{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:UBG6M3MSTAXMHPCJFMZCKIRHE2","short_pith_number":"pith:UBG6M3MS","schema_version":"1.0","canonical_sha256":"a04de66d92982ec3bc492b3225222726b4957319a309118a91632bd0937b43d6","source":{"kind":"arxiv","id":"1509.01870","version":5},"attestation_state":"computed","paper":{"title":"An intrinsic characterization of C*-simplicity","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GR"],"primary_cat":"math.OA","authors_text":"Matthew Kennedy","submitted_at":"2015-09-07T00:33:06Z","abstract_excerpt":"A group is said to be C*-simple if its reduced C*-algebra is simple. We establish an intrinsic (group-theoretic) characterization of groups with this property. Specifically, we prove that a discrete group is C*-simple if and only if it has no non-trivial amenable uniformly recurrent subgroups. We further prove that a group is C*-simple if and only if it satisfies an averaging property considered by Powers."},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1509.01870","kind":"arxiv","version":5},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2015-09-07T00:33:06Z","cross_cats_sorted":["math.GR"],"title_canon_sha256":"9db1effb4b8acb5afde968e28ad03b192777e8c0d80e599c0c0d431c0ff5d0e1","abstract_canon_sha256":"721c987a8e4203be28a22c669774ed01eca9a57591489eaaae4317b09907641c"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:02:50.207821Z","signature_b64":"lzcqbw/w2hMaazPYpTyds3H9qlPaDQyaUdy0XMmroShQYWgUOdqyYmpWjdKA1XZ4xUKPgDtaseGpgeana6oLCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a04de66d92982ec3bc492b3225222726b4957319a309118a91632bd0937b43d6","last_reissued_at":"2026-05-18T00:02:50.207053Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:02:50.207053Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"An intrinsic characterization of C*-simplicity","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GR"],"primary_cat":"math.OA","authors_text":"Matthew Kennedy","submitted_at":"2015-09-07T00:33:06Z","abstract_excerpt":"A group is said to be C*-simple if its reduced C*-algebra is simple. We establish an intrinsic (group-theoretic) characterization of groups with this property. Specifically, we prove that a discrete group is C*-simple if and only if it has no non-trivial amenable uniformly recurrent subgroups. We further prove that a group is C*-simple if and only if it satisfies an averaging property considered by Powers."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1509.01870","kind":"arxiv","version":5},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1509.01870","created_at":"2026-05-18T00:02:50.207264+00:00"},{"alias_kind":"arxiv_version","alias_value":"1509.01870v5","created_at":"2026-05-18T00:02:50.207264+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1509.01870","created_at":"2026-05-18T00:02:50.207264+00:00"},{"alias_kind":"pith_short_12","alias_value":"UBG6M3MSTAXM","created_at":"2026-05-18T12:29:44.643036+00:00"},{"alias_kind":"pith_short_16","alias_value":"UBG6M3MSTAXMHPCJ","created_at":"2026-05-18T12:29:44.643036+00:00"},{"alias_kind":"pith_short_8","alias_value":"UBG6M3MS","created_at":"2026-05-18T12:29:44.643036+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"1908.01329","citing_title":"A Groupoid Picture of Elek Algebras","ref_index":4,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/UBG6M3MSTAXMHPCJFMZCKIRHE2","json":"https://pith.science/pith/UBG6M3MSTAXMHPCJFMZCKIRHE2.json","graph_json":"https://pith.science/api/pith-number/UBG6M3MSTAXMHPCJFMZCKIRHE2/graph.json","events_json":"https://pith.science/api/pith-number/UBG6M3MSTAXMHPCJFMZCKIRHE2/events.json","paper":"https://pith.science/paper/UBG6M3MS"},"agent_actions":{"view_html":"https://pith.science/pith/UBG6M3MSTAXMHPCJFMZCKIRHE2","download_json":"https://pith.science/pith/UBG6M3MSTAXMHPCJFMZCKIRHE2.json","view_paper":"https://pith.science/paper/UBG6M3MS","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1509.01870&json=true","fetch_graph":"https://pith.science/api/pith-number/UBG6M3MSTAXMHPCJFMZCKIRHE2/graph.json","fetch_events":"https://pith.science/api/pith-number/UBG6M3MSTAXMHPCJFMZCKIRHE2/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/UBG6M3MSTAXMHPCJFMZCKIRHE2/action/timestamp_anchor","attest_storage":"https://pith.science/pith/UBG6M3MSTAXMHPCJFMZCKIRHE2/action/storage_attestation","attest_author":"https://pith.science/pith/UBG6M3MSTAXMHPCJFMZCKIRHE2/action/author_attestation","sign_citation":"https://pith.science/pith/UBG6M3MSTAXMHPCJFMZCKIRHE2/action/citation_signature","submit_replication":"https://pith.science/pith/UBG6M3MSTAXMHPCJFMZCKIRHE2/action/replication_record"}},"created_at":"2026-05-18T00:02:50.207264+00:00","updated_at":"2026-05-18T00:02:50.207264+00:00"}