{"paper":{"title":"Algorithms for experimenting with Zariski dense matrix groups over number fields","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.GR","authors_text":"A. Hulpke, A. S. Detinko, D. L. Flannery","submitted_at":"2026-05-22T15:57:58Z","abstract_excerpt":"Let $\\mathbb{P}$ be an algebraic number field. We provide a computational analog of the strong approximation theorem for finitely generated Zariski dense groups $H\\leq \\mathrm{SL}(n,\\mathbb{P})$, $n$ prime. That is, we present algorithms to find the set of congruence quotients of $H$ modulo all maximal ideals of a finitely generated subring $R$ of $\\mathbb{P}$ such that $H\\leq \\mathrm{SL}(n,R)$. The algorithms have been implemented in GAP. Potential applications are illustrated by a range of experiments in degree $2$, with a special focus on Bianchi groups."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2605.23798","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/2605.23798/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"}