{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2007:R4V2KBGSSTLZ62RPCA3IUQCNHT","short_pith_number":"pith:R4V2KBGS","canonical_record":{"source":{"id":"gr-qc/0703069","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"gr-qc","submitted_at":"2007-03-12T18:13:15Z","cross_cats_sorted":[],"title_canon_sha256":"33276acfa14236317fbbbd481c2d4c1472c8d08d72512000bf054b8b5faf0e8e","abstract_canon_sha256":"501bf531c9ff8225045327fd48669cd10688d794d000deaef5bf78ca3db7c16f"},"schema_version":"1.0"},"canonical_sha256":"8f2ba504d294d79f6a2f10368a404d3cf0f810b2884952dfa1c8d27e3ce578ac","source":{"kind":"arxiv","id":"gr-qc/0703069","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"gr-qc/0703069","created_at":"2026-07-04T15:25:07Z"},{"alias_kind":"arxiv_version","alias_value":"gr-qc/0703069v1","created_at":"2026-07-04T15:25:07Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.gr-qc/0703069","created_at":"2026-07-04T15:25:07Z"},{"alias_kind":"pith_short_12","alias_value":"R4V2KBGSSTLZ","created_at":"2026-07-04T15:25:07Z"},{"alias_kind":"pith_short_16","alias_value":"R4V2KBGSSTLZ62RP","created_at":"2026-07-04T15:25:07Z"},{"alias_kind":"pith_short_8","alias_value":"R4V2KBGS","created_at":"2026-07-04T15:25:07Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2007:R4V2KBGSSTLZ62RPCA3IUQCNHT","target":"record","payload":{"canonical_record":{"source":{"id":"gr-qc/0703069","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"gr-qc","submitted_at":"2007-03-12T18:13:15Z","cross_cats_sorted":[],"title_canon_sha256":"33276acfa14236317fbbbd481c2d4c1472c8d08d72512000bf054b8b5faf0e8e","abstract_canon_sha256":"501bf531c9ff8225045327fd48669cd10688d794d000deaef5bf78ca3db7c16f"},"schema_version":"1.0"},"canonical_sha256":"8f2ba504d294d79f6a2f10368a404d3cf0f810b2884952dfa1c8d27e3ce578ac","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-04T15:25:07.906663Z","signature_b64":"lLdsukMOdlv/a1FPxttcHZOAt2ObPoGZR3U9azHUxMxjUZ7zjDRH7jQikDZzByfG/UG7DXiTpaoOXU6FkUz3Bw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"8f2ba504d294d79f6a2f10368a404d3cf0f810b2884952dfa1c8d27e3ce578ac","last_reissued_at":"2026-07-04T15:25:07.906262Z","signature_status":"signed_v1","first_computed_at":"2026-07-04T15:25:07.906262Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"gr-qc/0703069","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-04T15:25:07Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ARPviJnvhCKR7+l/SbVz6R5VDAWP1dIfJFhkaINC8Iq8m6YwgePi2Pk17njSiwwe975BZr8KqNd+vHJ0j2h+CQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-05T17:37:04.838155Z"},"content_sha256":"9788e060b24ef682b485477baa2f73ce24324456830667a50b763f95fe67e12c","schema_version":"1.0","event_id":"sha256:9788e060b24ef682b485477baa2f73ce24324456830667a50b763f95fe67e12c"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2007:R4V2KBGSSTLZ62RPCA3IUQCNHT","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"High-order gauge-invariant perturbations of a spherical spacetime","license":"","headline":"","cross_cats":[],"primary_cat":"gr-qc","authors_text":"David Brizuela, Guillermo A. Mena Marugan, Jose M. Martin-Garcia","submitted_at":"2007-03-12T18:13:15Z","abstract_excerpt":"We complete the formulation of a general framework for the analysis of high-order nonspherical perturbations of a four-dimensional spherical spacetime by including a gauge-invariant description of the perturbations. We present a general algorithm to construct these invariants and provide explicit formulas for the case of second-order metric perturbations. We show that the well-known problem of lack of invariance for the first-order perturbations with l=0,1 propagates to increasing values of l for perturbations of higher order, owing to mode coupling. We also discuss in which circumstances it i"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"gr-qc/0703069","kind":"arxiv","version":1},"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/0703069/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":"2026-07-04T15:25:07Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"LZS2gYYQuwaqErREwNjyTi3AsnQLENV/LLgrQsVT4o70xWWLLSlXTvDSdCn4+dMOPhKGnZrWcCYSoBDGdQz/CQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-05T17:37:04.838668Z"},"content_sha256":"53d9d54ec13658a937b3f71e020d333d69c9bce3d7e53174291650e4f4c99133","schema_version":"1.0","event_id":"sha256:53d9d54ec13658a937b3f71e020d333d69c9bce3d7e53174291650e4f4c99133"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/R4V2KBGSSTLZ62RPCA3IUQCNHT/bundle.json","state_url":"https://pith.science/pith/R4V2KBGSSTLZ62RPCA3IUQCNHT/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/R4V2KBGSSTLZ62RPCA3IUQCNHT/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":"2026-08-05T17:37:04Z","links":{"resolver":"https://pith.science/pith/R4V2KBGSSTLZ62RPCA3IUQCNHT","bundle":"https://pith.science/pith/R4V2KBGSSTLZ62RPCA3IUQCNHT/bundle.json","state":"https://pith.science/pith/R4V2KBGSSTLZ62RPCA3IUQCNHT/state.json","well_known_bundle":"https://pith.science/.well-known/pith/R4V2KBGSSTLZ62RPCA3IUQCNHT/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2007:R4V2KBGSSTLZ62RPCA3IUQCNHT","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":"501bf531c9ff8225045327fd48669cd10688d794d000deaef5bf78ca3db7c16f","cross_cats_sorted":[],"license":"","primary_cat":"gr-qc","submitted_at":"2007-03-12T18:13:15Z","title_canon_sha256":"33276acfa14236317fbbbd481c2d4c1472c8d08d72512000bf054b8b5faf0e8e"},"schema_version":"1.0","source":{"id":"gr-qc/0703069","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"gr-qc/0703069","created_at":"2026-07-04T15:25:07Z"},{"alias_kind":"arxiv_version","alias_value":"gr-qc/0703069v1","created_at":"2026-07-04T15:25:07Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.gr-qc/0703069","created_at":"2026-07-04T15:25:07Z"},{"alias_kind":"pith_short_12","alias_value":"R4V2KBGSSTLZ","created_at":"2026-07-04T15:25:07Z"},{"alias_kind":"pith_short_16","alias_value":"R4V2KBGSSTLZ62RP","created_at":"2026-07-04T15:25:07Z"},{"alias_kind":"pith_short_8","alias_value":"R4V2KBGS","created_at":"2026-07-04T15:25:07Z"}],"graph_snapshots":[{"event_id":"sha256:53d9d54ec13658a937b3f71e020d333d69c9bce3d7e53174291650e4f4c99133","target":"graph","created_at":"2026-07-04T15:25:07Z","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/0703069/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We complete the formulation of a general framework for the analysis of high-order nonspherical perturbations of a four-dimensional spherical spacetime by including a gauge-invariant description of the perturbations. We present a general algorithm to construct these invariants and provide explicit formulas for the case of second-order metric perturbations. We show that the well-known problem of lack of invariance for the first-order perturbations with l=0,1 propagates to increasing values of l for perturbations of higher order, owing to mode coupling. We also discuss in which circumstances it i","authors_text":"David Brizuela, Guillermo A. Mena Marugan, Jose M. Martin-Garcia","cross_cats":[],"headline":"","license":"","primary_cat":"gr-qc","submitted_at":"2007-03-12T18:13:15Z","title":"High-order gauge-invariant perturbations of a spherical spacetime"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"gr-qc/0703069","kind":"arxiv","version":1},"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":"sha256:9788e060b24ef682b485477baa2f73ce24324456830667a50b763f95fe67e12c","target":"record","created_at":"2026-07-04T15:25:07Z","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":"501bf531c9ff8225045327fd48669cd10688d794d000deaef5bf78ca3db7c16f","cross_cats_sorted":[],"license":"","primary_cat":"gr-qc","submitted_at":"2007-03-12T18:13:15Z","title_canon_sha256":"33276acfa14236317fbbbd481c2d4c1472c8d08d72512000bf054b8b5faf0e8e"},"schema_version":"1.0","source":{"id":"gr-qc/0703069","kind":"arxiv","version":1}},"canonical_sha256":"8f2ba504d294d79f6a2f10368a404d3cf0f810b2884952dfa1c8d27e3ce578ac","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"8f2ba504d294d79f6a2f10368a404d3cf0f810b2884952dfa1c8d27e3ce578ac","first_computed_at":"2026-07-04T15:25:07.906262Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-04T15:25:07.906262Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"lLdsukMOdlv/a1FPxttcHZOAt2ObPoGZR3U9azHUxMxjUZ7zjDRH7jQikDZzByfG/UG7DXiTpaoOXU6FkUz3Bw==","signature_status":"signed_v1","signed_at":"2026-07-04T15:25:07.906663Z","signed_message":"canonical_sha256_bytes"},"source_id":"gr-qc/0703069","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:9788e060b24ef682b485477baa2f73ce24324456830667a50b763f95fe67e12c","sha256:53d9d54ec13658a937b3f71e020d333d69c9bce3d7e53174291650e4f4c99133"],"state_sha256":"d48df41d3a99b2f888b40ef3f77bc6f44ae7c26ab9ab4dc50fdfbba7f5748bc6"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"v6FuYuHfQapvDG86IW548wHCnpSECyFUQGuBinTw+4NRRB8wd79CtDSLwjW3qkW1W0/vSwx6kXUd02uPZzsVDw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-05T17:37:04.842796Z","bundle_sha256":"a7cb215f175d3964b93fb3806a51d7b48f5005b4511c10a66a1ffe11f0cda95a"}}