{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2005:UY6FZWKA4LAIP4RDJ6PTQTR727","short_pith_number":"pith:UY6FZWKA","canonical_record":{"source":{"id":"math/0510532","kind":"arxiv","version":4},"metadata":{"license":"","primary_cat":"math.GT","submitted_at":"2005-10-25T16:59:26Z","cross_cats_sorted":["math-ph","math.DG","math.MP"],"title_canon_sha256":"9f6f3695cded15fbebbee1242db52c0ae48bf53e876dfd6eab878afa4f6c243a","abstract_canon_sha256":"43feab29de344797330eb3413d0ec7563e654a7c314bcedda00a831e92a40b0c"},"schema_version":"1.0"},"canonical_sha256":"a63c5cd940e2c087f2234f9f384e3fd7c2ab8fbaadd36d05e2e91436ad92c2ea","source":{"kind":"arxiv","id":"math/0510532","version":4},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0510532","created_at":"2026-05-18T02:37:59Z"},{"alias_kind":"arxiv_version","alias_value":"math/0510532v4","created_at":"2026-05-18T02:37:59Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0510532","created_at":"2026-05-18T02:37:59Z"},{"alias_kind":"pith_short_12","alias_value":"UY6FZWKA4LAI","created_at":"2026-05-18T12:25:53Z"},{"alias_kind":"pith_short_16","alias_value":"UY6FZWKA4LAIP4RD","created_at":"2026-05-18T12:25:53Z"},{"alias_kind":"pith_short_8","alias_value":"UY6FZWKA","created_at":"2026-05-18T12:25:53Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2005:UY6FZWKA4LAIP4RDJ6PTQTR727","target":"record","payload":{"canonical_record":{"source":{"id":"math/0510532","kind":"arxiv","version":4},"metadata":{"license":"","primary_cat":"math.GT","submitted_at":"2005-10-25T16:59:26Z","cross_cats_sorted":["math-ph","math.DG","math.MP"],"title_canon_sha256":"9f6f3695cded15fbebbee1242db52c0ae48bf53e876dfd6eab878afa4f6c243a","abstract_canon_sha256":"43feab29de344797330eb3413d0ec7563e654a7c314bcedda00a831e92a40b0c"},"schema_version":"1.0"},"canonical_sha256":"a63c5cd940e2c087f2234f9f384e3fd7c2ab8fbaadd36d05e2e91436ad92c2ea","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:37:59.695797Z","signature_b64":"73lwu9QZPIUmSHXBpH9CacpPy7A0cQRclfY5X+tz95vowsUhzzP3M6+C0KTyP9stMzKhJzNyNFG5m97ncio2BQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a63c5cd940e2c087f2234f9f384e3fd7c2ab8fbaadd36d05e2e91436ad92c2ea","last_reissued_at":"2026-05-18T02:37:59.695247Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:37:59.695247Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"math/0510532","source_version":4,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:37:59Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"MsKT9WlS5k30/5tmu+nJJyCsMNkYfl4EBlDCaFM6hFQwgjbz+BMOhJwevDxxutjUDAWkOfaYUqkKFf+B10/3AA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T14:14:49.604071Z"},"content_sha256":"87dbdd50d0495de698e6a57c7cc2dd378f641eff433b6df98e658c7c317e5121","schema_version":"1.0","event_id":"sha256:87dbdd50d0495de698e6a57c7cc2dd378f641eff433b6df98e658c7c317e5121"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2005:UY6FZWKA4LAIP4RDJ6PTQTR727","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Refined Analytic Torsion as an Element of the Determinant Line","license":"","headline":"","cross_cats":["math-ph","math.DG","math.MP"],"primary_cat":"math.GT","authors_text":"Maxim Braverman, Thomas Kappeler","submitted_at":"2005-10-25T16:59:26Z","abstract_excerpt":"We construct a canonical element, called the refined analytic torsion, of the determinant line of the cohomology of a closed oriented odd-dimensional manifold M with coefficients in a flat complex vector bundle E. We compute the Ray-Singer norm of the refined analytic torsion. In particular, if there exists a flat Hermitian metric on E, we show that this norm is equal to 1. We prove a duality theorem, establishing a relationship between the refined analytic torsions corresponding to a flat connection and its dual."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0510532","kind":"arxiv","version":4},"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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:37:59Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"OTtZZxwlc73s1g7qFb/SUl3iCMH8H+CAqXZpRLNcoUgVTPx1Qo1jEbd/YcDRYczaojQqgL3+g1g4vxH23mDIAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T14:14:49.604433Z"},"content_sha256":"cfc12c130ca700e88492b3e532b6869177d5711ceec1394a5b23540efee3fcad","schema_version":"1.0","event_id":"sha256:cfc12c130ca700e88492b3e532b6869177d5711ceec1394a5b23540efee3fcad"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/UY6FZWKA4LAIP4RDJ6PTQTR727/bundle.json","state_url":"https://pith.science/pith/UY6FZWKA4LAIP4RDJ6PTQTR727/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/UY6FZWKA4LAIP4RDJ6PTQTR727/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":"2026-05-28T14:14:49Z","links":{"resolver":"https://pith.science/pith/UY6FZWKA4LAIP4RDJ6PTQTR727","bundle":"https://pith.science/pith/UY6FZWKA4LAIP4RDJ6PTQTR727/bundle.json","state":"https://pith.science/pith/UY6FZWKA4LAIP4RDJ6PTQTR727/state.json","well_known_bundle":"https://pith.science/.well-known/pith/UY6FZWKA4LAIP4RDJ6PTQTR727/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2005:UY6FZWKA4LAIP4RDJ6PTQTR727","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":"43feab29de344797330eb3413d0ec7563e654a7c314bcedda00a831e92a40b0c","cross_cats_sorted":["math-ph","math.DG","math.MP"],"license":"","primary_cat":"math.GT","submitted_at":"2005-10-25T16:59:26Z","title_canon_sha256":"9f6f3695cded15fbebbee1242db52c0ae48bf53e876dfd6eab878afa4f6c243a"},"schema_version":"1.0","source":{"id":"math/0510532","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0510532","created_at":"2026-05-18T02:37:59Z"},{"alias_kind":"arxiv_version","alias_value":"math/0510532v4","created_at":"2026-05-18T02:37:59Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0510532","created_at":"2026-05-18T02:37:59Z"},{"alias_kind":"pith_short_12","alias_value":"UY6FZWKA4LAI","created_at":"2026-05-18T12:25:53Z"},{"alias_kind":"pith_short_16","alias_value":"UY6FZWKA4LAIP4RD","created_at":"2026-05-18T12:25:53Z"},{"alias_kind":"pith_short_8","alias_value":"UY6FZWKA","created_at":"2026-05-18T12:25:53Z"}],"graph_snapshots":[{"event_id":"sha256:cfc12c130ca700e88492b3e532b6869177d5711ceec1394a5b23540efee3fcad","target":"graph","created_at":"2026-05-18T02:37:59Z","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"},"paper":{"abstract_excerpt":"We construct a canonical element, called the refined analytic torsion, of the determinant line of the cohomology of a closed oriented odd-dimensional manifold M with coefficients in a flat complex vector bundle E. We compute the Ray-Singer norm of the refined analytic torsion. In particular, if there exists a flat Hermitian metric on E, we show that this norm is equal to 1. We prove a duality theorem, establishing a relationship between the refined analytic torsions corresponding to a flat connection and its dual.","authors_text":"Maxim Braverman, Thomas Kappeler","cross_cats":["math-ph","math.DG","math.MP"],"headline":"","license":"","primary_cat":"math.GT","submitted_at":"2005-10-25T16:59:26Z","title":"Refined Analytic Torsion as an Element of the Determinant Line"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0510532","kind":"arxiv","version":4},"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":"sha256:87dbdd50d0495de698e6a57c7cc2dd378f641eff433b6df98e658c7c317e5121","target":"record","created_at":"2026-05-18T02:37:59Z","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":"43feab29de344797330eb3413d0ec7563e654a7c314bcedda00a831e92a40b0c","cross_cats_sorted":["math-ph","math.DG","math.MP"],"license":"","primary_cat":"math.GT","submitted_at":"2005-10-25T16:59:26Z","title_canon_sha256":"9f6f3695cded15fbebbee1242db52c0ae48bf53e876dfd6eab878afa4f6c243a"},"schema_version":"1.0","source":{"id":"math/0510532","kind":"arxiv","version":4}},"canonical_sha256":"a63c5cd940e2c087f2234f9f384e3fd7c2ab8fbaadd36d05e2e91436ad92c2ea","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a63c5cd940e2c087f2234f9f384e3fd7c2ab8fbaadd36d05e2e91436ad92c2ea","first_computed_at":"2026-05-18T02:37:59.695247Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:37:59.695247Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"73lwu9QZPIUmSHXBpH9CacpPy7A0cQRclfY5X+tz95vowsUhzzP3M6+C0KTyP9stMzKhJzNyNFG5m97ncio2BQ==","signature_status":"signed_v1","signed_at":"2026-05-18T02:37:59.695797Z","signed_message":"canonical_sha256_bytes"},"source_id":"math/0510532","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:87dbdd50d0495de698e6a57c7cc2dd378f641eff433b6df98e658c7c317e5121","sha256:cfc12c130ca700e88492b3e532b6869177d5711ceec1394a5b23540efee3fcad"],"state_sha256":"51dd7971f6c5fb8508d10fd72c8e5bc53f2f528125c0fe9073b19c9483d0d618"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"nIh/nKCrHlzPmQl/TW26wf2GS30vpOlUD3yVwZLUVdhMd6ZI7/5BzjvqrC1e9aCHfqOVQK0+VatLrdLcHG4pAg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-28T14:14:49.606512Z","bundle_sha256":"7f95d5310922ce09d26b04cee9de7a3c7c7b5bdefc83d11833bca64c096e0b4a"}}