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LIT-280: Towards a complete cohomology invariant for non-locality and contextuality

1 min read

Properties7
StatusActive — read in full 2026-09-27 (NOTE-253); worth reading for §§4–7, a correct and genuinely new result: a complete cohomological test for contextuality on cyclic scenarios, which closes the Hardy and Carù-2017 gaps. Read it knowing that §8's generalisation, its §8.1 Kochen–Specker example and Conjecture 9.1 are wrong as stated.
Version2
Tagscontextuality, quantum-foundations, mathematics
ExtendsLIT-279 — On the Cohomology of Contextuality
Extended byLIT-281 — Logical and Topological Contextuality in Quantum Mechanics and Beyond
Cited as “paper” byNOTE-253 — Towards a complete cohomology invariant for non-locality and contextuality
Cited as “source” byTHEORY-524 — On cyclic measurement scenarios, where the contexts' overlaps form one chordless N-cycle, the ℤ/2 Čech obstruction computed on the (N−1)-th iterated joint model is exact for logical and strong contextuality, the bound N − 1 being tight; beyond cycles no such result is established, the published extension is false on its own example, and the completeness conjecture fails on a Kochen–Specker cover that is never detected at any level

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Carù (2018), arXiv preprint — ARXIV-1807.04203

Standing in the record

Filed on 2026-09-27 at the owner’s request, as the sequel to LIT-279 on the line from LIT-277. published: is the arXiv v1 date (ADR-002). No published version is known.

It was filed Deferred, unread. NOTE-253 is the close reading of 2026-09-27, and it placed the work: Active — worth reading for §§4–7, a correct and genuinely new result: a complete cohomological test for contextuality on cyclic scenarios, which closes the Hardy and Carù-2017 gaps. Read it knowing that §8’s generalisation, its §8.1 Kochen–Specker example and Conjecture 9.1 are wrong as stated.

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