{"paper":{"title":"A Proof of a Conjecture of Zhi-Wei Sun on a Truncated Legendre-Symbol Determinant","license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Gaishi Yang, Yaoran Yang, Yutong Zhang","submitted_at":"2026-06-21T15:07:39Z","abstract_excerpt":"We prove Conjecture~3.4 of Zhi-Wei Sun by evaluating, for every prime $p\\equiv3\\pmod4$, a truncated Legendre-symbol determinant as $\\lfloor(p-2)/3\\rfloor^{2}x$. The argument reduces the determinant to inverse data for Chapman's full Legendre-symbol matrix and evaluates those data using Vsemirnov's factorization and a Schur-Pfaffian resolvent identity. OpenAI's ChatGPT produced the proof, which the authors independently checked and confirmed."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.22548","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2606.22548/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"}