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LIT-279: On the Cohomology of Contextuality

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Properties7
StatusActive — read in full 2026-09-27 (NOTE-252); worth reading for one result, the first complete false negative of the cohomological witness (§4 and Appendix A, about two pages), which is correct as I verified it. §5 proves its own programme empty for no-signalling models, and §6 is a standard correspondence plus one false proposition. The follow-up, arXiv 1807.04203, may supersede it; that is unverified, since it was not read.
Version2
Tagscontextuality, quantum-foundations, mathematics
Extended byLIT-280 — Towards a complete cohomology invariant for non-locality and contextuality
CorrectsLIT-277 — The Cohomology of Non-Locality and Contextuality
Cited as “paper” byNOTE-252 — On the Cohomology of 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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Carù (2017), Proc. QPL 2016, EPTCS 236, 21–39 — DOI-10.4204/EPTCS.236.2

Standing in the record

Filed on 2026-09-27 at the owner’s request, as the next paper on the line from LIT-277 and LIT-278. published: is the arXiv v1 date (ADR-002).

It was filed Deferred, unread. NOTE-252 is the close reading of 2026-09-27, and it placed the work: Active — worth reading for one result, the first complete false negative of the cohomological witness (§4 and Appendix A, about two pages), which is correct as I verified it. §5 proves its own programme empty for no-signalling models, and §6 is a standard correspondence plus one false proposition. The follow-up, arXiv 1807.04203, may supersede it; that is unverified, since it was not read.

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