Kharoof, AzizOkay, Cihan2025-02-282025-02-282024-07-010166-8641https://hdl.handle.net/11693/116998This paper offers a novel homotopical characterization of strongly contextual simplicial distributions with binary outcomes, specifically those defined on the cone of a 1-dimensional space. In the sheaf-theoretic framework, such distributions correspond to non-signaling distributions on measurement scenarios where each context contains 2 measurements with binary outcomes. To establish our results, we employ a homotopical approach that includes collapsing measurement spaces and introduce categories associated with simplicial distributions that can detect strong contextuality.EnglishCC BY 4.0 DEED (Attribution 4.0 International)https://creativecommons.org/licenses/by/4.0/Simplicial homotopyConvex setsQuantum contextualityPolytopesArticle10.1016/j.topol.2024.1089561879-3207