{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2026:VCIL6OQDJUIVG5Q2Q3I5J2IMAD","short_pith_number":"pith:VCIL6OQD","schema_version":"1.0","canonical_sha256":"a890bf3a034d1153761a86d1d4e90c00ecfe62311cf7b157a15acfd5e5638e69","source":{"kind":"arxiv","id":"2605.22683","version":1},"attestation_state":"computed","paper":{"title":"Tracially reflexive C*-algebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OA","authors_text":"Laurent Cantier","submitted_at":"2026-05-21T16:25:49Z","abstract_excerpt":"Motivated by a question of L. Robert, asking whether $\\rm L(T(A)) = Lsc_{C}(T(A))$ for any separable C*-algebra A, we introduce and initiate the study of \\emph{tracially reflexive C*-algebras}. We first prove that commutative C*-algebras are tracially reflexive. We also prove that tracial reflexiveness satisfies permanence properties, such as being preserved under inductive limits. Subsequently, we expose two criteria for tracial reflexiveness, using the Cuntz semigroup and a weak version of the Schr\\\"{o}der-Simpson theorem, respectively. In particular, separable topological dimension zero C*-"},"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":"2605.22683","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2026-05-21T16:25:49Z","cross_cats_sorted":[],"title_canon_sha256":"a290b1bd7f26ae73f87171abdd127c62657a93b6fd34f72707344192ebe3863a","abstract_canon_sha256":"03f26b1d7e517ca86c50845c037dba0ef4763127c0fc1901766181c639237130"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-22T02:04:50.115224Z","signature_b64":"+OsWcGgbHL7WhBfk1SuokHMMqf1B6zGCbUTv6P3G1TYuhq8eRV0FFh6r7nmHYEXJLPN0NdhpORlgeUs/hsOZCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a890bf3a034d1153761a86d1d4e90c00ecfe62311cf7b157a15acfd5e5638e69","last_reissued_at":"2026-05-22T02:04:50.114387Z","signature_status":"signed_v1","first_computed_at":"2026-05-22T02:04:50.114387Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Tracially reflexive C*-algebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OA","authors_text":"Laurent Cantier","submitted_at":"2026-05-21T16:25:49Z","abstract_excerpt":"Motivated by a question of L. Robert, asking whether $\\rm L(T(A)) = Lsc_{C}(T(A))$ for any separable C*-algebra A, we introduce and initiate the study of \\emph{tracially reflexive C*-algebras}. We first prove that commutative C*-algebras are tracially reflexive. We also prove that tracial reflexiveness satisfies permanence properties, such as being preserved under inductive limits. Subsequently, we expose two criteria for tracial reflexiveness, using the Cuntz semigroup and a weak version of the Schr\\\"{o}der-Simpson theorem, respectively. In particular, separable topological dimension zero C*-"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2605.22683","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/2605.22683/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"},"aliases":[{"alias_kind":"arxiv","alias_value":"2605.22683","created_at":"2026-05-22T02:04:50.114509+00:00"},{"alias_kind":"arxiv_version","alias_value":"2605.22683v1","created_at":"2026-05-22T02:04:50.114509+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2605.22683","created_at":"2026-05-22T02:04:50.114509+00:00"},{"alias_kind":"pith_short_12","alias_value":"VCIL6OQDJUIV","created_at":"2026-05-22T02:04:50.114509+00:00"},{"alias_kind":"pith_short_16","alias_value":"VCIL6OQDJUIVG5Q2","created_at":"2026-05-22T02:04:50.114509+00:00"},{"alias_kind":"pith_short_8","alias_value":"VCIL6OQD","created_at":"2026-05-22T02:04:50.114509+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/VCIL6OQDJUIVG5Q2Q3I5J2IMAD","json":"https://pith.science/pith/VCIL6OQDJUIVG5Q2Q3I5J2IMAD.json","graph_json":"https://pith.science/api/pith-number/VCIL6OQDJUIVG5Q2Q3I5J2IMAD/graph.json","events_json":"https://pith.science/api/pith-number/VCIL6OQDJUIVG5Q2Q3I5J2IMAD/events.json","paper":"https://pith.science/paper/VCIL6OQD"},"agent_actions":{"view_html":"https://pith.science/pith/VCIL6OQDJUIVG5Q2Q3I5J2IMAD","download_json":"https://pith.science/pith/VCIL6OQDJUIVG5Q2Q3I5J2IMAD.json","view_paper":"https://pith.science/paper/VCIL6OQD","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2605.22683&json=true","fetch_graph":"https://pith.science/api/pith-number/VCIL6OQDJUIVG5Q2Q3I5J2IMAD/graph.json","fetch_events":"https://pith.science/api/pith-number/VCIL6OQDJUIVG5Q2Q3I5J2IMAD/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/VCIL6OQDJUIVG5Q2Q3I5J2IMAD/action/timestamp_anchor","attest_storage":"https://pith.science/pith/VCIL6OQDJUIVG5Q2Q3I5J2IMAD/action/storage_attestation","attest_author":"https://pith.science/pith/VCIL6OQDJUIVG5Q2Q3I5J2IMAD/action/author_attestation","sign_citation":"https://pith.science/pith/VCIL6OQDJUIVG5Q2Q3I5J2IMAD/action/citation_signature","submit_replication":"https://pith.science/pith/VCIL6OQDJUIVG5Q2Q3I5J2IMAD/action/replication_record"}},"created_at":"2026-05-22T02:04:50.114509+00:00","updated_at":"2026-05-22T02:04:50.114509+00:00"}