{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:ZJ236HH3GMCC62R6WJ7WQERHDI","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"93e71d1e897ea45e8a0bcb7080d2f1c741bcac95939d7692e608420cbaa76bf1","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2012-05-08T04:43:21Z","title_canon_sha256":"025839a8c0dbcd782d40de17c0b95eef2abb6c4fe49239e81e7fe208ffafd66b"},"schema_version":"1.0","source":{"id":"1205.1590","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1205.1590","created_at":"2026-05-18T00:37:37Z"},{"alias_kind":"arxiv_version","alias_value":"1205.1590v2","created_at":"2026-05-18T00:37:37Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1205.1590","created_at":"2026-05-18T00:37:37Z"},{"alias_kind":"pith_short_12","alias_value":"ZJ236HH3GMCC","created_at":"2026-05-18T12:27:30Z"},{"alias_kind":"pith_short_16","alias_value":"ZJ236HH3GMCC62R6","created_at":"2026-05-18T12:27:30Z"},{"alias_kind":"pith_short_8","alias_value":"ZJ236HH3","created_at":"2026-05-18T12:27:30Z"}],"graph_snapshots":[{"event_id":"sha256:398cc8edb71fbb191a4d33d8640b1d5bc1df52950a8e1def890c989af2652409","target":"graph","created_at":"2026-05-18T00:37:37Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"We consider a crossed product of a unital simple separable nuclear stably finite Z-stable C*-algebra A by a strongly outer cocycle action of a discrete countable amenable group \\Gamma. Under the assumption that A has finitely many extremal tracial states and \\Gamma is elementary amenable, we show that the twisted crossed product C*-algebra is Z-stable. As an application, we also prove that all strongly outer cocycle actions of the Klein bottle group on Z are cocycle conjugate to each other. This is the first classification result for actions of non-abelian infinite groups on stably finite C*-a","authors_text":"Hiroki Matui, Yasuhiko Sato","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2012-05-08T04:43:21Z","title":"Z-stability of crossed products by strongly outer actions II"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1205.1590","kind":"arxiv","version":2},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:691e073ae3bb65d194618f2a20af8ac04bdf7ef13ea75bfd6d835d6d8cc70b45","target":"record","created_at":"2026-05-18T00:37:37Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"93e71d1e897ea45e8a0bcb7080d2f1c741bcac95939d7692e608420cbaa76bf1","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2012-05-08T04:43:21Z","title_canon_sha256":"025839a8c0dbcd782d40de17c0b95eef2abb6c4fe49239e81e7fe208ffafd66b"},"schema_version":"1.0","source":{"id":"1205.1590","kind":"arxiv","version":2}},"canonical_sha256":"ca75bf1cfb33042f6a3eb27f6812271a3389739a70aea370ede98fc8391a0333","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ca75bf1cfb33042f6a3eb27f6812271a3389739a70aea370ede98fc8391a0333","first_computed_at":"2026-05-18T00:37:37.678308Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:37:37.678308Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ls6+nT4IxxQ3J8gHsCH7rWHv1cvmzrRTj/SbtEbU2ER6b+OAvx0SYiRDLzgcbmpdyRDuENjADzrixXPRhaRECA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:37:37.679123Z","signed_message":"canonical_sha256_bytes"},"source_id":"1205.1590","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:691e073ae3bb65d194618f2a20af8ac04bdf7ef13ea75bfd6d835d6d8cc70b45","sha256:398cc8edb71fbb191a4d33d8640b1d5bc1df52950a8e1def890c989af2652409"],"state_sha256":"255138e0154363981eb6e62aeb0bb4a771b15396f9260f371d8b876edbe65ba8"}