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Mercer's argument relied upon the Spectral Theorem for Bimodules of Muhly, Saito and Solel [15, Theorem 2.5]. Unfortunately, the arguments in the literature supporting [15, Theorem 2.5] contain gaps, and hence Mercer's proof is incomplete.\n  In this paper, we use the outline in [16, Remark 2.17] to give a proof of Mercer's Theorem under the additional hypothesis th"},"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":"1202.6408","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2012-02-28T23:17:47Z","cross_cats_sorted":[],"title_canon_sha256":"266a5487facab9a96ced167694909657d2ca3cbb20f5e55307f96db1f5f51700","abstract_canon_sha256":"1eb71b1fd3a5806ef26436eb55eb0076a53873e6ca858a35a1132e840620b083"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:15:00.643026Z","signature_b64":"q8bk8C33AbNGNMUw/iuNEfXHze8QFJ8XW0IkAsD+tmN/tXiDo4QEEgcA1koBxTYRLKVkZdwrRHLCH2dQn5eODg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f092a83caadfbadbe8b37248ea8325e3169fe568248de785bb41dca0948d6e89","last_reissued_at":"2026-05-18T01:15:00.642622Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:15:00.642622Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Bimodules over Cartan MASAs in von Neumann Algebras, Norming Algebras, and Mercer's Theorem","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OA","authors_text":"David R. Pitts, Jan Cameron, Vrej Zarikian","submitted_at":"2012-02-28T23:17:47Z","abstract_excerpt":"In a 1991 paper, R. Mercer asserted that a Cartan bimodule isomorphism between Cartan bimodule algebras A_1 and A_2 extends uniquely to a normal *-isomorphism of the von Neumann algebras generated by A_1 and A_2 [13, Corollary 4.3]. Mercer's argument relied upon the Spectral Theorem for Bimodules of Muhly, Saito and Solel [15, Theorem 2.5]. Unfortunately, the arguments in the literature supporting [15, Theorem 2.5] contain gaps, and hence Mercer's proof is incomplete.\n  In this paper, we use the outline in [16, Remark 2.17] to give a proof of Mercer's Theorem under the additional hypothesis th"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1202.6408","kind":"arxiv","version":2},"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":"1202.6408","created_at":"2026-05-18T01:15:00.642688+00:00"},{"alias_kind":"arxiv_version","alias_value":"1202.6408v2","created_at":"2026-05-18T01:15:00.642688+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1202.6408","created_at":"2026-05-18T01:15:00.642688+00:00"},{"alias_kind":"pith_short_12","alias_value":"6CJKQPFK365N","created_at":"2026-05-18T12:26:56.085431+00:00"},{"alias_kind":"pith_short_16","alias_value":"6CJKQPFK365NX2FT","created_at":"2026-05-18T12:26:56.085431+00:00"},{"alias_kind":"pith_short_8","alias_value":"6CJKQPFK","created_at":"2026-05-18T12:26:56.085431+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/6CJKQPFK365NX2FTOJEOVAZF4M","json":"https://pith.science/pith/6CJKQPFK365NX2FTOJEOVAZF4M.json","graph_json":"https://pith.science/api/pith-number/6CJKQPFK365NX2FTOJEOVAZF4M/graph.json","events_json":"https://pith.science/api/pith-number/6CJKQPFK365NX2FTOJEOVAZF4M/events.json","paper":"https://pith.science/paper/6CJKQPFK"},"agent_actions":{"view_html":"https://pith.science/pith/6CJKQPFK365NX2FTOJEOVAZF4M","download_json":"https://pith.science/pith/6CJKQPFK365NX2FTOJEOVAZF4M.json","view_paper":"https://pith.science/paper/6CJKQPFK","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1202.6408&json=true","fetch_graph":"https://pith.science/api/pith-number/6CJKQPFK365NX2FTOJEOVAZF4M/graph.json","fetch_events":"https://pith.science/api/pith-number/6CJKQPFK365NX2FTOJEOVAZF4M/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/6CJKQPFK365NX2FTOJEOVAZF4M/action/timestamp_anchor","attest_storage":"https://pith.science/pith/6CJKQPFK365NX2FTOJEOVAZF4M/action/storage_attestation","attest_author":"https://pith.science/pith/6CJKQPFK365NX2FTOJEOVAZF4M/action/author_attestation","sign_citation":"https://pith.science/pith/6CJKQPFK365NX2FTOJEOVAZF4M/action/citation_signature","submit_replication":"https://pith.science/pith/6CJKQPFK365NX2FTOJEOVAZF4M/action/replication_record"}},"created_at":"2026-05-18T01:15:00.642688+00:00","updated_at":"2026-05-18T01:15:00.642688+00:00"}