{"paper":{"title":"Certifying Arithmeticity for Two Degree-Six Symplectic Hypergeometric Monodromy Groups","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.RT"],"primary_cat":"math.GR","authors_text":"Anna Wienhard, Diaaeldin Taha, J. Maxwell Riestenberg, Steve Trettel","submitted_at":"2026-05-25T15:14:18Z","abstract_excerpt":"We prove arithmeticity for two degree-six symplectic hypergeometric monodromy groups, called C-47, and C-55 in the paper \\cite{BajpaiDonaNitsche2025Thin} by Bajpai-Dona-Nitsche. This settles two of the three remaining cases, whose classification was left open by \\cite{BajpaiDonaNitsche2025Thin}. The arithmeticity certificates were found with AlphaEvolve and then independently verified with exact matrix arithmetic over $\\QQ$ using a computer. We include illustrations of limit sets of several degree-six symplectic hypergeometric monodromy groups. Based on these illustration we conjecture C-32 to"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2605.25935","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/2605.25935/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"}