["N2", "KIN"],
"DIMENSION": "L1"
},
{
"NAME": "E_v",
"DOF": "v",
"DOMAIN": "|x| < x_max",
"ENVIRONMENT_QUANTITY": "velocity",
"IDENTIFICATION": "v is the time derivative of x",
"FALSIFIER": "a measured velocity differing from dx/dt beyond uncertainty",
"FALSIFIER_CLASS": "F2",
"BEARS": ["KIN"],
"DIMENSION": "L1 T-1"
},
{
"NAME": "E_z",
"DOF": "z",
"DOMAIN": "always",
"ENVIRONMENT_QUANTITY": "height",
"IDENTIFICATION": "z is the height above the track",
"FALSIFIER": "any measured z different from 0",
"FALSIFIER_CLASS": "F3",
"BEARS": ["FREE_Z", "C_NOZ"],
"DIMENSION": "L1"
}
]
}
}
</pre>

E_x and E_z name outside measurements as their falsifiers, so they are F3. E_v is F2: anyone can check it from the recorded values alone. The checker reports <code>TrM PASS</code> and <code>IC1-IC4 PASS</code>: three quantities, three DOF, one entry each way. E_z identifies z, which C_NOZ fixes; z stays in the manifold, and E_z bears C_NOZ. Built step by step on [[The Principia Machina/Tutorial/3 Write the Translation Manifold|tutorial step 3]].

Governing sections: [[The Principia Machina/TPS/2.1 The Full Kernel and immutability|TPS 2.1]], [[The Principia Machina/TPS/2.3 The Translation Manifold|2.3]] and [[The Principia Machina/TPS/5.5 The new-container flow|5.5]].

----
Previous: [[The Principia Machina/Inputs/Prime Kernel|The Prime Kernel]]. Next: [[The Principia Machina/Inputs/Measure Set|The Measure Set]].

[[Category:The Principia Machina]]