{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2004:BRAXKLCSROSECWFS2DPKNMMEBM","short_pith_number":"pith:BRAXKLCS","canonical_record":{"source":{"id":"math/0411019","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"math.OA","submitted_at":"2004-11-01T01:18:15Z","cross_cats_sorted":["math.KT"],"title_canon_sha256":"f28f488209d7a815f6e3fa4a85410a8c45be458713593221beb92568bdd2c149","abstract_canon_sha256":"f6d37a49e5ae440842408f2a4950e222a701da63f3c40c59ab10ff1689b3620d"},"schema_version":"1.0"},"canonical_sha256":"0c41752c528ba44158b2d0dea6b1840b045a44db59fe123419536bd5fcf164d4","source":{"kind":"arxiv","id":"math/0411019","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0411019","created_at":"2026-07-04T14:39:19Z"},{"alias_kind":"arxiv_version","alias_value":"math/0411019v1","created_at":"2026-07-04T14:39:19Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0411019","created_at":"2026-07-04T14:39:19Z"},{"alias_kind":"pith_short_12","alias_value":"BRAXKLCSROSE","created_at":"2026-07-04T14:39:19Z"},{"alias_kind":"pith_short_16","alias_value":"BRAXKLCSROSECWFS","created_at":"2026-07-04T14:39:19Z"},{"alias_kind":"pith_short_8","alias_value":"BRAXKLCS","created_at":"2026-07-04T14:39:19Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2004:BRAXKLCSROSECWFS2DPKNMMEBM","target":"record","payload":{"canonical_record":{"source":{"id":"math/0411019","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"math.OA","submitted_at":"2004-11-01T01:18:15Z","cross_cats_sorted":["math.KT"],"title_canon_sha256":"f28f488209d7a815f6e3fa4a85410a8c45be458713593221beb92568bdd2c149","abstract_canon_sha256":"f6d37a49e5ae440842408f2a4950e222a701da63f3c40c59ab10ff1689b3620d"},"schema_version":"1.0"},"canonical_sha256":"0c41752c528ba44158b2d0dea6b1840b045a44db59fe123419536bd5fcf164d4","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-04T14:39:19.292502Z","signature_b64":"rqY4h9rK/DrAUPwwOuvlWiJOFNIVCeaSOLyzJD8MB35afjr5X/BPVrxGVT9+GWEXxH/L9rppJssRkc1x14WPCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0c41752c528ba44158b2d0dea6b1840b045a44db59fe123419536bd5fcf164d4","last_reissued_at":"2026-07-04T14:39:19.292118Z","signature_status":"signed_v1","first_computed_at":"2026-07-04T14:39:19.292118Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"math/0411019","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-04T14:39:19Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Wo3kPeJtU2wfh/peq2SQreIrELO4+d0fNfXMpeaR4jAC/WehlYeh95hu8jH5I0SSCP3U+rdWLq7QutyVcmcPDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-04T18:27:15.714958Z"},"content_sha256":"8a76f81818abd30117e906800ce91cafbcea55dff7428e4409c63fba6a9c5aa9","schema_version":"1.0","event_id":"sha256:8a76f81818abd30117e906800ce91cafbcea55dff7428e4409c63fba6a9c5aa9"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2004:BRAXKLCSROSECWFS2DPKNMMEBM","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The Local Index Formula in Semifinite von Neumann Algebras I: Spectral Flow","license":"","headline":"","cross_cats":["math.KT"],"primary_cat":"math.OA","authors_text":"Adam Rennie, Alan L. Carey, Fyodor A. Sukochev, John Phillips","submitted_at":"2004-11-01T01:18:15Z","abstract_excerpt":"We generalise the local index formula of Connes and Moscovici to the case of spectral triples for a *-subalgebra \\A of a general semifinite von Neumann algebra. In this setting it gives a formula for spectral flow along a path joining an unbounded self adjoint Breuer-Fredholm operator, affiliated to the von Neumann algebra, to a unitarily equivalent operator. Our proof is novel even in the setting of the original theorem and relies on the introduction of a function valued cocycle which is `almost' a (b,B)-cocycle in the cyclic cohomology of \\A."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0411019","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/0411019/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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-04T14:39:19Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"W+aiZkXgqfwAfkF/8sB+4x0ILLI4R1H3m1JkXjRhwxyDiTiDeJw3zD3PqknsfSb3kDeSf2ki+vKizo+NnYI/Cg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-04T18:27:15.715363Z"},"content_sha256":"1f87a41d60d54b7898b28522fcb06b010d95004a57ac5fd6da07f5c166042b98","schema_version":"1.0","event_id":"sha256:1f87a41d60d54b7898b28522fcb06b010d95004a57ac5fd6da07f5c166042b98"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/BRAXKLCSROSECWFS2DPKNMMEBM/bundle.json","state_url":"https://pith.science/pith/BRAXKLCSROSECWFS2DPKNMMEBM/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/BRAXKLCSROSECWFS2DPKNMMEBM/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-07-04T18:27:15Z","links":{"resolver":"https://pith.science/pith/BRAXKLCSROSECWFS2DPKNMMEBM","bundle":"https://pith.science/pith/BRAXKLCSROSECWFS2DPKNMMEBM/bundle.json","state":"https://pith.science/pith/BRAXKLCSROSECWFS2DPKNMMEBM/state.json","well_known_bundle":"https://pith.science/.well-known/pith/BRAXKLCSROSECWFS2DPKNMMEBM/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2004:BRAXKLCSROSECWFS2DPKNMMEBM","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"f6d37a49e5ae440842408f2a4950e222a701da63f3c40c59ab10ff1689b3620d","cross_cats_sorted":["math.KT"],"license":"","primary_cat":"math.OA","submitted_at":"2004-11-01T01:18:15Z","title_canon_sha256":"f28f488209d7a815f6e3fa4a85410a8c45be458713593221beb92568bdd2c149"},"schema_version":"1.0","source":{"id":"math/0411019","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0411019","created_at":"2026-07-04T14:39:19Z"},{"alias_kind":"arxiv_version","alias_value":"math/0411019v1","created_at":"2026-07-04T14:39:19Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0411019","created_at":"2026-07-04T14:39:19Z"},{"alias_kind":"pith_short_12","alias_value":"BRAXKLCSROSE","created_at":"2026-07-04T14:39:19Z"},{"alias_kind":"pith_short_16","alias_value":"BRAXKLCSROSECWFS","created_at":"2026-07-04T14:39:19Z"},{"alias_kind":"pith_short_8","alias_value":"BRAXKLCS","created_at":"2026-07-04T14:39:19Z"}],"graph_snapshots":[{"event_id":"sha256:1f87a41d60d54b7898b28522fcb06b010d95004a57ac5fd6da07f5c166042b98","target":"graph","created_at":"2026-07-04T14:39:19Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/math/0411019/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We generalise the local index formula of Connes and Moscovici to the case of spectral triples for a *-subalgebra \\A of a general semifinite von Neumann algebra. In this setting it gives a formula for spectral flow along a path joining an unbounded self adjoint Breuer-Fredholm operator, affiliated to the von Neumann algebra, to a unitarily equivalent operator. Our proof is novel even in the setting of the original theorem and relies on the introduction of a function valued cocycle which is `almost' a (b,B)-cocycle in the cyclic cohomology of \\A.","authors_text":"Adam Rennie, Alan L. Carey, Fyodor A. Sukochev, John Phillips","cross_cats":["math.KT"],"headline":"","license":"","primary_cat":"math.OA","submitted_at":"2004-11-01T01:18:15Z","title":"The Local Index Formula in Semifinite von Neumann Algebras I: Spectral Flow"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0411019","kind":"arxiv","version":1},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:8a76f81818abd30117e906800ce91cafbcea55dff7428e4409c63fba6a9c5aa9","target":"record","created_at":"2026-07-04T14:39:19Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"f6d37a49e5ae440842408f2a4950e222a701da63f3c40c59ab10ff1689b3620d","cross_cats_sorted":["math.KT"],"license":"","primary_cat":"math.OA","submitted_at":"2004-11-01T01:18:15Z","title_canon_sha256":"f28f488209d7a815f6e3fa4a85410a8c45be458713593221beb92568bdd2c149"},"schema_version":"1.0","source":{"id":"math/0411019","kind":"arxiv","version":1}},"canonical_sha256":"0c41752c528ba44158b2d0dea6b1840b045a44db59fe123419536bd5fcf164d4","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"0c41752c528ba44158b2d0dea6b1840b045a44db59fe123419536bd5fcf164d4","first_computed_at":"2026-07-04T14:39:19.292118Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-04T14:39:19.292118Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"rqY4h9rK/DrAUPwwOuvlWiJOFNIVCeaSOLyzJD8MB35afjr5X/BPVrxGVT9+GWEXxH/L9rppJssRkc1x14WPCw==","signature_status":"signed_v1","signed_at":"2026-07-04T14:39:19.292502Z","signed_message":"canonical_sha256_bytes"},"source_id":"math/0411019","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8a76f81818abd30117e906800ce91cafbcea55dff7428e4409c63fba6a9c5aa9","sha256:1f87a41d60d54b7898b28522fcb06b010d95004a57ac5fd6da07f5c166042b98"],"state_sha256":"c0702281e4b1175f8b2a0c98e1fdd486b8e6195e0ad97a091bdae1e3ce3b1a79"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"tuD9WPCckWLyyXp24QZNABh/sHIk2gkDs00Nk2Q38gYxMT9r/a86NpSZ8EL9WXWZTBLUwRiDaHE03ERqg/wuCQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-04T18:27:15.717593Z","bundle_sha256":"4e025231542a54d9104803611c5ed413f4f70f6c374f6a79d22ff56629b7e703"}}