The Principia Machina/Diagrams/08 Regime and contradiction tests

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The specification Contents: parts, tables, diagrams TPS 0.5.0 (declared 2026-10-03, revision 8; machine-optimized text) Decisions (the foundations record, one line each)

Structural diagram 8 of 12. Part of the TPM hub.

• KIND: process
• LANGUAGE: Mermaid decision
• GENERATED FROM: static, TPS SR3, SR7, SR8
• STATUS: hand-authored at TPS 0.1.0; superseded by TPX at its first build
• SOURCE SHA-256: 81f2bef51d17b32597f10d20da32e289ae3b9cdaa2ec0bff0842e002f6b1ecda
• KEY: key for process diagrams: what each shape and arrow means; definition of terms; contents of the specification

Rendered live from the source, which is the text equivalent and is shown under the drawing; a wide drawing scrolls sideways inside its frame.

Source (the text equivalent; Mermaid)

%% 08 Regime and contradiction tests. process/Mermaid decision. Generated from: static, TPS SR3, SR7, SR8.
flowchart TD
  A[record at allocation<br/>3.2.4] --> B[REGIME L: verifiable by<br/>re-derivation, no empirical input]
  A --> C[REGIME M: value with combined<br/>standard uncertainty u_c per GUM]
  B --> LL[L-L test: conjunction with<br/>the TFK derives a contradiction]
  C --> S8[SR8: with two or more standing<br/>M records of one quantity and<br/>reduced chi-square above 1,<br/>apply the scale factor S first]
  S8 --> MM[M-M test: difference above<br/>k times the combined uncertainty]
  C --> LM[L-M test: the M value fails the<br/>M-M test against the L record's<br/>derived value]
  LM --> S7[SR7: never strikes the L<br/>derivation; named gap, or DOMAIN<br/>finding when a of r is 0]
  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 task
  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 u_c per the GUM. L-L contradiction is derivation of a contradiction with the TFK. For M records, SR8 first 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 then 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).