{"paper":{"title":"A unified approach for classifying simple nuclear $C^\\ast$-algebras","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.OA","authors_text":"Ben Bouwen, James Gabe","submitted_at":"2024-12-20T15:12:49Z","abstract_excerpt":"We provide a new proof of the Kirchberg--Phillips theorem by adapting the framework laid out by Carri\\'on--Gabe--Schafhauser--Tikuisis--White for classifying separable simple unital nuclear stably finite $\\mathcal Z$-stable $C^\\ast$-algebras satisfying the UCT. Not only does this give a unified approach to classifying stably finite and purely infinite $C^\\ast$-algebras, in contrast to the other proofs of the Kirchberg--Phillips theorem, our proof does not rely on Kirchberg's Geneva Theorems, but instead implies them as corollaries (for nuclear $C^\\ast$-algebras)."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2412.15968","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/2412.15968/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"}