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CLAIM-320: Within one fixed measurement scenario, two no-signalling empirical models can agree on all but one of their contexts and on every single-observable marginal while their contextual fractions are 1 and 0, so keeping most local judgement distributions does not fix their global compatibility

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Properties8
StatusActive
Rolethesis
Warrantdemonstrated
Tagscontextuality, mathematics
Linepragmatic-transport
GroundsCASE-037 — The parity triangle with uniform weights: a no-signalling, strongly contextual model beside a family of point sections that glues, LIT-265 — The contextual fraction as a measure of contextuality, THEORY-165 — Within a fixed measurement scenario, the non-contextual fraction is the value of a linear programme whose constraint vector is the empirical model's probability table, and the contextual fraction is convex under mixing
SupportsCLAIM-105 — In documented reconstruction chains, steps that keep most local judgements commonly change their global compatibility: translation preserves local meanings while changing the global structure of meaning
ComplementsCLAIM-319 — Over a scenario of n contexts in an odd cycle, changing the support of one context takes the contextual fraction from 1 to 0 while the other n − 1 contexts and every marginal are kept exactly, at a weighted observational distortion of 1/n, so within a scenario the fraction's Lipschitz constant against that distortion is at least n; and any change of global extension needs a contextual model on one side

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The claim

This is the possibility CLAIM-105’s headline needs, stated on its own so that its warrant can be. A78 asked: “Can communicative reconstruction preserve most local pragmatic judgments while substantially changing their global compatibility structure?” A84’s planned Appendix F example was “Two locally similar empirical models with different global compatibility”. The manuscript dropped it; CASE-037 recovers it.

On X = {A, B, C} with the cover {AB, BC, AC} and binary outcomes, take the supports S_AB = S_BC = {(0,0), (1,1)} and S_AC = {(0,1), (1,0)}, each allowed outcome at 1/2. Every single-observable marginal is uniform, so the model is no-signalling. No global assignment satisfies all three supports, because A = B = C contradicts A ≠ C, so the model is strongly contextual and its contextual fraction is 1. Change S_AC to {(0,0), (1,1)}, still at 1/2 each. Two of the three contexts are unchanged, and so is every single-observable marginal. The new model is the marginal of the global distribution with 1/2 on (0,0,0) and 1/2 on (1,1,1), so its contextual fraction is 0.

So within one scenario the fraction falls from 1 to 0 while most of the local tables are kept. The two AC tables have disjoint supports, a total-variation distance of 1 in that context, so the jump is consistent with THEORY-165’s Lipschitz bound: the fraction does not jump within a fixed scenario, and here one context moved as far as it can.

What it does not say

  • That reconstruction chains, or pragmatic judgements, behave this way. The weights are stipulated (CASE-037: “This parity example demonstrates an obstruction, not a claim about actual judgments”). That documented chains do so is CLAIM-105’s thesis, which is interpretive; CLAIM-201 holds the form the data read so far leave open.
  • That global compatibility can change at small local distortion everywhere. The pair keeps two contexts exactly and changes the third completely; by THEORY-165, within a fixed scenario a large change of the fraction needs a large change in some context.
  • That the pair is one step of a transport. By Theorem 2 of LIT-265 a free operation cannot raise the fraction, so the step from 0 to 1 is not a free operation, and Δ_CF is undefined at any step that signals.

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