{"paper":{"title":"Operator solutions of linear systems and small cancellation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO","math.GR"],"primary_cat":"quant-ph","authors_text":"Lu-Ming Zhang, William Slofstra","submitted_at":"2024-12-13T17:40:42Z","abstract_excerpt":"We show that if a graph has minimum vertex degree at least d and girth at least g, where (d, g) is (3, 6) or (4, 4), then the incidence system of the graph has a (possibly infinite-dimensional) quantum solution over $\\mathbb{Z}_p$ for every choice of vertex weights and integer $p \\geq 2$. In particular, there are linear systems over $\\mathbb{Z}_p$, for $p$ an odd prime, such that the corresponding linear system nonlocal game has a perfect commuting-operator strategy, but no perfect classical strategy."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2412.10305","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2412.10305/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}