{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:XXVR4BLBSTQICKFSQ5O43XXYNV","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":"909c74fa5ae307a78c01fa8a380f1bb5e5ccecfcccf0979f18f6cdc22658de2b","cross_cats_sorted":["math.DS"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2012-04-26T06:16:01Z","title_canon_sha256":"a75806749d02dfd03b38da9c7a63771f31194c7959914de1ad67ecc4f8c63925"},"schema_version":"1.0","source":{"id":"1204.5836","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1204.5836","created_at":"2026-05-17T23:53:18Z"},{"alias_kind":"arxiv_version","alias_value":"1204.5836v1","created_at":"2026-05-17T23:53:18Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1204.5836","created_at":"2026-05-17T23:53:18Z"},{"alias_kind":"pith_short_12","alias_value":"XXVR4BLBSTQI","created_at":"2026-05-18T12:27:27Z"},{"alias_kind":"pith_short_16","alias_value":"XXVR4BLBSTQICKFS","created_at":"2026-05-18T12:27:27Z"},{"alias_kind":"pith_short_8","alias_value":"XXVR4BLB","created_at":"2026-05-18T12:27:27Z"}],"graph_snapshots":[{"event_id":"sha256:7781fdd1fba38e7311721fd9aae80fd125114281b616710a83136ec4e433de5a","target":"graph","created_at":"2026-05-17T23:53:18Z","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 completely classify the extreme tracial states onthe cores of the C*-algebras associated with self-similar maps on compact metric spaces. We present a complete list of them. The extreme tracial states are the union of the discrete type tracial states given by measures supported on the finite orbits of the branch points and a continuous type tracial state given by the Hutchinson measure on the original self-similar set.","authors_text":"Tsuyoshi Kajiwara, Yasuo Watatani","cross_cats":["math.DS"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2012-04-26T06:16:01Z","title":"Traces on cores of C*-algebras associated with self-similar maps"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1204.5836","kind":"arxiv","version":1},"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:a8c2494930af7bc428e09be39c0c1f1205d21077eee798e7a4ebbad45c5c8d48","target":"record","created_at":"2026-05-17T23:53:18Z","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":"909c74fa5ae307a78c01fa8a380f1bb5e5ccecfcccf0979f18f6cdc22658de2b","cross_cats_sorted":["math.DS"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2012-04-26T06:16:01Z","title_canon_sha256":"a75806749d02dfd03b38da9c7a63771f31194c7959914de1ad67ecc4f8c63925"},"schema_version":"1.0","source":{"id":"1204.5836","kind":"arxiv","version":1}},"canonical_sha256":"bdeb1e056194e08128b2875dcddef86d7787ccdc9af49375e02dffc373546913","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"bdeb1e056194e08128b2875dcddef86d7787ccdc9af49375e02dffc373546913","first_computed_at":"2026-05-17T23:53:18.772472Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:53:18.772472Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"OmohHTfAzZYOs/EKTMhLW3La5CsT89E2w4wjc7ylde28eoL1oSsERxIJGZH0YVBMKx7iUcKoSdvqBaJe8r9RBw==","signature_status":"signed_v1","signed_at":"2026-05-17T23:53:18.773215Z","signed_message":"canonical_sha256_bytes"},"source_id":"1204.5836","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a8c2494930af7bc428e09be39c0c1f1205d21077eee798e7a4ebbad45c5c8d48","sha256:7781fdd1fba38e7311721fd9aae80fd125114281b616710a83136ec4e433de5a"],"state_sha256":"718e84ea945218c3178517abdd85b7b370e455cd2146bd51bca31809b423c5a8"}