{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2005:6OPHYSQMLBCSXTF6IWN3EASZ4F","short_pith_number":"pith:6OPHYSQM","canonical_record":{"source":{"id":"gr-qc/0502064","kind":"arxiv","version":5},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2005-02-14T17:18:30Z","cross_cats_sorted":[],"title_canon_sha256":"3c5bf0a667475f5e39e2d6eefdae82871978b260e6268d81b81ae8a422711683","abstract_canon_sha256":"ff4929d3f687fb2ee63ba68e384d07713dec641334b8b8b433a43996c192894c"},"schema_version":"1.0"},"canonical_sha256":"f39e7c4a0c58452bccbe459bb20259e1717a2b5cf1ec88e35408b6bc6978872f","source":{"kind":"arxiv","id":"gr-qc/0502064","version":5},"source_aliases":[{"alias_kind":"arxiv","alias_value":"gr-qc/0502064","created_at":"2026-07-05T01:33:09Z"},{"alias_kind":"arxiv_version","alias_value":"gr-qc/0502064v5","created_at":"2026-07-05T01:33:09Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.gr-qc/0502064","created_at":"2026-07-05T01:33:09Z"},{"alias_kind":"pith_short_12","alias_value":"6OPHYSQMLBCS","created_at":"2026-07-05T01:33:09Z"},{"alias_kind":"pith_short_16","alias_value":"6OPHYSQMLBCSXTF6","created_at":"2026-07-05T01:33:09Z"},{"alias_kind":"pith_short_8","alias_value":"6OPHYSQM","created_at":"2026-07-05T01:33:09Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2005:6OPHYSQMLBCSXTF6IWN3EASZ4F","target":"record","payload":{"canonical_record":{"source":{"id":"gr-qc/0502064","kind":"arxiv","version":5},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2005-02-14T17:18:30Z","cross_cats_sorted":[],"title_canon_sha256":"3c5bf0a667475f5e39e2d6eefdae82871978b260e6268d81b81ae8a422711683","abstract_canon_sha256":"ff4929d3f687fb2ee63ba68e384d07713dec641334b8b8b433a43996c192894c"},"schema_version":"1.0"},"canonical_sha256":"f39e7c4a0c58452bccbe459bb20259e1717a2b5cf1ec88e35408b6bc6978872f","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T01:33:09.848360Z","signature_b64":"g7niv27BZPGCSb4H6aWnoX1fg/djGo4wmutNL2I+TvmvbscFNELH9fIuInEGrO93JB9MxjAwc9G7cGa3mPljBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f39e7c4a0c58452bccbe459bb20259e1717a2b5cf1ec88e35408b6bc6978872f","last_reissued_at":"2026-07-05T01:33:09.847921Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T01:33:09.847921Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"gr-qc/0502064","source_version":5,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T01:33:09Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ySIg6jEdYiSPZIynqsMNhlY1W0+MB9CAx/GneOlDN8QxEdeUBPr6N/0Z0+yL0QriV/+4B3FaBbT4VIH8T72kAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-13T16:10:16.685624Z"},"content_sha256":"c7a8c01e56e9d88b8fe6a3cd15628b2b5687263d92b1320f6907309ee7d0eae6","schema_version":"1.0","event_id":"sha256:c7a8c01e56e9d88b8fe6a3cd15628b2b5687263d92b1320f6907309ee7d0eae6"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2005:6OPHYSQMLBCSXTF6IWN3EASZ4F","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Gauge-invariant Non-spherical Metric Perturbations of Schwarzschild Black-Hole Spacetimes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"gr-qc","authors_text":"Alessandro Nagar, Luciano Rezzolla","submitted_at":"2005-02-14T17:18:30Z","abstract_excerpt":"The theory of gauge-invariant non-spherical metric perturbations of Schwarzschild black hole spacetimes is now well established. Yet, as different notations and conventions have been used throughout the years, the literature on the subject is often confusing and sometimes confused. The purpose of this paper is to review and collect the relevant expressions related to the Regge-Wheeler and Zerilli equations for the odd and even-parity perturbations of a Schwarzschild spacetime. Special attention is paid to the form they assume in the presence of matter-sources and, for the two most popular conv"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"gr-qc/0502064","kind":"arxiv","version":5},"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/gr-qc/0502064/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":"2026-07-05T01:33:09Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"7c6dYWl2sc6NGnEY39sPErgWBwrmhzC7ATlm/0kT1925RUpv/Pc9YCtHDcVu+kM+iC9Otl0Xa/gQ15b4eakdBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-13T16:10:16.695865Z"},"content_sha256":"7110bb7959a40fe06f384cc45f9cf582fd4efd81de6129f838f58c95eaaa00eb","schema_version":"1.0","event_id":"sha256:7110bb7959a40fe06f384cc45f9cf582fd4efd81de6129f838f58c95eaaa00eb"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/6OPHYSQMLBCSXTF6IWN3EASZ4F/bundle.json","state_url":"https://pith.science/pith/6OPHYSQMLBCSXTF6IWN3EASZ4F/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/6OPHYSQMLBCSXTF6IWN3EASZ4F/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":"2026-08-13T16:10:16Z","links":{"resolver":"https://pith.science/pith/6OPHYSQMLBCSXTF6IWN3EASZ4F","bundle":"https://pith.science/pith/6OPHYSQMLBCSXTF6IWN3EASZ4F/bundle.json","state":"https://pith.science/pith/6OPHYSQMLBCSXTF6IWN3EASZ4F/state.json","well_known_bundle":"https://pith.science/.well-known/pith/6OPHYSQMLBCSXTF6IWN3EASZ4F/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2005:6OPHYSQMLBCSXTF6IWN3EASZ4F","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":"ff4929d3f687fb2ee63ba68e384d07713dec641334b8b8b433a43996c192894c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2005-02-14T17:18:30Z","title_canon_sha256":"3c5bf0a667475f5e39e2d6eefdae82871978b260e6268d81b81ae8a422711683"},"schema_version":"1.0","source":{"id":"gr-qc/0502064","kind":"arxiv","version":5}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"gr-qc/0502064","created_at":"2026-07-05T01:33:09Z"},{"alias_kind":"arxiv_version","alias_value":"gr-qc/0502064v5","created_at":"2026-07-05T01:33:09Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.gr-qc/0502064","created_at":"2026-07-05T01:33:09Z"},{"alias_kind":"pith_short_12","alias_value":"6OPHYSQMLBCS","created_at":"2026-07-05T01:33:09Z"},{"alias_kind":"pith_short_16","alias_value":"6OPHYSQMLBCSXTF6","created_at":"2026-07-05T01:33:09Z"},{"alias_kind":"pith_short_8","alias_value":"6OPHYSQM","created_at":"2026-07-05T01:33:09Z"}],"graph_snapshots":[{"event_id":"sha256:7110bb7959a40fe06f384cc45f9cf582fd4efd81de6129f838f58c95eaaa00eb","target":"graph","created_at":"2026-07-05T01:33:09Z","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/gr-qc/0502064/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"The theory of gauge-invariant non-spherical metric perturbations of Schwarzschild black hole spacetimes is now well established. Yet, as different notations and conventions have been used throughout the years, the literature on the subject is often confusing and sometimes confused. The purpose of this paper is to review and collect the relevant expressions related to the Regge-Wheeler and Zerilli equations for the odd and even-parity perturbations of a Schwarzschild spacetime. Special attention is paid to the form they assume in the presence of matter-sources and, for the two most popular conv","authors_text":"Alessandro Nagar, Luciano Rezzolla","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2005-02-14T17:18:30Z","title":"Gauge-invariant Non-spherical Metric Perturbations of Schwarzschild Black-Hole Spacetimes"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"gr-qc/0502064","kind":"arxiv","version":5},"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:c7a8c01e56e9d88b8fe6a3cd15628b2b5687263d92b1320f6907309ee7d0eae6","target":"record","created_at":"2026-07-05T01:33:09Z","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":"ff4929d3f687fb2ee63ba68e384d07713dec641334b8b8b433a43996c192894c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2005-02-14T17:18:30Z","title_canon_sha256":"3c5bf0a667475f5e39e2d6eefdae82871978b260e6268d81b81ae8a422711683"},"schema_version":"1.0","source":{"id":"gr-qc/0502064","kind":"arxiv","version":5}},"canonical_sha256":"f39e7c4a0c58452bccbe459bb20259e1717a2b5cf1ec88e35408b6bc6978872f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f39e7c4a0c58452bccbe459bb20259e1717a2b5cf1ec88e35408b6bc6978872f","first_computed_at":"2026-07-05T01:33:09.847921Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T01:33:09.847921Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"g7niv27BZPGCSb4H6aWnoX1fg/djGo4wmutNL2I+TvmvbscFNELH9fIuInEGrO93JB9MxjAwc9G7cGa3mPljBg==","signature_status":"signed_v1","signed_at":"2026-07-05T01:33:09.848360Z","signed_message":"canonical_sha256_bytes"},"source_id":"gr-qc/0502064","source_kind":"arxiv","source_version":5}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c7a8c01e56e9d88b8fe6a3cd15628b2b5687263d92b1320f6907309ee7d0eae6","sha256:7110bb7959a40fe06f384cc45f9cf582fd4efd81de6129f838f58c95eaaa00eb"],"state_sha256":"4b0eb6929930698ec33bfaefcb5a8271d21a4904621365ac7e21446934461163"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"J7tipthqU13YyGmNwBBpm85UxXLINYfzL51RX3/mOsBdf5EF1H2vGhqDY+X1V5qKkPNMyEMkWV7bz83cluFQBg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-13T16:10:16.726466Z","bundle_sha256":"e4123ddb23e7eff85ce7b37e281c0d503768099690b36a0f87e50ddaf40f6a0b"}}