{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2012:XXVR4BLBSTQICKFSQ5O43XXYNV","short_pith_number":"pith:XXVR4BLB","schema_version":"1.0","canonical_sha256":"bdeb1e056194e08128b2875dcddef86d7787ccdc9af49375e02dffc373546913","source":{"kind":"arxiv","id":"1204.5836","version":1},"attestation_state":"computed","paper":{"title":"Traces on cores of C*-algebras associated with self-similar maps","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DS"],"primary_cat":"math.OA","authors_text":"Tsuyoshi Kajiwara, Yasuo Watatani","submitted_at":"2012-04-26T06:16:01Z","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."},"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":"1204.5836","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2012-04-26T06:16:01Z","cross_cats_sorted":["math.DS"],"title_canon_sha256":"a75806749d02dfd03b38da9c7a63771f31194c7959914de1ad67ecc4f8c63925","abstract_canon_sha256":"909c74fa5ae307a78c01fa8a380f1bb5e5ccecfcccf0979f18f6cdc22658de2b"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:53:18.773215Z","signature_b64":"OmohHTfAzZYOs/EKTMhLW3La5CsT89E2w4wjc7ylde28eoL1oSsERxIJGZH0YVBMKx7iUcKoSdvqBaJe8r9RBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"bdeb1e056194e08128b2875dcddef86d7787ccdc9af49375e02dffc373546913","last_reissued_at":"2026-05-17T23:53:18.772472Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:53:18.772472Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Traces on cores of C*-algebras associated with self-similar maps","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DS"],"primary_cat":"math.OA","authors_text":"Tsuyoshi Kajiwara, Yasuo Watatani","submitted_at":"2012-04-26T06:16:01Z","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."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1204.5836","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":""},"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":"1204.5836","created_at":"2026-05-17T23:53:18.772615+00:00"},{"alias_kind":"arxiv_version","alias_value":"1204.5836v1","created_at":"2026-05-17T23:53:18.772615+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1204.5836","created_at":"2026-05-17T23:53:18.772615+00:00"},{"alias_kind":"pith_short_12","alias_value":"XXVR4BLBSTQI","created_at":"2026-05-18T12:27:27.928770+00:00"},{"alias_kind":"pith_short_16","alias_value":"XXVR4BLBSTQICKFS","created_at":"2026-05-18T12:27:27.928770+00:00"},{"alias_kind":"pith_short_8","alias_value":"XXVR4BLB","created_at":"2026-05-18T12:27:27.928770+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/XXVR4BLBSTQICKFSQ5O43XXYNV","json":"https://pith.science/pith/XXVR4BLBSTQICKFSQ5O43XXYNV.json","graph_json":"https://pith.science/api/pith-number/XXVR4BLBSTQICKFSQ5O43XXYNV/graph.json","events_json":"https://pith.science/api/pith-number/XXVR4BLBSTQICKFSQ5O43XXYNV/events.json","paper":"https://pith.science/paper/XXVR4BLB"},"agent_actions":{"view_html":"https://pith.science/pith/XXVR4BLBSTQICKFSQ5O43XXYNV","download_json":"https://pith.science/pith/XXVR4BLBSTQICKFSQ5O43XXYNV.json","view_paper":"https://pith.science/paper/XXVR4BLB","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1204.5836&json=true","fetch_graph":"https://pith.science/api/pith-number/XXVR4BLBSTQICKFSQ5O43XXYNV/graph.json","fetch_events":"https://pith.science/api/pith-number/XXVR4BLBSTQICKFSQ5O43XXYNV/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/XXVR4BLBSTQICKFSQ5O43XXYNV/action/timestamp_anchor","attest_storage":"https://pith.science/pith/XXVR4BLBSTQICKFSQ5O43XXYNV/action/storage_attestation","attest_author":"https://pith.science/pith/XXVR4BLBSTQICKFSQ5O43XXYNV/action/author_attestation","sign_citation":"https://pith.science/pith/XXVR4BLBSTQICKFSQ5O43XXYNV/action/citation_signature","submit_replication":"https://pith.science/pith/XXVR4BLBSTQICKFSQ5O43XXYNV/action/replication_record"}},"created_at":"2026-05-17T23:53:18.772615+00:00","updated_at":"2026-05-17T23:53:18.772615+00:00"}