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LIT-277: The Cohomology of Non-Locality and Contextuality

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Properties8
StatusActive — read in full 2026-09-27 (NOTE-250); worth reading as the short original source of the cohomological obstruction to contextuality. It gives the exact definition (a relative Čech class, with coefficients the free abelian group on support sections), the vanishing criterion and its two known failures. Its results are small propositions with complete proofs, plus machine-checked mod-2 computations that I reproduced. It calls itself "work in progress" (§1), and the conceptual development is in Abramsky et al.'s CSL 2015 "Contextuality, Cohomology and Paradox" (not read). A reading of that paper would show whether it supersedes this one.
Version2
Tagscontextuality, quantum-foundations, mathematics
ExtendsLIT-016 — The sheaf-theoretic structure of non-locality and contextuality
Extended byLIT-278 — Contextuality, Cohomology and Paradox
Corrected byLIT-279 — On the Cohomology of Contextuality
Cited as “paper” byNOTE-250 — The Cohomology of Non-Locality and Contextuality
Cited as “source” byTHEORY-526 — The Čech cohomology obstruction of a support section is a sound but incomplete witness of contextuality: it vanishes exactly when the section lies in a compatible family of integer combinations of support sections, so it is non-zero on every section of every All-vs-Nothing model, over any coefficient ring, on a connected cover, yet it misses the Hardy model entirely, part of a strongly contextual Kochen–Specker cover, and every section of a strongly contextual model on the fully symmetric (2,2,4) Bell cover

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Abramsky, Mansfield & Barbosa (2011), Proc. QPL 2011, EPTCS 95, 1–14 (2012) — DOI-10.4204/EPTCS.95.1

Standing in the record

Filed on 2026-09-27 at the owner’s request. It is the cohomological companion to LIT-016 and THEORY-012, and the correct version of the construction LIT-276’s v2 appendix attempts. published: is the arXiv v1 date (ADR-002).

It was filed Deferred, unread. NOTE-250 is the close reading of 2026-09-27, and it placed the work: Active — worth reading as the short original source of the cohomological obstruction to contextuality. It gives the exact definition (a relative Čech class, with coefficients the free abelian group on support sections), the vanishing criterion and its two known failures. Its results are small propositions with complete proofs, plus machine-checked mod-2 computations that I reproduced. It calls itself “work in progress” (§1), and the conceptual development is in Abramsky et al.’s CSL 2015 “Contextuality, Cohomology and Paradox” (not read). A reading of that paper would show whether it supersedes this one.

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