{"paper":{"title":"Proof of the Kresch-Tamvakis Conjecture","license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","headline":"","cross_cats":["math.AG","math.CA","math.CO"],"primary_cat":"math.NT","authors_text":"John S. Caughman, Taiyo S. Terada","submitted_at":"2023-09-16T04:23:11Z","abstract_excerpt":"In this paper we resolve a conjecture of Kresch and Tamvakis. Our result is the following.\n  Theorem: For any positive integer $D$ and any integers $i,j$ $(0\\leq i,j \\leq D)$, the absolute value of the following hypergeometric series is at most 1: \\begin{equation*}\n  {_4F_3} \\left[ \\begin{array}{c} -i, \\; i+1, \\; -j, \\; j+1 \\\\ 1, \\; D+2, \\; -D \\end{array} ; 1 \\right].\n  \\end{equation*}\n  To prove this theorem, we use the Biedenharn-Elliott identity, the theory of Leonard pairs, and the Perron-Frobenius theorem."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2309.08869","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/2309.08869/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"}