{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2004:TXF6SPX262QNTVCQRTQ5CRAGLF","short_pith_number":"pith:TXF6SPX2","schema_version":"1.0","canonical_sha256":"9dcbe93efaf6a0d9d4508ce1d14406595f88a5738707990f68223659ee37db96","source":{"kind":"arxiv","id":"math/0411021","version":1},"attestation_state":"computed","paper":{"title":"The Local Index Formula in Semifinite von Neumann Algebras II: The Even Case","license":"","headline":"","cross_cats":["math.KT"],"primary_cat":"math.OA","authors_text":"Adam Rennie, Alan L. Carey, Fyodor A. Sukochev, John Phillips","submitted_at":"2004-11-01T01:29:33Z","abstract_excerpt":"We generalise the even local index formula of Connes and Moscovici to the case of spectral triples for a *-subalgebra \\A of a general semifinite von Neumann algebra. The proof is a variant of that for the odd case which appears in Part I. To allow for algebras with a non-trivial centre we have to establish a theory of unbounded Fredholm operators in a general semifinite von Neumann algebra and in particular prove a generalised McKean-Singer 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":"math/0411021","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"math.OA","submitted_at":"2004-11-01T01:29:33Z","cross_cats_sorted":["math.KT"],"title_canon_sha256":"3190867d29f1ea0df63d96a99522cd564e35eb17c9ebdb301f34758df1cc1b61","abstract_canon_sha256":"a0b1faf86c6ed58721c2317d4c4c25c84c79e94b12aa96998689c63a21503ac9"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-04T14:39:19.316749Z","signature_b64":"HNxDBCaCHBh8+cR3i2etD5jsAw8cSfgDkpMK3JTYyU18g/MC3NtYy2AAn/c6xuDVbMtqYCRWkWMMeUau1s1AAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9dcbe93efaf6a0d9d4508ce1d14406595f88a5738707990f68223659ee37db96","last_reissued_at":"2026-07-04T14:39:19.316354Z","signature_status":"signed_v1","first_computed_at":"2026-07-04T14:39:19.316354Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The Local Index Formula in Semifinite von Neumann Algebras II: The Even Case","license":"","headline":"","cross_cats":["math.KT"],"primary_cat":"math.OA","authors_text":"Adam Rennie, Alan L. Carey, Fyodor A. Sukochev, John Phillips","submitted_at":"2004-11-01T01:29:33Z","abstract_excerpt":"We generalise the even local index formula of Connes and Moscovici to the case of spectral triples for a *-subalgebra \\A of a general semifinite von Neumann algebra. The proof is a variant of that for the odd case which appears in Part I. To allow for algebras with a non-trivial centre we have to establish a theory of unbounded Fredholm operators in a general semifinite von Neumann algebra and in particular prove a generalised McKean-Singer formula."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0411021","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/math/0411021/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":"math/0411021","created_at":"2026-07-04T14:39:19.316412+00:00"},{"alias_kind":"arxiv_version","alias_value":"math/0411021v1","created_at":"2026-07-04T14:39:19.316412+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0411021","created_at":"2026-07-04T14:39:19.316412+00:00"},{"alias_kind":"pith_short_12","alias_value":"TXF6SPX262QN","created_at":"2026-07-04T14:39:19.316412+00:00"},{"alias_kind":"pith_short_16","alias_value":"TXF6SPX262QNTVCQ","created_at":"2026-07-04T14:39:19.316412+00:00"},{"alias_kind":"pith_short_8","alias_value":"TXF6SPX2","created_at":"2026-07-04T14:39:19.316412+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/TXF6SPX262QNTVCQRTQ5CRAGLF","json":"https://pith.science/pith/TXF6SPX262QNTVCQRTQ5CRAGLF.json","graph_json":"https://pith.science/api/pith-number/TXF6SPX262QNTVCQRTQ5CRAGLF/graph.json","events_json":"https://pith.science/api/pith-number/TXF6SPX262QNTVCQRTQ5CRAGLF/events.json","paper":"https://pith.science/paper/TXF6SPX2"},"agent_actions":{"view_html":"https://pith.science/pith/TXF6SPX262QNTVCQRTQ5CRAGLF","download_json":"https://pith.science/pith/TXF6SPX262QNTVCQRTQ5CRAGLF.json","view_paper":"https://pith.science/paper/TXF6SPX2","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=math/0411021&json=true","fetch_graph":"https://pith.science/api/pith-number/TXF6SPX262QNTVCQRTQ5CRAGLF/graph.json","fetch_events":"https://pith.science/api/pith-number/TXF6SPX262QNTVCQRTQ5CRAGLF/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/TXF6SPX262QNTVCQRTQ5CRAGLF/action/timestamp_anchor","attest_storage":"https://pith.science/pith/TXF6SPX262QNTVCQRTQ5CRAGLF/action/storage_attestation","attest_author":"https://pith.science/pith/TXF6SPX262QNTVCQRTQ5CRAGLF/action/author_attestation","sign_citation":"https://pith.science/pith/TXF6SPX262QNTVCQRTQ5CRAGLF/action/citation_signature","submit_replication":"https://pith.science/pith/TXF6SPX262QNTVCQRTQ5CRAGLF/action/replication_record"}},"created_at":"2026-07-04T14:39:19.316412+00:00","updated_at":"2026-07-04T14:39:19.316412+00:00"}