{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2000:JVYZK2PHRXTKE364ZSMOB7YYR6","short_pith_number":"pith:JVYZK2PH","canonical_record":{"source":{"id":"math/0004045","kind":"arxiv","version":2},"metadata":{"license":"","primary_cat":"math.AG","submitted_at":"2000-04-07T23:44:50Z","cross_cats_sorted":[],"title_canon_sha256":"d48e6c3f8a7792a22f4b733405e5b1dde00e2a972b7389cb52ac8cec88e686bf","abstract_canon_sha256":"011572ed6f0cf6b4d4de2d10c164fc653ae95062d8b5c1f68fd02fb77a4f7f34"},"schema_version":"1.0"},"canonical_sha256":"4d719569e78de6a26fdccc98e0ff188f83b2b09b4866d2d02c0759c5147b7b91","source":{"kind":"arxiv","id":"math/0004045","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0004045","created_at":"2026-07-04T14:34:27Z"},{"alias_kind":"arxiv_version","alias_value":"math/0004045v2","created_at":"2026-07-04T14:34:27Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0004045","created_at":"2026-07-04T14:34:27Z"},{"alias_kind":"pith_short_12","alias_value":"JVYZK2PHRXTK","created_at":"2026-07-04T14:34:27Z"},{"alias_kind":"pith_short_16","alias_value":"JVYZK2PHRXTKE364","created_at":"2026-07-04T14:34:27Z"},{"alias_kind":"pith_short_8","alias_value":"JVYZK2PH","created_at":"2026-07-04T14:34:27Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2000:JVYZK2PHRXTKE364ZSMOB7YYR6","target":"record","payload":{"canonical_record":{"source":{"id":"math/0004045","kind":"arxiv","version":2},"metadata":{"license":"","primary_cat":"math.AG","submitted_at":"2000-04-07T23:44:50Z","cross_cats_sorted":[],"title_canon_sha256":"d48e6c3f8a7792a22f4b733405e5b1dde00e2a972b7389cb52ac8cec88e686bf","abstract_canon_sha256":"011572ed6f0cf6b4d4de2d10c164fc653ae95062d8b5c1f68fd02fb77a4f7f34"},"schema_version":"1.0"},"canonical_sha256":"4d719569e78de6a26fdccc98e0ff188f83b2b09b4866d2d02c0759c5147b7b91","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-04T14:34:27.128777Z","signature_b64":"+vfscx1iJ5s/CIWXezNWzSMxycvsm6EAVVLiElWFJYaF0sgtYEndU+xkT3FB/BdWB1tIen1BMEWizkkUaKCiAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4d719569e78de6a26fdccc98e0ff188f83b2b09b4866d2d02c0759c5147b7b91","last_reissued_at":"2026-07-04T14:34:27.128348Z","signature_status":"signed_v1","first_computed_at":"2026-07-04T14:34:27.128348Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"math/0004045","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-04T14:34:27Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"7XsmBJ3+KiDZywsV6jOX1czPrNQPVkt4VtNA7vrp6NVTXLixXq3x0M78+fJxSO1e9t2ab3Hhf97R6S2X6+yICw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-16T19:15:38.710848Z"},"content_sha256":"44984d31970fb1d4f23b5694f9d36405841454961b733fdc9a82a2f1d2a64a72","schema_version":"1.0","event_id":"sha256:44984d31970fb1d4f23b5694f9d36405841454961b733fdc9a82a2f1d2a64a72"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2000:JVYZK2PHRXTKE364ZSMOB7YYR6","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Ray Singer Analytic Torsion of Calabi Yau manifolds I","license":"","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Andrey Todorov","submitted_at":"2000-04-07T23:44:50Z","abstract_excerpt":"In this paper we generalized the variational formulas for the determinants of the Laplacians on functions of CY metrics to forms of type (0,q) on CY manifolds. We also computed the Ray Singer Analytic torsion on CY manifolds we proved that it is bounded by a constant. In case of even dimensional CY manifolds the Ray Singer Analytic torsion is zero. The interesting case is the odd dimensional one."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0004045","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/math/0004045/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":"2026-07-04T14:34:27Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"or50M/K91GX4ovgg5ASe7/ZlRZcwLR3MOfXdVs/p1zoxK8vsAR8/YFMfHrJeex4Lp4CaffoKgK6wcu8Zpmb+Ag==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-16T19:15:38.711790Z"},"content_sha256":"5cea4b102edd13c6b79e3ced7145023afd86134d582326ef6c3e22abd2fcd547","schema_version":"1.0","event_id":"sha256:5cea4b102edd13c6b79e3ced7145023afd86134d582326ef6c3e22abd2fcd547"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/JVYZK2PHRXTKE364ZSMOB7YYR6/bundle.json","state_url":"https://pith.science/pith/JVYZK2PHRXTKE364ZSMOB7YYR6/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/JVYZK2PHRXTKE364ZSMOB7YYR6/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":"2026-08-16T19:15:38Z","links":{"resolver":"https://pith.science/pith/JVYZK2PHRXTKE364ZSMOB7YYR6","bundle":"https://pith.science/pith/JVYZK2PHRXTKE364ZSMOB7YYR6/bundle.json","state":"https://pith.science/pith/JVYZK2PHRXTKE364ZSMOB7YYR6/state.json","well_known_bundle":"https://pith.science/.well-known/pith/JVYZK2PHRXTKE364ZSMOB7YYR6/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2000:JVYZK2PHRXTKE364ZSMOB7YYR6","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":"011572ed6f0cf6b4d4de2d10c164fc653ae95062d8b5c1f68fd02fb77a4f7f34","cross_cats_sorted":[],"license":"","primary_cat":"math.AG","submitted_at":"2000-04-07T23:44:50Z","title_canon_sha256":"d48e6c3f8a7792a22f4b733405e5b1dde00e2a972b7389cb52ac8cec88e686bf"},"schema_version":"1.0","source":{"id":"math/0004045","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0004045","created_at":"2026-07-04T14:34:27Z"},{"alias_kind":"arxiv_version","alias_value":"math/0004045v2","created_at":"2026-07-04T14:34:27Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0004045","created_at":"2026-07-04T14:34:27Z"},{"alias_kind":"pith_short_12","alias_value":"JVYZK2PHRXTK","created_at":"2026-07-04T14:34:27Z"},{"alias_kind":"pith_short_16","alias_value":"JVYZK2PHRXTKE364","created_at":"2026-07-04T14:34:27Z"},{"alias_kind":"pith_short_8","alias_value":"JVYZK2PH","created_at":"2026-07-04T14:34:27Z"}],"graph_snapshots":[{"event_id":"sha256:5cea4b102edd13c6b79e3ced7145023afd86134d582326ef6c3e22abd2fcd547","target":"graph","created_at":"2026-07-04T14:34:27Z","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/0004045/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"In this paper we generalized the variational formulas for the determinants of the Laplacians on functions of CY metrics to forms of type (0,q) on CY manifolds. We also computed the Ray Singer Analytic torsion on CY manifolds we proved that it is bounded by a constant. In case of even dimensional CY manifolds the Ray Singer Analytic torsion is zero. The interesting case is the odd dimensional one.","authors_text":"Andrey Todorov","cross_cats":[],"headline":"","license":"","primary_cat":"math.AG","submitted_at":"2000-04-07T23:44:50Z","title":"Ray Singer Analytic Torsion of Calabi Yau manifolds I"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0004045","kind":"arxiv","version":2},"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":"sha256:44984d31970fb1d4f23b5694f9d36405841454961b733fdc9a82a2f1d2a64a72","target":"record","created_at":"2026-07-04T14:34:27Z","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":"011572ed6f0cf6b4d4de2d10c164fc653ae95062d8b5c1f68fd02fb77a4f7f34","cross_cats_sorted":[],"license":"","primary_cat":"math.AG","submitted_at":"2000-04-07T23:44:50Z","title_canon_sha256":"d48e6c3f8a7792a22f4b733405e5b1dde00e2a972b7389cb52ac8cec88e686bf"},"schema_version":"1.0","source":{"id":"math/0004045","kind":"arxiv","version":2}},"canonical_sha256":"4d719569e78de6a26fdccc98e0ff188f83b2b09b4866d2d02c0759c5147b7b91","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"4d719569e78de6a26fdccc98e0ff188f83b2b09b4866d2d02c0759c5147b7b91","first_computed_at":"2026-07-04T14:34:27.128348Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-04T14:34:27.128348Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"+vfscx1iJ5s/CIWXezNWzSMxycvsm6EAVVLiElWFJYaF0sgtYEndU+xkT3FB/BdWB1tIen1BMEWizkkUaKCiAg==","signature_status":"signed_v1","signed_at":"2026-07-04T14:34:27.128777Z","signed_message":"canonical_sha256_bytes"},"source_id":"math/0004045","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:44984d31970fb1d4f23b5694f9d36405841454961b733fdc9a82a2f1d2a64a72","sha256:5cea4b102edd13c6b79e3ced7145023afd86134d582326ef6c3e22abd2fcd547"],"state_sha256":"3595d51f60ad78d66e09b241043d4b37acf846964838e1ee0bf58fee454fb6c0"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"YkFjICVLsbdqrsSK0GK7QfEoY4xZzkI9noxoyiu/OccdaxwJL0Zt0vcY2RVfpejXYOOeMFPYXf+rOqRGQu/GDw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-16T19:15:38.717921Z","bundle_sha256":"931c7680f1f17bcc40d19a5e63caddb4a089fc0ba30ffc52664276f567e7cca5"}}