The objection
CLAIM-105, from A78: “Translation may preserve local meanings while changing the global structure of meaning”, “potentially the most interesting connection we’ve found”. Its defeat condition: “preservation of the context-wise judgement distributions always carries preservation of their global compatibility (overlap consistency, global extension, contextual fraction), so that the global structure adds nothing to predict.” The manuscript keeps it as its Abstract’s last sentence.
What the record has read about behavioural data. Dzhafarov, Zhang and Kujala (LIT-264, read in NOTE-235) apply the Contextuality-by-Default criterion to five kinds of behavioural data, two of them previously published as contextual. “None is contextual.” The note’s key insight: a response distribution that depends on context is inconsistent connectedness, “a trivial sense of contextuality”, and “Behavioural data have plenty of the first and, so far, none of the second.” CLAIM-125, from Wang, Sadrzadeh, Abramsky and Cervantes (LIT-851): “69 of the 90 systems signal” and “34 signal enough that they cannot be contextual at all”. The paper tests none of the 90 for contextuality (LIT-851’s status note). Among the line’s claims, LIT-264 is cited by CLAIM-041 alone, against reading order effects as nonclassical, and by none of CLAIM-038, CLAIM-044 or CLAIM-105.
The dilemma. “Global compatibility” in CLAIM-105 is one of two things.
- Contextuality proper: no global extension, a positive contextual fraction, or contextuality in the CbD sense. The data the record has read have none. If source and target models are both noncontextual, there is no contextuality to gain or lose, and “preservation of the context-wise judgement distributions always carries preservation” of it, which is the defeat condition met by default. CLAIM-105’s own reading of the contextual fraction adds that it “cannot rise along free operations” and is “Lipschitz in the probability table” within a scenario (THEORY-165). The one instance of the headline in the record is built from CASE-037, the parity triangle, a no-signalling, strongly contextual model (contextual fraction 1): changed in one context it gives CLAIM-105’s recovered pair, with fractions 1 and 0. CASE-037 is stipulated.
- Overlap consistency: whether a content’s distribution is the same in every context that measures it. A change in it is a change in inconsistent connectedness, which NOTE-235 calls the trivial sense, and which is ordinary context dependence. CLAIM-038 says the theory is distinct “from merely saying that meanings are fuzzy, ambiguous, or context-dependent”.
Overlap consistency is also not global structure beyond the local distributions. It is computed from them. For a content q measured in contexts C and C′, let d = TV(p, p′), where p and p′ are q’s marginals from the distributions in C and C′. If a transformation moves each context’s distribution by at most ε in total variation, it moves each marginal by at most ε, since marginalizing does not increase total variation. By the triangle inequality the new discrepancy d̃ satisfies |d̃ − d| ≤ 2ε. So keeping the local distributions nearly fixed keeps overlap consistency nearly fixed, and on this horn the global structure adds nothing to predict, which is again the defeat condition.
On the first horn the headline has no case but a constructed one. On the second it is the context dependence CLAIM-038 sets the theory apart from. The record holds both CLAIM-105’s headline and CLAIM-078’s “it needs neither quantum contextuality nor exact Noether laws”, and the evidence it has read favours the second.
How much contextuality a data set shows also depends on how its outcomes are coded: CLAIM-245 shows that a deterministic recoding within each context can make a noncontextual signalling system contextual in the CbD sense, or the reverse. So a contextual result would itself need a coding fixed in advance.
What it does not say
It does not say a contextual pragmatic data set cannot exist, nor that CLAIM-105 is false. LIT-264 offers the absence of contextuality as a working hypothesis, and the record has read one paper’s five data sets and one paper’s signalling counts. It does not touch the change of scenario, where the contextual fraction can jump (CLAIM-105, “Only a change of scenario can make it jump”). It says the headline, as stated over a fixed scenario, is either unsupported or not distinctive.
What would answer it
- A documented pragmatic data set that is contextual in the CbD sense, with its signalling accounted for and its coding fixed in advance, and a transformation that keeps its local distributions while changing that.
- Or a restatement of CLAIM-105 about a change of cover or scenario, which the continuity results leave open.
- Or a restatement about overlap consistency alone, conceding that it is context dependence and saying what the theory adds to it.
Note of 2026-10-15: split under ADR-043
ADR-043’s classification found this objection compound: an empirical premise, that the behavioural data the record has read show no contextuality proper (LIT-264, LIT-851), and a dilemma drawn from it, whose second horn is the 2ε bound on overlap discrepancy. The premise is now CLAIM-325, scoped by CASE-053 to data the record has read and to pragmatic or meaning judgements, and this claim rests on it. CLAIM-201 relies on the same premise. This claim keeps the dilemma: the two readings of “global compatibility” come from CLAIM-105’s own defeat condition, the first horn follows from the premise, and the second is derived, so it is now marked demonstrated, conditional on CLAIM-325. The title changed, because the old one led with the empirical finding: it was “The record’s own reading finds contextuality proper in no behavioural data set, so the headline that translation changes global structure is either about contextuality, for which there is no case but a constructed one, or about inconsistent connectedness, the ordinary context dependence the line says it goes beyond”. The new title states the premise as a condition.
Note of 2026-10-21: non-closure is not contextuality
A8 §5 and A9 §7 of the exchange of 2026-10-20 asked whether THEORY-820’s non-closed common refinement is a contextuality obstruction, and said it is not. A9: “the joint representation (A,B) does exist. What fails is its informational closure, not its mathematical consistency or the existence of a joint distribution.” That is right: the local descriptions glue (CLAIM-197), and a property of the glued description fails. It is a second instance, from dynamics, of this claim’s warning that context dependence is not contextuality. A9 separated logical, representational and dynamical compatibility. The three-bit chain passes the first two and fails the third. CLAIM-044’s note of 2026-10-21 records the same table from A10.
Note of 2026-10-28: split under ADR-061
The first horn said the headline “has no case but a constructed one”: the one instance in the record is CASE-037, which is stipulated. That is a verdict on support, and it is now ARG-032, from CASE-037 to CLAIM-105, Rejected. This claim keeps the dilemma and the 2ε bound, which are about the subject matter, and undercuts that argument. Its objection to CLAIM-105 stays, because the second horn says the headline is “not distinctive”.