The Principia Machina/Diagrams/08 Regime and contradiction tests

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Structural diagram 8 of 13. Part of the TPM hub.

• KIND: process
• LANGUAGE: Mermaid
• GENERATED FROM: static, TPS SR3, SR7, SR8
• STATUS: hand-authored at TPS 0.1.0; checked against TPS 0.3.0 on 2026-09-28: owed a redraw (the node "normalize by DIMENSION and a transformation" predates normalization to coherent SI and the KIND audit block, 4.4.4; not drawn: the trajectory interim, 4.4.13); checked against revision 7 on 2026-09-29, declared final as TPS 0.4.0 on 2026-09-30: also owed a redraw (the trajectory interim is ended: the tests run over equal CONDITIONS, 4.4.13; not drawn: a VERIFICATION tested only against its own TARGET, 3.3.6); checked against revision 8, proposed as TPS 0.5.0, on 2026-09-30: no change bears on it; superseded by TPX at its first build
• SOURCE SHA-256: 92fe5e6fb50ec2ecab8fe8ddb74ceb0fc856f03013549a6dbbbde705d402524a

Rendered live from the source, which is the text equivalent and is shown under the drawing. The key to the shapes is in the panel.

Source (the text equivalent; Mermaid)

%% 08 Regime and contradiction tests. process/Mermaid decision. TPS SR3, SR7, SR8.
flowchart TD
  A[record at allocation, TPS 3.2.4] --> B[REGIME L: re-derivable, no data]
  A --> C[REGIME M: a value with u_c]
  B --> LL[L-L test: contradiction with the TFK]
  C --> Q[same TrM entry named? TPS 4.4.4]
  Q -- no --> REF[(test refused)]
  Q -- yes --> NRM[normalize by DIMENSION and a transformation]
  NRM --> S8[SR8: scale by the scatter first]
  S8 --> MM[M-M test: difference vs k times u]
  C --> LM[L-M test: M value vs derived value]
  LM --> S7[SR7: never strikes an L derivation]
  MM -- survives S --> CONTRA[(contradiction)]
  MM -- does not survive S --> NONE[(not a contradiction)]

  classDef task fill:#eaecf0,stroke:#a2a9b1,color:#202122
  classDef human fill:#eaf3ff,stroke:#36c,color:#202122
  classDef data fill:#fef6e7,stroke:#ac6600,color:#202122
  classDef bad fill:#fee7e6,stroke:#d33,color:#202122
  classDef good fill:#d5fdf4,stroke:#14866d,color:#202122
  class A,B,C,LL,S8,MM,LM,S7,Q,NRM task
  class REF bad
  class CONTRA bad
  class NONE good

Text equivalent

Each record is assigned one regime at allocation (3.2.4): L, verifiable by re-derivation with no empirical input, or M, carrying a value with its combined standard uncertainty u_c per the Guide to the Expression of Uncertainty in Measurement (GUM). L-L contradiction is derivation of a contradiction with the Full Kernel (TFK). Two M values are compared only when both name the same entry of the Translation Manifold (TrM); both are first normalized to coherent SI units under the unit grammar, a difference of dimension is refused, and a difference of KIND is not tested but opens an audit block (3.2.11, 4.4.4); the drawing's node for normalization predates this. SR8 then applies the scale factor S when two or more standing M records of one quantity give a reduced chi-square above 1; the M-M test compares the difference with k times the combined uncertainty. L-M applies the M-M test against the L record's derived value, and SR7 governs the outcome. A contradiction that does not survive S is not a contradiction (SR3, SR7, SR8). The M-M and L-M tests, and SR8's scale groups, take only records with equal CONDITIONS: the SITUATION records, the initial and boundary values, in each record's assumptions, and the point AT where its value holds, computed by the calculator; the machine tests a pair whose DOF is fixed, or whose values are fully stated at a point, and lists every other pair of one QUANTITY for inspection (4.4.13). A VERIFICATION record enters SR3 only against its own TARGET and no SR8 group (3.3.6).