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LIT-278: Contextuality, Cohomology and Paradox

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Properties7
StatusActive — read in full 2026-09-27 (NOTE-251); worth reading as the place where the cohomological witness is shown complete for a named, large class (every All-vs-Nothing model, over any ring). It is also where the obstruction is defined as a connecting homomorphism. It does not supersede LIT-277. It re-derives none of LIT-277's computations, and it drops its negative results: the Hardy false positive and the strongly contextual cover with γ = 0. Its "paradox" title-word is supported by about one page of analogy and one worked identification.
Version2
Tagscontextuality, quantum-foundations, mathematics, logic
ExtendsLIT-277 — The Cohomology of Non-Locality and Contextuality
SupportsCLAIM-141 — Causal-loop consistency and sheaf contextuality are both local-to-global problems, but passing to distributions affects them oppositely: a loop with no deterministic solution has a distributional fixed point, while a model with no global section in its supports has no global distribution either
Cited as “paper” byNOTE-251 — Contextuality, Cohomology and Paradox
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, Barbosa, Kishida, Lal & Mansfield (2015), CSL 2015, LIPIcs 41, 211–228 — DOI-10.4230/LIPIcs.CSL.2015.211

Standing in the record

Filed on 2026-09-27 at the owner’s request, as the follow-up to LIT-277 (Abramsky, Mansfield & Barbosa 2011). published: is the arXiv v1 date (ADR-002).

It was filed Deferred, unread. NOTE-251 is the close reading of 2026-09-27, and it placed the work: Active — worth reading as the place where the cohomological witness is shown complete for a named, large class (every All-vs-Nothing model, over any ring). It is also where the obstruction is defined as a connecting homomorphism. It does not supersede LIT-277. It re-derives none of LIT-277’s computations, and it drops its negative results: the Hardy false positive and the strongly contextual cover with γ = 0. Its “paradox” title-word is supported by about one page of analogy and one worked identification.

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