The claim
A84, Proposition II: global noncontextuality is preserved under local postprocessing “induced by a common global stochastic channel”. Manuscript §6: “Suppose source e is the collection of marginals of a global distribution p, and each K_C is the appropriate restriction of one global stochastic kernel K_X into the target full outcome space. Then (K_X)#p has the required target marginals and is a global extension of the transported model.”
What it does not say
C6: “Without a common global kernel or a compatible target cover, preservation is not automatic.” It gives a sufficient condition for a transport (TERM-008) not to create contextuality. It says nothing about transports that destroy or create it, which is where CLAIM-105 and QUESTION-004 sit.
What was checked
C7 Appendix A, read on 2026-10-09: “assume a source global law p and a target global kernel K_X such that every K_C#e_C equals the marginal of K_X#p on τ(C). Then K_X#p is an explicit global extension.” As written this assumes its conclusion: the equality of marginals is the hypothesis. The manuscript’s statement is the real one. Each K_C is “the appropriate restriction” of K_X, which reads as naturality: the marginal of K_X on τ(C) depends only on the source outcome’s restriction to C and equals K_C applied to it. Then the marginal of K_X#p on τ(C) is K_C#(ρ_C#p) = K_C#e_C, since p’s marginal on C is e_C. That is the one-line argument the manuscript gives (“direct by compatibility of pushforward with marginalization”), and it holds. Active, on that reading of “appropriate restriction”; Appendix A’s own proof restates the hypothesis and adds nothing. Appendix A also adds the right limit: “The assertion becomes false if one assumes only local kernels with no globally compatible realization.”
Prior art
This proposition is a special case of Karvonen’s “Categories of Empirical Models” (LIT-846). His natural transformation σ is exactly the component on the whole measurement set, a single global kernel, and his Lemma 3.12 states the limit that local kernels need not glue. The record’s reader drew this mapping; Karvonen does not mention translation. The manuscript should cite it, and this claim now names it in its grounds, with the THEORY that states the general result (THEORY-174): classical simulations between scenarios, cover-changing ones included, never create contextuality. The open remainder is CLAIM-125.
Note of 2026-10-27: grounded in the proved half
The status review of this date (ADR-057) moved this claim’s ground from THEORY-174 to THEORY-720. The claim uses the classical simulations and their monotonicity, that they never create contextuality, which is proved in refereed venues and Active as THEORY-720. It does not use THEORY-174’s characterization, that a map is such a simulation exactly when a non-contextual model of the hom scenario induces it. That half waits on an independent proof of the corrected Theorem 44 and stays Proposed.