{"paper":{"title":"Advancing Geometry with AI: Multi-agent Generation of Polytopes","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cs.CG","math.MG"],"primary_cat":"math.CO","authors_text":"Adam Zsolt Wagner, Alex Davies, Ali Eslami, Bogdan Georgiev, Geordie Williamson, Grzegorz Swirszcz, Pushmeet Kohli, Sam Blackwell, Sebastien Racaniere, Theophane Weber","submitted_at":"2025-01-30T19:43:34Z","abstract_excerpt":"Polytopes are one of the most primitive concepts underlying geometry. Discovery and study of polytopes with complex structures provides a means of advancing scientific knowledge. Construction of polytopes with specific extremal structure is very difficult and time-consuming. Having an automated tool for the generation of such extremal examples is therefore of great value. We present an Artificial Intelligence system capable of generating novel polytopes with very high complexity, whose abilities we demonstrate in three different and challenging scenarios: the Hirsch Conjecture, the k-neighbour"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2502.05199","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/2502.05199/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"}