{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2013:UYXQMER4LIJZKJNNP7MZDRCCZL","short_pith_number":"pith:UYXQMER4","schema_version":"1.0","canonical_sha256":"a62f06123c5a139525ad7fd991c442cac35dcb547278b930384a038856873aa4","source":{"kind":"arxiv","id":"1303.1062","version":1},"attestation_state":"computed","paper":{"title":"Isomorphisms of Lattices of Bures-Closed Bimodules over Cartan MASAs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OA","authors_text":"Adam H. Fuller, David R. Pitts","submitted_at":"2013-03-05T15:19:34Z","abstract_excerpt":"For i=1,2, let (M_i,D_i) be pairs consisting of a Cartan MASA D_i in a von Neumann algebra M_i, let atom(D_i) be the set of atoms of D_i, and let S_i be the lattice of Bures-closed D_i bimodules in M_i. We show that when M_i have separable preduals, there is a lattice isomorphism between S_1 and S_2 if and only if the sets {(Q_1, Q_2) \\in atom(D_i) x atom(D_i): Q_1 M_i Q_2 \\neq (0)} have the same cardinality. In particular, when D_i is non-atomic, S_i is isomorphic to the lattice of projections in L^\\infty([0,1],m) where m is Lebesgue measure, regardless of the isomorphism classes of M_1 and M"},"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":"1303.1062","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2013-03-05T15:19:34Z","cross_cats_sorted":[],"title_canon_sha256":"20b35e5582c635c87d711501f22372ad262d5304d4b7d0a84278613fb0738fe9","abstract_canon_sha256":"cdac9f6162ec81fe11c78ba6f4c21b7aca5c058bedcc9c61ff34be904fa9d33a"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:15:00.613035Z","signature_b64":"GDhUdENC9WBv6yR4ntvu4BnkUoOK8eMoumxfH9KPbaFiVHjvPQ1ZZyh7uAr580S9kp8/al+RAVA77E6QOoSWCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a62f06123c5a139525ad7fd991c442cac35dcb547278b930384a038856873aa4","last_reissued_at":"2026-05-18T01:15:00.612544Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:15:00.612544Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Isomorphisms of Lattices of Bures-Closed Bimodules over Cartan MASAs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OA","authors_text":"Adam H. Fuller, David R. Pitts","submitted_at":"2013-03-05T15:19:34Z","abstract_excerpt":"For i=1,2, let (M_i,D_i) be pairs consisting of a Cartan MASA D_i in a von Neumann algebra M_i, let atom(D_i) be the set of atoms of D_i, and let S_i be the lattice of Bures-closed D_i bimodules in M_i. We show that when M_i have separable preduals, there is a lattice isomorphism between S_1 and S_2 if and only if the sets {(Q_1, Q_2) \\in atom(D_i) x atom(D_i): Q_1 M_i Q_2 \\neq (0)} have the same cardinality. In particular, when D_i is non-atomic, S_i is isomorphic to the lattice of projections in L^\\infty([0,1],m) where m is Lebesgue measure, regardless of the isomorphism classes of M_1 and M"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1303.1062","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":"1303.1062","created_at":"2026-05-18T01:15:00.612615+00:00"},{"alias_kind":"arxiv_version","alias_value":"1303.1062v1","created_at":"2026-05-18T01:15:00.612615+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1303.1062","created_at":"2026-05-18T01:15:00.612615+00:00"},{"alias_kind":"pith_short_12","alias_value":"UYXQMER4LIJZ","created_at":"2026-05-18T12:28:02.375192+00:00"},{"alias_kind":"pith_short_16","alias_value":"UYXQMER4LIJZKJNN","created_at":"2026-05-18T12:28:02.375192+00:00"},{"alias_kind":"pith_short_8","alias_value":"UYXQMER4","created_at":"2026-05-18T12:28:02.375192+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/UYXQMER4LIJZKJNNP7MZDRCCZL","json":"https://pith.science/pith/UYXQMER4LIJZKJNNP7MZDRCCZL.json","graph_json":"https://pith.science/api/pith-number/UYXQMER4LIJZKJNNP7MZDRCCZL/graph.json","events_json":"https://pith.science/api/pith-number/UYXQMER4LIJZKJNNP7MZDRCCZL/events.json","paper":"https://pith.science/paper/UYXQMER4"},"agent_actions":{"view_html":"https://pith.science/pith/UYXQMER4LIJZKJNNP7MZDRCCZL","download_json":"https://pith.science/pith/UYXQMER4LIJZKJNNP7MZDRCCZL.json","view_paper":"https://pith.science/paper/UYXQMER4","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1303.1062&json=true","fetch_graph":"https://pith.science/api/pith-number/UYXQMER4LIJZKJNNP7MZDRCCZL/graph.json","fetch_events":"https://pith.science/api/pith-number/UYXQMER4LIJZKJNNP7MZDRCCZL/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/UYXQMER4LIJZKJNNP7MZDRCCZL/action/timestamp_anchor","attest_storage":"https://pith.science/pith/UYXQMER4LIJZKJNNP7MZDRCCZL/action/storage_attestation","attest_author":"https://pith.science/pith/UYXQMER4LIJZKJNNP7MZDRCCZL/action/author_attestation","sign_citation":"https://pith.science/pith/UYXQMER4LIJZKJNNP7MZDRCCZL/action/citation_signature","submit_replication":"https://pith.science/pith/UYXQMER4LIJZKJNNP7MZDRCCZL/action/replication_record"}},"created_at":"2026-05-18T01:15:00.612615+00:00","updated_at":"2026-05-18T01:15:00.612615+00:00"}