{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:MXCAQUHVM7CZJXE6XNHZGSEFNV","short_pith_number":"pith:MXCAQUHV","canonical_record":{"source":{"id":"1209.3731","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2012-09-17T17:47:17Z","cross_cats_sorted":[],"title_canon_sha256":"29c445caadbd0265a212eba432c7b996936d50e8d1877ea4c4697548f2d14375","abstract_canon_sha256":"6fd1158dac3058ebd081685ec3f848d62c3b36e154cafb158afa0637f12e7600"},"schema_version":"1.0"},"canonical_sha256":"65c40850f567c594dc9ebb4f9348856d5b4524210af69bb5f413350d5d0a2ba7","source":{"kind":"arxiv","id":"1209.3731","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1209.3731","created_at":"2026-05-18T03:28:17Z"},{"alias_kind":"arxiv_version","alias_value":"1209.3731v2","created_at":"2026-05-18T03:28:17Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1209.3731","created_at":"2026-05-18T03:28:17Z"},{"alias_kind":"pith_short_12","alias_value":"MXCAQUHVM7CZ","created_at":"2026-05-18T12:27:14Z"},{"alias_kind":"pith_short_16","alias_value":"MXCAQUHVM7CZJXE6","created_at":"2026-05-18T12:27:14Z"},{"alias_kind":"pith_short_8","alias_value":"MXCAQUHV","created_at":"2026-05-18T12:27:14Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:MXCAQUHVM7CZJXE6XNHZGSEFNV","target":"record","payload":{"canonical_record":{"source":{"id":"1209.3731","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2012-09-17T17:47:17Z","cross_cats_sorted":[],"title_canon_sha256":"29c445caadbd0265a212eba432c7b996936d50e8d1877ea4c4697548f2d14375","abstract_canon_sha256":"6fd1158dac3058ebd081685ec3f848d62c3b36e154cafb158afa0637f12e7600"},"schema_version":"1.0"},"canonical_sha256":"65c40850f567c594dc9ebb4f9348856d5b4524210af69bb5f413350d5d0a2ba7","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:28:17.413014Z","signature_b64":"lC25sMjv6+eCEP4v8w+NuQ1NGCldB32pzhvUGF6URDig3hG8pQXrignK3Kio9bdCEwfYZcKitBodPFoqZ92aBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"65c40850f567c594dc9ebb4f9348856d5b4524210af69bb5f413350d5d0a2ba7","last_reissued_at":"2026-05-18T03:28:17.412354Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:28:17.412354Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1209.3731","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":"2026-05-18T03:28:17Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"sRvzEomAHYs2kYP1CUacNEuuqVqFH5mHeSC6l73WH4dK6U/Smt6/HOSsV5J1ZO6qfK7X5iQ9n61IozTSxOR/Bg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-05T01:02:07.331363Z"},"content_sha256":"caa4a5add16892d7f554561bc9a4eec228139a757ec049399a3c03076f8ee1aa","schema_version":"1.0","event_id":"sha256:caa4a5add16892d7f554561bc9a4eec228139a757ec049399a3c03076f8ee1aa"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:MXCAQUHVM7CZJXE6XNHZGSEFNV","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Linear perturbations of self-gravitating spherically symmetric configurations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"gr-qc","authors_text":"Eliana Chaverra, N\\'estor Ortiz, Olivier Sarbach","submitted_at":"2012-09-17T17:47:17Z","abstract_excerpt":"We present a new covariant, gauge-invariant formalism describing linear metric perturbation fields on any spherically symmetric background in general relativity. The advantage of this formalism relies in the fact that it does not require a decomposition of the perturbations into spherical tensor harmonics. Furthermore, it does not assume the background to be vacuum, nor does it require its staticity. In the particular case of vacuum perturbations, we derive two master equations describing the propagation of arbitrary linear gravitational waves on a Schwarzschild black hole. When decomposed int"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1209.3731","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":"2026-05-18T03:28:17Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"K1W9wuErcRHax26LDyBFjiDCkGvPR8aNw/PK/aDR0DRoJcOXraj/a5qG4e8yDRlpK+kPDOrdIhKDEAUD0OF6Bg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-05T01:02:07.331715Z"},"content_sha256":"5922298153fc4eed826b7f8a00c999d474cf51efbb957fe7f3ac0c029e105fe4","schema_version":"1.0","event_id":"sha256:5922298153fc4eed826b7f8a00c999d474cf51efbb957fe7f3ac0c029e105fe4"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/MXCAQUHVM7CZJXE6XNHZGSEFNV/bundle.json","state_url":"https://pith.science/pith/MXCAQUHVM7CZJXE6XNHZGSEFNV/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/MXCAQUHVM7CZJXE6XNHZGSEFNV/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":"2026-06-05T01:02:07Z","links":{"resolver":"https://pith.science/pith/MXCAQUHVM7CZJXE6XNHZGSEFNV","bundle":"https://pith.science/pith/MXCAQUHVM7CZJXE6XNHZGSEFNV/bundle.json","state":"https://pith.science/pith/MXCAQUHVM7CZJXE6XNHZGSEFNV/state.json","well_known_bundle":"https://pith.science/.well-known/pith/MXCAQUHVM7CZJXE6XNHZGSEFNV/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:MXCAQUHVM7CZJXE6XNHZGSEFNV","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":"6fd1158dac3058ebd081685ec3f848d62c3b36e154cafb158afa0637f12e7600","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2012-09-17T17:47:17Z","title_canon_sha256":"29c445caadbd0265a212eba432c7b996936d50e8d1877ea4c4697548f2d14375"},"schema_version":"1.0","source":{"id":"1209.3731","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1209.3731","created_at":"2026-05-18T03:28:17Z"},{"alias_kind":"arxiv_version","alias_value":"1209.3731v2","created_at":"2026-05-18T03:28:17Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1209.3731","created_at":"2026-05-18T03:28:17Z"},{"alias_kind":"pith_short_12","alias_value":"MXCAQUHVM7CZ","created_at":"2026-05-18T12:27:14Z"},{"alias_kind":"pith_short_16","alias_value":"MXCAQUHVM7CZJXE6","created_at":"2026-05-18T12:27:14Z"},{"alias_kind":"pith_short_8","alias_value":"MXCAQUHV","created_at":"2026-05-18T12:27:14Z"}],"graph_snapshots":[{"event_id":"sha256:5922298153fc4eed826b7f8a00c999d474cf51efbb957fe7f3ac0c029e105fe4","target":"graph","created_at":"2026-05-18T03:28:17Z","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 present a new covariant, gauge-invariant formalism describing linear metric perturbation fields on any spherically symmetric background in general relativity. The advantage of this formalism relies in the fact that it does not require a decomposition of the perturbations into spherical tensor harmonics. Furthermore, it does not assume the background to be vacuum, nor does it require its staticity. In the particular case of vacuum perturbations, we derive two master equations describing the propagation of arbitrary linear gravitational waves on a Schwarzschild black hole. When decomposed int","authors_text":"Eliana Chaverra, N\\'estor Ortiz, Olivier Sarbach","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2012-09-17T17:47:17Z","title":"Linear perturbations of self-gravitating spherically symmetric configurations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1209.3731","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:caa4a5add16892d7f554561bc9a4eec228139a757ec049399a3c03076f8ee1aa","target":"record","created_at":"2026-05-18T03:28:17Z","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":"6fd1158dac3058ebd081685ec3f848d62c3b36e154cafb158afa0637f12e7600","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2012-09-17T17:47:17Z","title_canon_sha256":"29c445caadbd0265a212eba432c7b996936d50e8d1877ea4c4697548f2d14375"},"schema_version":"1.0","source":{"id":"1209.3731","kind":"arxiv","version":2}},"canonical_sha256":"65c40850f567c594dc9ebb4f9348856d5b4524210af69bb5f413350d5d0a2ba7","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"65c40850f567c594dc9ebb4f9348856d5b4524210af69bb5f413350d5d0a2ba7","first_computed_at":"2026-05-18T03:28:17.412354Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:28:17.412354Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"lC25sMjv6+eCEP4v8w+NuQ1NGCldB32pzhvUGF6URDig3hG8pQXrignK3Kio9bdCEwfYZcKitBodPFoqZ92aBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T03:28:17.413014Z","signed_message":"canonical_sha256_bytes"},"source_id":"1209.3731","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:caa4a5add16892d7f554561bc9a4eec228139a757ec049399a3c03076f8ee1aa","sha256:5922298153fc4eed826b7f8a00c999d474cf51efbb957fe7f3ac0c029e105fe4"],"state_sha256":"bdfc87af29409addcbbc1de7593af8e229c984816e88f1ac7bedb035238d6b35"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"d5vs3Oea+gcKYUMp1e3SrXPZ++SiIdH8cHQkXKakaqb8ZgdNO2c3yfO75f22FISuySFUV36QbFxkLTlACL+CAQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-05T01:02:07.333802Z","bundle_sha256":"7ef2fdc275702010a81c4700b130f6783d1db299b5e3dea18a52dcc869a02eda"}}