{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:KW7THHBZ3QJ2KWW56PBAZ2T7HI","short_pith_number":"pith:KW7THHBZ","canonical_record":{"source":{"id":"1711.01992","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2017-11-06T16:24:14Z","cross_cats_sorted":["astro-ph.CO"],"title_canon_sha256":"04a5f4c29d5bc32edc80792c92ba0b5e47ef04a0b285b6fc632a62ef8a623ad5","abstract_canon_sha256":"5d8740776a0bc41038640ac0fa8cdcf11ba3189ddf23883268b3c42edad9686c"},"schema_version":"1.0"},"canonical_sha256":"55bf339c39dc13a55addf3c20cea7f3a16c5793ac311cdadc01cec7a40c8c37e","source":{"kind":"arxiv","id":"1711.01992","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1711.01992","created_at":"2026-05-18T00:22:58Z"},{"alias_kind":"arxiv_version","alias_value":"1711.01992v2","created_at":"2026-05-18T00:22:58Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1711.01992","created_at":"2026-05-18T00:22:58Z"},{"alias_kind":"pith_short_12","alias_value":"KW7THHBZ3QJ2","created_at":"2026-05-18T12:31:28Z"},{"alias_kind":"pith_short_16","alias_value":"KW7THHBZ3QJ2KWW5","created_at":"2026-05-18T12:31:28Z"},{"alias_kind":"pith_short_8","alias_value":"KW7THHBZ","created_at":"2026-05-18T12:31:28Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:KW7THHBZ3QJ2KWW56PBAZ2T7HI","target":"record","payload":{"canonical_record":{"source":{"id":"1711.01992","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2017-11-06T16:24:14Z","cross_cats_sorted":["astro-ph.CO"],"title_canon_sha256":"04a5f4c29d5bc32edc80792c92ba0b5e47ef04a0b285b6fc632a62ef8a623ad5","abstract_canon_sha256":"5d8740776a0bc41038640ac0fa8cdcf11ba3189ddf23883268b3c42edad9686c"},"schema_version":"1.0"},"canonical_sha256":"55bf339c39dc13a55addf3c20cea7f3a16c5793ac311cdadc01cec7a40c8c37e","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:22:58.012391Z","signature_b64":"MXUznQgrPhK10JvmvT/bteU1GMRX90RlE2Z2Da8AdIJQsA8n6N2qTOiChu2AZiHBMz0XLnG47TEWUNpNWqR4Bw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"55bf339c39dc13a55addf3c20cea7f3a16c5793ac311cdadc01cec7a40c8c37e","last_reissued_at":"2026-05-18T00:22:58.011714Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:22:58.011714Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1711.01992","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":"2026-05-18T00:22:58Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"OCUzZ1gp/RI6Uj086kNg1b4WFUykx41O0hW/DtPuafCTL/UqAui/xCp9znc+CEEjVfY6HC7kkU0ZzFtPRDTUBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-05T02:40:56.711837Z"},"content_sha256":"445f151dc075cfd05e9e88411bc443c77d14b15699475b80c214e7b1833e93f6","schema_version":"1.0","event_id":"sha256:445f151dc075cfd05e9e88411bc443c77d14b15699475b80c214e7b1833e93f6"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:KW7THHBZ3QJ2KWW56PBAZ2T7HI","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"General theories of linear gravitational perturbations to a Schwarzschild Black Hole","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["astro-ph.CO"],"primary_cat":"gr-qc","authors_text":"Macarena Lagos, Oliver J. Tattersall, Pedro G. Ferreira","submitted_at":"2017-11-06T16:24:14Z","abstract_excerpt":"We use the covariant formulation proposed in Tattersall et al (2017) to analyse the structure of linear perturbations about a spherically symmetric background in different families of gravity theories, and hence study how quasi-normal modes of perturbed black holes may be affected by modifications to General Relativity. We restrict ourselves to single-tensor, scalar-tensor and vector-tensor diffeomorphism-invariant gravity models in a Schwarzschild black hole background. We show explicitly the full covariant form of the quadratic actions in such cases, which allow us to then analyse odd parity"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1711.01992","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":""},"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":"2026-05-18T00:22:58Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"oDf8el1z0qkKxRKfyskIcRNA8ErVqcAyTet8oCcsV41NK0cJMoQxXx7eD1Q2THzz5i4/q0djYQqDGOfV7ycEBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-05T02:40:56.712200Z"},"content_sha256":"20b12ed8d47e0c1366bc84406d3ebde07ffc0cf92ed5d73b806af0b65a37520b","schema_version":"1.0","event_id":"sha256:20b12ed8d47e0c1366bc84406d3ebde07ffc0cf92ed5d73b806af0b65a37520b"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/KW7THHBZ3QJ2KWW56PBAZ2T7HI/bundle.json","state_url":"https://pith.science/pith/KW7THHBZ3QJ2KWW56PBAZ2T7HI/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/KW7THHBZ3QJ2KWW56PBAZ2T7HI/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":"2026-06-05T02:40:56Z","links":{"resolver":"https://pith.science/pith/KW7THHBZ3QJ2KWW56PBAZ2T7HI","bundle":"https://pith.science/pith/KW7THHBZ3QJ2KWW56PBAZ2T7HI/bundle.json","state":"https://pith.science/pith/KW7THHBZ3QJ2KWW56PBAZ2T7HI/state.json","well_known_bundle":"https://pith.science/.well-known/pith/KW7THHBZ3QJ2KWW56PBAZ2T7HI/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:KW7THHBZ3QJ2KWW56PBAZ2T7HI","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":"5d8740776a0bc41038640ac0fa8cdcf11ba3189ddf23883268b3c42edad9686c","cross_cats_sorted":["astro-ph.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2017-11-06T16:24:14Z","title_canon_sha256":"04a5f4c29d5bc32edc80792c92ba0b5e47ef04a0b285b6fc632a62ef8a623ad5"},"schema_version":"1.0","source":{"id":"1711.01992","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1711.01992","created_at":"2026-05-18T00:22:58Z"},{"alias_kind":"arxiv_version","alias_value":"1711.01992v2","created_at":"2026-05-18T00:22:58Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1711.01992","created_at":"2026-05-18T00:22:58Z"},{"alias_kind":"pith_short_12","alias_value":"KW7THHBZ3QJ2","created_at":"2026-05-18T12:31:28Z"},{"alias_kind":"pith_short_16","alias_value":"KW7THHBZ3QJ2KWW5","created_at":"2026-05-18T12:31:28Z"},{"alias_kind":"pith_short_8","alias_value":"KW7THHBZ","created_at":"2026-05-18T12:31:28Z"}],"graph_snapshots":[{"event_id":"sha256:20b12ed8d47e0c1366bc84406d3ebde07ffc0cf92ed5d73b806af0b65a37520b","target":"graph","created_at":"2026-05-18T00:22:58Z","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 use the covariant formulation proposed in Tattersall et al (2017) to analyse the structure of linear perturbations about a spherically symmetric background in different families of gravity theories, and hence study how quasi-normal modes of perturbed black holes may be affected by modifications to General Relativity. We restrict ourselves to single-tensor, scalar-tensor and vector-tensor diffeomorphism-invariant gravity models in a Schwarzschild black hole background. We show explicitly the full covariant form of the quadratic actions in such cases, which allow us to then analyse odd parity","authors_text":"Macarena Lagos, Oliver J. Tattersall, Pedro G. Ferreira","cross_cats":["astro-ph.CO"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2017-11-06T16:24:14Z","title":"General theories of linear gravitational perturbations to a Schwarzschild Black Hole"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1711.01992","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":"sha256:445f151dc075cfd05e9e88411bc443c77d14b15699475b80c214e7b1833e93f6","target":"record","created_at":"2026-05-18T00:22:58Z","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":"5d8740776a0bc41038640ac0fa8cdcf11ba3189ddf23883268b3c42edad9686c","cross_cats_sorted":["astro-ph.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2017-11-06T16:24:14Z","title_canon_sha256":"04a5f4c29d5bc32edc80792c92ba0b5e47ef04a0b285b6fc632a62ef8a623ad5"},"schema_version":"1.0","source":{"id":"1711.01992","kind":"arxiv","version":2}},"canonical_sha256":"55bf339c39dc13a55addf3c20cea7f3a16c5793ac311cdadc01cec7a40c8c37e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"55bf339c39dc13a55addf3c20cea7f3a16c5793ac311cdadc01cec7a40c8c37e","first_computed_at":"2026-05-18T00:22:58.011714Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:22:58.011714Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"MXUznQgrPhK10JvmvT/bteU1GMRX90RlE2Z2Da8AdIJQsA8n6N2qTOiChu2AZiHBMz0XLnG47TEWUNpNWqR4Bw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:22:58.012391Z","signed_message":"canonical_sha256_bytes"},"source_id":"1711.01992","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:445f151dc075cfd05e9e88411bc443c77d14b15699475b80c214e7b1833e93f6","sha256:20b12ed8d47e0c1366bc84406d3ebde07ffc0cf92ed5d73b806af0b65a37520b"],"state_sha256":"4ba68bb4d71b5d5109a09b853c6abda57f61fb426ac82e040ca7d66713474b33"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ApxPr+QZgYgatwhohboHcqIX05QuDDDVvld02daZ8m7a2DfwnFaDUTyJZdTB1WpkeGwE9gXFahBKRFxrvU8CCQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-05T02:40:56.714337Z","bundle_sha256":"baa619c4c579072e9d38ba299ea47466ac5543cc11b082638a14c65eb7eee864"}}