The objection
Raw tables signal. From finite samples, the relative frequencies of a content’s values in two contexts need not agree when the true probabilities do, and they disagree more often the fewer the occurrences. So the plug-in signalling Δ̂ = Σ over contents of |⟨R̂⟩_c − ⟨R̂⟩_c′| is positive in expectation even when the true marginals are equal.
A worked case. Take a rank-2 system with no signalling at all: in both contexts, each of the two contents is +1 or −1 with probability 1/2, so Δ = 0. Observe one occurrence per context. Each estimated mean ⟨R̂⟩ is then +1 or −1. The two contexts’ occurrences are independent, so for each content the two estimates differ with probability 1/2, and its term |⟨R̂⟩_c − ⟨R̂⟩_c′| is 0 or 2 with probability 1/2 each. So Δ̂ takes only the values 0, 2 and 4, and its expectation is 2, half the largest possible value, where the true Δ is 0.
Those are the values NOTE-654 reports. Its limitations: “51 of 90 systems have Δ exactly 0, 2 or 4, and 18 have err(Δ) = 1.41. Both patterns suggest one or a few occurrences per context.” NOTE-654 draws the consequence only for the systems with Δ = 0: “18 of the 21 with Δ = 0 have err(Δ) of 1 or more, so even those are not evidence of non-signalling.” The same counts make the signalling systems weak evidence of signalling. CLAIM-125 states “69 of the 90 systems signal” and “34 signal enough that they cannot be contextual at all”, and concludes, without the caveat: “So for language data signalling is the typical case, not an edge case, and an extension to signalling data is not optional.” CLAIM-127 repeats the count.
The data are not judgements. NOTE-654: the probabilities “are relative frequencies of interpretations that the authors assigned by hand to BNC and ukWaC occurrences. No annotation protocol or agreement is reported.” It leaves open “Whether a human-judgement version (proposed in §5) gives the same Δ levels as corpus frequencies.” CLAIM-127 separates the two: “Corpus estimates involve no elicitation at all.” CLAIM-125 still speaks of “language data”.
The proposed quantities have no estimators.
- The contextual fraction. CLAIM-105: “the contextual fraction is defined only without signalling”. Raw estimates usually signal, so it is undefined on them. Using it needs a projection onto the no-signalling tables, for which the record has no rule, or a CbD treatment, whose verdict depends on how the system is represented (THEORY-168). THEORY-165’s Lipschitz bound holds for no-signalling tables within one scenario, and its constant “depends on the scenario and is not bounded here”. So no bound on sampling error follows from it.
- Per-content signalling Δ.* Its plug-in estimate is biased upward, as above.
- Deficiency (TERM-028’s δ_Q). It is an infimum over Markov kernels from one rendering space to the other of a supremum over states. For renderings that are texts or images, the kernels act on an unbounded space. It is a finite linear programme only when the states are finite and the likelihoods known. The one held-out “Blackwell experiment” in the exchange is a task-loss comparison instead (CASE-042, THEORY-176).
What it does not say
- It does not say signalling is rare. Elicited judgements have their own routes to signalling (CLAIM-127, “Two routes to signalling”), and order effects are signalling in the CbD sense. CLAIM-125’s “not optional” may well be right. Its stated evidence does not carry it.
- It does not say LIT-851’s signalling result is wrong. Its Proposition 1 is a proof (THEORY-177); the objection is to the counts read off its appendix.
What would answer it
- Estimators with bias correction and a stated sampling error, or a test for signalling with a stated null hypothesis, applied to LIT-851’s systems with their occurrence counts.
- CLAIM-125’s evidence restated from elicited judgements, if the claim is about pragmatic data.
- For deficiency, a computable surrogate on a finite designed state space with known or estimated likelihoods.
Note of 2026-10-27: the edge says what the claim uses
The status review of this date (ADR-057, ADR-058) re-grounded the claim in THEORY-722 (Active, split from THEORY-168) in place of THEORY-168: “The verdict on a fixed set of measurements therefore depends on which variables represent them”, which is all the claim uses.
Note of 2026-10-28: split under ADR-061
The title’s second half, that the line’s evidence that signalling is typical “rests on plug-in estimates from one or a few occurrences”, was a verdict on support. It is now ARG-037, from LIT-851’s counts to CLAIM-125, Rejected, the version 1 inference CLAIM-125’s version 2 already gave up. This claim keeps the estimator result, which is about the subject matter, and undercuts that argument in place of objecting to CLAIM-125. Its objection to CLAIM-105 stays, since it is about the contextual fraction.