{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2011:RHJPSHEFHVETQUTTOB43YCMADA","short_pith_number":"pith:RHJPSHEF","schema_version":"1.0","canonical_sha256":"89d2f91c853d493852737079bc0980181774d50b3654fec3a3a23abeb0b3f24d","source":{"kind":"arxiv","id":"1108.5021","version":1},"attestation_state":"computed","paper":{"title":"Approximate double commutants in von Neumann algebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.FA"],"primary_cat":"math.OA","authors_text":"Don Hadwin","submitted_at":"2011-08-25T06:36:14Z","abstract_excerpt":"Richard Kadison showed that not every commutative von Neumann subalgebra of a factor von Neumann algebra is equal to its relative double commutant. We prove that every commutative C*-subalgebra of a centrally prime C*-algebra $B$ equals its relative approximate double commutant. If $B$ is a von Neumann algebra, there is a related distance formula."},"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":"1108.5021","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2011-08-25T06:36:14Z","cross_cats_sorted":["math.FA"],"title_canon_sha256":"ffa622ed1b565dfc34d660aeb59ba94d04c588f27049799757d41ac4b0b336ce","abstract_canon_sha256":"25534e8e34fcec604ec1e8ced87aa66df0d1c58a76e5ec1adc860b60db18df09"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:14:45.569879Z","signature_b64":"UxJSbtxvSj6L0gbrR+Xjj8SpxOU8C9DjeW5zAQDiAywPbYn/qAPANLRkwTePwXNPNLCAc91eDRxuwNS3z2sNCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"89d2f91c853d493852737079bc0980181774d50b3654fec3a3a23abeb0b3f24d","last_reissued_at":"2026-05-18T04:14:45.569418Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:14:45.569418Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Approximate double commutants in von Neumann algebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.FA"],"primary_cat":"math.OA","authors_text":"Don Hadwin","submitted_at":"2011-08-25T06:36:14Z","abstract_excerpt":"Richard Kadison showed that not every commutative von Neumann subalgebra of a factor von Neumann algebra is equal to its relative double commutant. We prove that every commutative C*-subalgebra of a centrally prime C*-algebra $B$ equals its relative approximate double commutant. If $B$ is a von Neumann algebra, there is a related distance formula."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1108.5021","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":"1108.5021","created_at":"2026-05-18T04:14:45.569487+00:00"},{"alias_kind":"arxiv_version","alias_value":"1108.5021v1","created_at":"2026-05-18T04:14:45.569487+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1108.5021","created_at":"2026-05-18T04:14:45.569487+00:00"},{"alias_kind":"pith_short_12","alias_value":"RHJPSHEFHVET","created_at":"2026-05-18T12:26:41.206345+00:00"},{"alias_kind":"pith_short_16","alias_value":"RHJPSHEFHVETQUTT","created_at":"2026-05-18T12:26:41.206345+00:00"},{"alias_kind":"pith_short_8","alias_value":"RHJPSHEF","created_at":"2026-05-18T12:26:41.206345+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/RHJPSHEFHVETQUTTOB43YCMADA","json":"https://pith.science/pith/RHJPSHEFHVETQUTTOB43YCMADA.json","graph_json":"https://pith.science/api/pith-number/RHJPSHEFHVETQUTTOB43YCMADA/graph.json","events_json":"https://pith.science/api/pith-number/RHJPSHEFHVETQUTTOB43YCMADA/events.json","paper":"https://pith.science/paper/RHJPSHEF"},"agent_actions":{"view_html":"https://pith.science/pith/RHJPSHEFHVETQUTTOB43YCMADA","download_json":"https://pith.science/pith/RHJPSHEFHVETQUTTOB43YCMADA.json","view_paper":"https://pith.science/paper/RHJPSHEF","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1108.5021&json=true","fetch_graph":"https://pith.science/api/pith-number/RHJPSHEFHVETQUTTOB43YCMADA/graph.json","fetch_events":"https://pith.science/api/pith-number/RHJPSHEFHVETQUTTOB43YCMADA/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/RHJPSHEFHVETQUTTOB43YCMADA/action/timestamp_anchor","attest_storage":"https://pith.science/pith/RHJPSHEFHVETQUTTOB43YCMADA/action/storage_attestation","attest_author":"https://pith.science/pith/RHJPSHEFHVETQUTTOB43YCMADA/action/author_attestation","sign_citation":"https://pith.science/pith/RHJPSHEFHVETQUTTOB43YCMADA/action/citation_signature","submit_replication":"https://pith.science/pith/RHJPSHEFHVETQUTTOB43YCMADA/action/replication_record"}},"created_at":"2026-05-18T04:14:45.569487+00:00","updated_at":"2026-05-18T04:14:45.569487+00:00"}