{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2005:LEYZO3HL6765UOGJWOTURG3NZJ","short_pith_number":"pith:LEYZO3HL","canonical_record":{"source":{"id":"math/0512376","kind":"arxiv","version":2},"metadata":{"license":"","primary_cat":"math.DG","submitted_at":"2005-12-15T19:25:45Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"5c8fc78c0b526deaa6310ce7ff48954c0982fe86b63eca0cf43b6f09fed406a2","abstract_canon_sha256":"9e3635eefc20aa7f6898220dfce53235464404aed9fb5b91dd81d55bbe24fa8e"},"schema_version":"1.0"},"canonical_sha256":"5931976cebf7fdda38c9b3a7489b6dca584de1923e7498c3b66d4047bd9063fe","source":{"kind":"arxiv","id":"math/0512376","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0512376","created_at":"2026-07-04T14:52:15Z"},{"alias_kind":"arxiv_version","alias_value":"math/0512376v2","created_at":"2026-07-04T14:52:15Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0512376","created_at":"2026-07-04T14:52:15Z"},{"alias_kind":"pith_short_12","alias_value":"LEYZO3HL6765","created_at":"2026-07-04T14:52:15Z"},{"alias_kind":"pith_short_16","alias_value":"LEYZO3HL6765UOGJ","created_at":"2026-07-04T14:52:15Z"},{"alias_kind":"pith_short_8","alias_value":"LEYZO3HL","created_at":"2026-07-04T14:52:15Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2005:LEYZO3HL6765UOGJWOTURG3NZJ","target":"record","payload":{"canonical_record":{"source":{"id":"math/0512376","kind":"arxiv","version":2},"metadata":{"license":"","primary_cat":"math.DG","submitted_at":"2005-12-15T19:25:45Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"5c8fc78c0b526deaa6310ce7ff48954c0982fe86b63eca0cf43b6f09fed406a2","abstract_canon_sha256":"9e3635eefc20aa7f6898220dfce53235464404aed9fb5b91dd81d55bbe24fa8e"},"schema_version":"1.0"},"canonical_sha256":"5931976cebf7fdda38c9b3a7489b6dca584de1923e7498c3b66d4047bd9063fe","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-04T14:52:15.646048Z","signature_b64":"6NhNF2JmDhY5iRnNewEdwMQ6IQ9h47kfUT4HSM3VfBwoyeXw1R8/vtuWuF6fc11KwOGpYLA2OhzmgccLz4ZNAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5931976cebf7fdda38c9b3a7489b6dca584de1923e7498c3b66d4047bd9063fe","last_reissued_at":"2026-07-04T14:52:15.645699Z","signature_status":"signed_v1","first_computed_at":"2026-07-04T14:52:15.645699Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"math/0512376","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":"2026-07-04T14:52:15Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"dg0S0RShFiU/BiX36j2y7HTzJ2mk/rjH8Lt5q+eQQAXQ5/NZWgkZc7wuegz2Axf5cNYuXKrbHlvSQYYr8zXKCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-04T10:26:41.000377Z"},"content_sha256":"6bf6644b4773fe12ac82051e23ac0931e50905e7de63b5baba5cc1e46ee973d6","schema_version":"1.0","event_id":"sha256:6bf6644b4773fe12ac82051e23ac0931e50905e7de63b5baba5cc1e46ee973d6"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2005:LEYZO3HL6765UOGJWOTURG3NZJ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On the renormalized volumes for conformally compact Einstein manifolds","license":"","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.DG","authors_text":"Alice Chang, Jie Qing, Paul Yang","submitted_at":"2005-12-15T19:25:45Z","abstract_excerpt":"We study the renormalized volume of a conformally compact Einstein manifold. In even dimensions, we derive the analogue of the Chern-Gauss-Bonnet formula incorporating the renormalized volume. When the dimension is odd, we relate the renormalized volume to the conformal primitive of the $Q$-curvature. We show how all the global information come from the Scattering."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0512376","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/0512376/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":"2026-07-04T14:52:15Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"+4BTCi0sBHEoCYySCeBz80CT7IPv45R0wpY3K0qlIJx3zsX++vkcRroKLacp2KN2GlQKlAPawUmCKesBPCLNDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-04T10:26:41.000940Z"},"content_sha256":"2264efb60396b12ee7b9742d00dbb2acdcccce860794f0008c7e6ef99a89a33e","schema_version":"1.0","event_id":"sha256:2264efb60396b12ee7b9742d00dbb2acdcccce860794f0008c7e6ef99a89a33e"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/LEYZO3HL6765UOGJWOTURG3NZJ/bundle.json","state_url":"https://pith.science/pith/LEYZO3HL6765UOGJWOTURG3NZJ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/LEYZO3HL6765UOGJWOTURG3NZJ/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":"2026-08-04T10:26:41Z","links":{"resolver":"https://pith.science/pith/LEYZO3HL6765UOGJWOTURG3NZJ","bundle":"https://pith.science/pith/LEYZO3HL6765UOGJWOTURG3NZJ/bundle.json","state":"https://pith.science/pith/LEYZO3HL6765UOGJWOTURG3NZJ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/LEYZO3HL6765UOGJWOTURG3NZJ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2005:LEYZO3HL6765UOGJWOTURG3NZJ","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":"9e3635eefc20aa7f6898220dfce53235464404aed9fb5b91dd81d55bbe24fa8e","cross_cats_sorted":["math-ph","math.MP"],"license":"","primary_cat":"math.DG","submitted_at":"2005-12-15T19:25:45Z","title_canon_sha256":"5c8fc78c0b526deaa6310ce7ff48954c0982fe86b63eca0cf43b6f09fed406a2"},"schema_version":"1.0","source":{"id":"math/0512376","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0512376","created_at":"2026-07-04T14:52:15Z"},{"alias_kind":"arxiv_version","alias_value":"math/0512376v2","created_at":"2026-07-04T14:52:15Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0512376","created_at":"2026-07-04T14:52:15Z"},{"alias_kind":"pith_short_12","alias_value":"LEYZO3HL6765","created_at":"2026-07-04T14:52:15Z"},{"alias_kind":"pith_short_16","alias_value":"LEYZO3HL6765UOGJ","created_at":"2026-07-04T14:52:15Z"},{"alias_kind":"pith_short_8","alias_value":"LEYZO3HL","created_at":"2026-07-04T14:52:15Z"}],"graph_snapshots":[{"event_id":"sha256:2264efb60396b12ee7b9742d00dbb2acdcccce860794f0008c7e6ef99a89a33e","target":"graph","created_at":"2026-07-04T14:52:15Z","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/0512376/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We study the renormalized volume of a conformally compact Einstein manifold. In even dimensions, we derive the analogue of the Chern-Gauss-Bonnet formula incorporating the renormalized volume. When the dimension is odd, we relate the renormalized volume to the conformal primitive of the $Q$-curvature. We show how all the global information come from the Scattering.","authors_text":"Alice Chang, Jie Qing, Paul Yang","cross_cats":["math-ph","math.MP"],"headline":"","license":"","primary_cat":"math.DG","submitted_at":"2005-12-15T19:25:45Z","title":"On the renormalized volumes for conformally compact Einstein manifolds"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0512376","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":"sha256:6bf6644b4773fe12ac82051e23ac0931e50905e7de63b5baba5cc1e46ee973d6","target":"record","created_at":"2026-07-04T14:52:15Z","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":"9e3635eefc20aa7f6898220dfce53235464404aed9fb5b91dd81d55bbe24fa8e","cross_cats_sorted":["math-ph","math.MP"],"license":"","primary_cat":"math.DG","submitted_at":"2005-12-15T19:25:45Z","title_canon_sha256":"5c8fc78c0b526deaa6310ce7ff48954c0982fe86b63eca0cf43b6f09fed406a2"},"schema_version":"1.0","source":{"id":"math/0512376","kind":"arxiv","version":2}},"canonical_sha256":"5931976cebf7fdda38c9b3a7489b6dca584de1923e7498c3b66d4047bd9063fe","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"5931976cebf7fdda38c9b3a7489b6dca584de1923e7498c3b66d4047bd9063fe","first_computed_at":"2026-07-04T14:52:15.645699Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-04T14:52:15.645699Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"6NhNF2JmDhY5iRnNewEdwMQ6IQ9h47kfUT4HSM3VfBwoyeXw1R8/vtuWuF6fc11KwOGpYLA2OhzmgccLz4ZNAg==","signature_status":"signed_v1","signed_at":"2026-07-04T14:52:15.646048Z","signed_message":"canonical_sha256_bytes"},"source_id":"math/0512376","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:6bf6644b4773fe12ac82051e23ac0931e50905e7de63b5baba5cc1e46ee973d6","sha256:2264efb60396b12ee7b9742d00dbb2acdcccce860794f0008c7e6ef99a89a33e"],"state_sha256":"3cd0b5148961954683541582e6b2da9114677f999f7effd28bb3520c671e7761"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"fM0WlDfytVxCk41ZA/FjbmZpCcPTX9vZ0FC06dEFS3oVLz2PahB4ISUl6AmV2AGdiRJAaPI1pM7NAL584R4tAQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-04T10:26:41.004592Z","bundle_sha256":"1dfce2f5d068f4dde193bc48aa6d872908ab1abdfbd46db74a0d4bf460d7d31f"}}