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The Principia Machina/Diagrams/08 Regime and contradiction tests: Difference between revisions

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m Add live rendering (graphviz tag / #mermaid) above the text-equivalent source; PMP-TPM diagrams, 2026-09-16
Diagram 08 Regime and contradiction tests: source, text equivalent, TPS 0.1.0 addresses
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''Structural diagram 8 of 12. Part of [[The Principia Machina/Hub|the TPM hub]].''
''Structural diagram 8 of 12.'' Part of [[The Principia Machina/Hub|the TPM hub]].
 
* KIND: process
* KIND: process
* LANGUAGE: Mermaid decision
* LANGUAGE: Mermaid decision
* GENERATED FROM: static, SR3, SR7, SR8
* GENERATED FROM: static, TPS SR3, SR7, SR8
* STATUS: hand-authored at PMP-TPM 0.2.0 from foundations record 0.5.0 section 4.1; superseded by TPX at its first build (D21, structural diagram pages are TPX output).
* STATUS: hand-authored at TPS 0.1.0; superseded by TPX at its first build
* SOURCE SHA-256: <code>c026cf1db028e6f12253c42eeeda056e7c5b5576b867157e356f7052cd5471d7</code>


The diagram is rendered live from the source below, which is its text equivalent (4.1). If rendering is unavailable the source still stands.
Rendered live from the source below, which is the text equivalent; if rendering is unavailable the source still stands.


{{#mermaid:flowchart TD
{{#mermaid:
   A[Record allocated] --&gt; Q{Regime?}
%% 08 Regime and contradiction tests. process/Mermaid decision. Generated from: static, TPS SR3, SR7, SR8.
  Q -- L: re-derivable from TFK plus ASSUMPTIONS, no empirical input --&gt; L[L record]
flowchart TD
   Q -- M: value with combined standard uncertainty u_c per GUM --&gt; M[M record; Type B components enumerated]
   A[record at allocation 3.2.4] --> B[REGIME L: verifiable by re-derivation, no empirical input]
   L --&gt; LL{Against another L}
   A --> C[REGIME M: value with combined standard uncertainty u_c per GUM]
  LL --&gt; T1[L-L: conjunction with TFK derives a contradiction?]
   B --> LL[L-L test: conjunction with the TFK derives a contradiction]
   M --&gt; S8[SR8: if N &gt;= 2 standing M records of one quantity and chi2 over N-1 &gt; 1, scale each u by S]
   C --> S8[SR8: with N of 2 or more standing M records and chi-square over N minus 1 above 1, apply the scale factor S first]
   S8 --&gt; MM{Against another M}
   S8 --> MM[M-M test: difference above k times the root of u1 squared plus u2 squared]
  MM --&gt; T2[M-M: abs x1 - x2 &gt; k sqrt u1^2 + u2^2 ?]
   C --> LM[L-M test: the M value fails the M-M test against the L record's derived value]
   M --&gt; LM{Against an L}
   LM --> S7[SR7: never strikes the L derivation; named gap, or DOMAIN finding when a of r is 0]
  LM --&gt; T3[L-M: M value fails M-M test against L's derived value?]
   MM -- survives S --> CONTRA[contradiction]
   T3 -- yes --&gt; SR7[SR7: never strikes the L derivation; named gap if a r &gt; 0, DOMAIN finding if a r = 0]
   MM -- does not survive S --> NONE[not a contradiction]
   T1 -- yes --&gt; SR5[to SR4-SR6 ordering]
   T2 -- yes --&gt; SR5
  T1 -- no --&gt; OK[No contradiction]
  T2 -- no --&gt; OK
  T3 -- no --&gt; OK
}}
}}


<pre>
== Text equivalent ==
flowchart TD
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).
  A[Record allocated] --&gt; Q{Regime?}
 
  Q -- L: re-derivable from TFK plus ASSUMPTIONS, no empirical input --&gt; L[L record]
[[Category:The Principia Machina]]
  Q -- M: value with combined standard uncertainty u_c per GUM --&gt; M[M record; Type B components enumerated]
 
  L --&gt; LL{Against another L}
  LL --&gt; T1[L-L: conjunction with TFK derives a contradiction?]
  M --&gt; S8[SR8: if N &gt;= 2 standing M records of one quantity and chi2 over N-1 &gt; 1, scale each u by S]
  S8 --&gt; MM{Against another M}
  MM --&gt; T2[M-M: abs x1 - x2 &gt; k sqrt u1^2 + u2^2 ?]
  M --&gt; LM{Against an L}
  LM --&gt; T3[L-M: M value fails M-M test against L's derived value?]
  T3 -- yes --&gt; SR7[SR7: never strikes the L derivation; named gap if a r &gt; 0, DOMAIN finding if a r = 0]
  T1 -- yes --&gt; SR5[to SR4-SR6 ordering]
  T2 -- yes --&gt; SR5
  T1 -- no --&gt; OK[No contradiction]
  T2 -- no --&gt; OK
  T3 -- no --&gt; OK
</pre>

Revision as of 19:49, 17 September 2026

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: c026cf1db028e6f12253c42eeeda056e7c5b5576b867157e356f7052cd5471d7

Rendered live from the source below, which is the text equivalent; if rendering is unavailable the source still stands.

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).

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