{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2007:EBPA7ARSACAUI6C3N4O3EBQJP3","short_pith_number":"pith:EBPA7ARS","canonical_record":{"source":{"id":"gr-qc/0703035","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"gr-qc","submitted_at":"2007-03-06T13:19:45Z","cross_cats_sorted":["astro-ph","math.DG"],"title_canon_sha256":"4bfe2c76a2ef1402f30009a08c8823fd01ba3b078edbf99ae5ac217b1012cab2","abstract_canon_sha256":"01989f262d02560fed4ca93dc96668f727cc10cca37bcd46a7e42ebfb9a3254b"},"schema_version":"1.0"},"canonical_sha256":"205e0f8232008144785b6f1db206097ece3876a58d22f715c1d203765e666570","source":{"kind":"arxiv","id":"gr-qc/0703035","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"gr-qc/0703035","created_at":"2026-07-04T14:59:57Z"},{"alias_kind":"arxiv_version","alias_value":"gr-qc/0703035v1","created_at":"2026-07-04T14:59:57Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.gr-qc/0703035","created_at":"2026-07-04T14:59:57Z"},{"alias_kind":"pith_short_12","alias_value":"EBPA7ARSACAU","created_at":"2026-07-04T14:59:57Z"},{"alias_kind":"pith_short_16","alias_value":"EBPA7ARSACAUI6C3","created_at":"2026-07-04T14:59:57Z"},{"alias_kind":"pith_short_8","alias_value":"EBPA7ARS","created_at":"2026-07-04T14:59:57Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2007:EBPA7ARSACAUI6C3N4O3EBQJP3","target":"record","payload":{"canonical_record":{"source":{"id":"gr-qc/0703035","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"gr-qc","submitted_at":"2007-03-06T13:19:45Z","cross_cats_sorted":["astro-ph","math.DG"],"title_canon_sha256":"4bfe2c76a2ef1402f30009a08c8823fd01ba3b078edbf99ae5ac217b1012cab2","abstract_canon_sha256":"01989f262d02560fed4ca93dc96668f727cc10cca37bcd46a7e42ebfb9a3254b"},"schema_version":"1.0"},"canonical_sha256":"205e0f8232008144785b6f1db206097ece3876a58d22f715c1d203765e666570","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-04T14:59:57.621416Z","signature_b64":"rxGxFPGBlqHdUXsh4dmaH/XLg4nY4Pqmkp9emoMNppk7jrZQ/4P6iiITEZf7pywwApIeZaeR2ixnYdTm1V7VBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"205e0f8232008144785b6f1db206097ece3876a58d22f715c1d203765e666570","last_reissued_at":"2026-07-04T14:59:57.621022Z","signature_status":"signed_v1","first_computed_at":"2026-07-04T14:59:57.621022Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"gr-qc/0703035","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":"2026-07-04T14:59:57Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"63JEtZguCLwpljOzev9PQpcOgzpw+5HXjt/NYnoAC4a9h3QnqHgVonf8Cz8KJ97QeZxTu+pIeiOie4o/bKqzCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-15T21:28:50.169519Z"},"content_sha256":"1b0edb9aafc2b800f410f59b271555b099d8be36f303022c6ebe791c9a4b6ea2","schema_version":"1.0","event_id":"sha256:1b0edb9aafc2b800f410f59b271555b099d8be36f303022c6ebe791c9a4b6ea2"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2007:EBPA7ARSACAUI6C3N4O3EBQJP3","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"3+1 Formalism and Bases of Numerical Relativity","license":"","headline":"","cross_cats":["astro-ph","math.DG"],"primary_cat":"gr-qc","authors_text":"CNRS / Observatoire de Paris), Eric Gourgoulhon (LUTH","submitted_at":"2007-03-06T13:19:45Z","abstract_excerpt":"These lecture notes provide some introduction to the 3+1 formalism of general relativity, which is the foundation of most modern numerical relativity. The text is rather self-contained, with detailed calculations and numerous examples. Contents: 1. Introduction, 2. Geometry of hypersurfaces, 3. Geometry of foliations, 4. 3+1 decomposition of Einstein equation, 5. 3+1 equations for matter and electromagnetic field, 6. Conformal decomposition, 7. Asymptotic flatness and global quantities, 8. The initial data problem, 9. Choice of foliation and spatial coordinates, 10. Evolution schemes."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"gr-qc/0703035","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/0703035/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":"2026-07-04T14:59:57Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"3Hc/6rpoNxATagl3kpf568Dyx8LSRMbgDlMtah/QLtoOJYDAWlI9xOYhqLpkd1DhfDUwpxtVb0ohgmSOSfV8CA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-15T21:28:50.170348Z"},"content_sha256":"1f746c8ccfb85175a86b1e902a07b2c2ff1a0fdcd987aace21d2b1427f17ad9c","schema_version":"1.0","event_id":"sha256:1f746c8ccfb85175a86b1e902a07b2c2ff1a0fdcd987aace21d2b1427f17ad9c"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/EBPA7ARSACAUI6C3N4O3EBQJP3/bundle.json","state_url":"https://pith.science/pith/EBPA7ARSACAUI6C3N4O3EBQJP3/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/EBPA7ARSACAUI6C3N4O3EBQJP3/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":"2026-08-15T21:28:50Z","links":{"resolver":"https://pith.science/pith/EBPA7ARSACAUI6C3N4O3EBQJP3","bundle":"https://pith.science/pith/EBPA7ARSACAUI6C3N4O3EBQJP3/bundle.json","state":"https://pith.science/pith/EBPA7ARSACAUI6C3N4O3EBQJP3/state.json","well_known_bundle":"https://pith.science/.well-known/pith/EBPA7ARSACAUI6C3N4O3EBQJP3/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2007:EBPA7ARSACAUI6C3N4O3EBQJP3","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":"01989f262d02560fed4ca93dc96668f727cc10cca37bcd46a7e42ebfb9a3254b","cross_cats_sorted":["astro-ph","math.DG"],"license":"","primary_cat":"gr-qc","submitted_at":"2007-03-06T13:19:45Z","title_canon_sha256":"4bfe2c76a2ef1402f30009a08c8823fd01ba3b078edbf99ae5ac217b1012cab2"},"schema_version":"1.0","source":{"id":"gr-qc/0703035","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"gr-qc/0703035","created_at":"2026-07-04T14:59:57Z"},{"alias_kind":"arxiv_version","alias_value":"gr-qc/0703035v1","created_at":"2026-07-04T14:59:57Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.gr-qc/0703035","created_at":"2026-07-04T14:59:57Z"},{"alias_kind":"pith_short_12","alias_value":"EBPA7ARSACAU","created_at":"2026-07-04T14:59:57Z"},{"alias_kind":"pith_short_16","alias_value":"EBPA7ARSACAUI6C3","created_at":"2026-07-04T14:59:57Z"},{"alias_kind":"pith_short_8","alias_value":"EBPA7ARS","created_at":"2026-07-04T14:59:57Z"}],"graph_snapshots":[{"event_id":"sha256:1f746c8ccfb85175a86b1e902a07b2c2ff1a0fdcd987aace21d2b1427f17ad9c","target":"graph","created_at":"2026-07-04T14:59:57Z","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/0703035/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"These lecture notes provide some introduction to the 3+1 formalism of general relativity, which is the foundation of most modern numerical relativity. The text is rather self-contained, with detailed calculations and numerous examples. Contents: 1. Introduction, 2. Geometry of hypersurfaces, 3. Geometry of foliations, 4. 3+1 decomposition of Einstein equation, 5. 3+1 equations for matter and electromagnetic field, 6. Conformal decomposition, 7. Asymptotic flatness and global quantities, 8. The initial data problem, 9. Choice of foliation and spatial coordinates, 10. Evolution schemes.","authors_text":"CNRS / Observatoire de Paris), Eric Gourgoulhon (LUTH","cross_cats":["astro-ph","math.DG"],"headline":"","license":"","primary_cat":"gr-qc","submitted_at":"2007-03-06T13:19:45Z","title":"3+1 Formalism and Bases of Numerical Relativity"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"gr-qc/0703035","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":"sha256:1b0edb9aafc2b800f410f59b271555b099d8be36f303022c6ebe791c9a4b6ea2","target":"record","created_at":"2026-07-04T14:59:57Z","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":"01989f262d02560fed4ca93dc96668f727cc10cca37bcd46a7e42ebfb9a3254b","cross_cats_sorted":["astro-ph","math.DG"],"license":"","primary_cat":"gr-qc","submitted_at":"2007-03-06T13:19:45Z","title_canon_sha256":"4bfe2c76a2ef1402f30009a08c8823fd01ba3b078edbf99ae5ac217b1012cab2"},"schema_version":"1.0","source":{"id":"gr-qc/0703035","kind":"arxiv","version":1}},"canonical_sha256":"205e0f8232008144785b6f1db206097ece3876a58d22f715c1d203765e666570","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"205e0f8232008144785b6f1db206097ece3876a58d22f715c1d203765e666570","first_computed_at":"2026-07-04T14:59:57.621022Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-04T14:59:57.621022Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"rxGxFPGBlqHdUXsh4dmaH/XLg4nY4Pqmkp9emoMNppk7jrZQ/4P6iiITEZf7pywwApIeZaeR2ixnYdTm1V7VBg==","signature_status":"signed_v1","signed_at":"2026-07-04T14:59:57.621416Z","signed_message":"canonical_sha256_bytes"},"source_id":"gr-qc/0703035","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1b0edb9aafc2b800f410f59b271555b099d8be36f303022c6ebe791c9a4b6ea2","sha256:1f746c8ccfb85175a86b1e902a07b2c2ff1a0fdcd987aace21d2b1427f17ad9c"],"state_sha256":"926636cec79338715b9bad26bcbe1576c0a5d029a3c124cacae469a3a1c87e0e"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Jg/nn+52c5XowiBicm9/4UK48+XaiNFtx5BngGy0yCr/98Ln9uT0rtLqRB/r74eAIEDpAT5YmSi0tJ0wJ3THAw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-15T21:28:50.176744Z","bundle_sha256":"fe0fbd0ac6e905fc40ac36438ab2d72853f585aa712cb3fb98e99a969ffbd0af"}}