{"paper":{"title":"Universal violation of pentagon inequalities in four-state systems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"quant-ph","authors_text":"Mordecai Waegell, P. K. Aravind","submitted_at":"2011-11-21T02:02:09Z","abstract_excerpt":"The 60 real vectors derived from the vertices of a 600-cell are shown to yield a number of pentagon inequalities that are satisfied by realistic noncontextual theories but violated by quantum mechanics. The replicas of these inequalities cover Hilbert space so densely that every real four-dimensional vector violates at least one of them. It is pointed out that this set of 60 vectors contains numerous \"N-gons\" (generalizations of pentagons) that may be of interest in connection with demonstrations of contextuality."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1111.4713","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}