{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,3]],"date-time":"2026-06-03T04:23:33Z","timestamp":1780460613740,"version":"3.54.1"},"reference-count":23,"publisher":"MDPI AG","issue":"8","license":[{"start":{"date-parts":[[2023,7,27]],"date-time":"2023-07-27T00:00:00Z","timestamp":1690416000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/100000181","name":"US Air Force Office of Scientific Research","doi-asserted-by":"publisher","award":["FA9550-21-1-0002"],"award-info":[{"award-number":["FA9550-21-1-0002"]}],"id":[{"id":"10.13039\/100000181","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>Simplicial distributions are combinatorial models describing distributions on spaces of measurements and outcomes that generalize nonsignaling distributions on contextuality scenarios. This paper studies simplicial distributions on two-dimensional measurement spaces by introducing new topological methods. Two key ingredients are a geometric interpretation of Fourier\u2013Motzkin elimination and a technique based on the collapsing of measurement spaces. Using the first one, we provide a new proof of Fine\u2019s theorem characterizing noncontextual distributions in N-cycle scenarios. Our approach goes beyond these scenarios and can describe noncontextual distributions in scenarios obtained by gluing cycle scenarios of various sizes. The second technique is used for detecting contextual vertices and deriving new Bell inequalities. Combined with these methods, we explore a monoid structure on simplicial distributions.<\/jats:p>","DOI":"10.3390\/e25081127","type":"journal-article","created":{"date-parts":[[2023,7,28]],"date-time":"2023-07-28T01:51:47Z","timestamp":1690509107000},"page":"1127","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":5,"title":["Topological Methods for Studying Contextuality: N-Cycle Scenarios and Beyond"],"prefix":"10.3390","volume":"25","author":[{"given":"Aziz","family":"Kharoof","sequence":"first","affiliation":[{"name":"Mathematics Department, Bilkent University, Ankara 06800, T\u00fcrkiye"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-4475-4221","authenticated-orcid":false,"given":"Selman","family":"Ipek","sequence":"additional","affiliation":[{"name":"Mathematics Department, Bilkent University, Ankara 06800, T\u00fcrkiye"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Cihan","family":"Okay","sequence":"additional","affiliation":[{"name":"Mathematics Department, Bilkent University, Ankara 06800, T\u00fcrkiye"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2023,7,27]]},"reference":[{"key":"ref_1","first-page":"195","article-title":"On the Einstein Podolsky Rosen paradox","volume":"1","author":"Bell","year":"1964","journal-title":"Phys. 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