{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2005:YNOQJ7QLW2R3P6AIKA2BGNVYQI","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":"a9d9bae55bfe258dbef3083a1eaced8012d8ff50554e87d5b07f486c577d480d","cross_cats_sorted":["astro-ph","hep-th"],"license":"","primary_cat":"gr-qc","submitted_at":"2005-07-06T13:56:36Z","title_canon_sha256":"afeb983102e1f9bb38e1d8c2bffebbe7a77f5d5ab5c5883459319a9ef0ade707"},"schema_version":"1.0","source":{"id":"gr-qc/0507020","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"gr-qc/0507020","created_at":"2026-07-04T16:55:16Z"},{"alias_kind":"arxiv_version","alias_value":"gr-qc/0507020v2","created_at":"2026-07-04T16:55:16Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.gr-qc/0507020","created_at":"2026-07-04T16:55:16Z"},{"alias_kind":"pith_short_12","alias_value":"YNOQJ7QLW2R3","created_at":"2026-07-04T16:55:16Z"},{"alias_kind":"pith_short_16","alias_value":"YNOQJ7QLW2R3P6AI","created_at":"2026-07-04T16:55:16Z"},{"alias_kind":"pith_short_8","alias_value":"YNOQJ7QL","created_at":"2026-07-04T16:55:16Z"}],"graph_snapshots":[{"event_id":"sha256:e16e4298ce93246e790b33fa3ec4d2820e8e40ccdb6bb17b839a439227b7f594","target":"graph","created_at":"2026-07-04T16:55:16Z","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/0507020/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We present the concomitant decomposition of an (s+2)-dimensional spacetime both with respect to a timelike and a spacelike direction. The formalism we develop is suited for the study of the initial value problem and for canonical gravitational dynamics in brane-world scenarios. The bulk metric is replaced by two sets of variables. The first set consist of one tensorial (the induced metric $g_{ij}$), one vectorial ($M^{i}$) and one scalar ($M$) dynamical quantity, all defined on the s-space. Their time evolutions are related to the second fundamental form (the extrinsic curvature $K_{ij}$), the","authors_text":"L\\'aszl\\'o \\'A. Gergely, Zolt\\'an Kov\\'acs","cross_cats":["astro-ph","hep-th"],"headline":"","license":"","primary_cat":"gr-qc","submitted_at":"2005-07-06T13:56:36Z","title":"Gravitational dynamics in s+1+1 dimensions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"gr-qc/0507020","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":"sha256:1e91dc2bcedc7b4dabf353b0813d3e36cd25a151c1a5bcd4afd53e9ce3c08067","target":"record","created_at":"2026-07-04T16:55:16Z","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":"a9d9bae55bfe258dbef3083a1eaced8012d8ff50554e87d5b07f486c577d480d","cross_cats_sorted":["astro-ph","hep-th"],"license":"","primary_cat":"gr-qc","submitted_at":"2005-07-06T13:56:36Z","title_canon_sha256":"afeb983102e1f9bb38e1d8c2bffebbe7a77f5d5ab5c5883459319a9ef0ade707"},"schema_version":"1.0","source":{"id":"gr-qc/0507020","kind":"arxiv","version":2}},"canonical_sha256":"c35d04fe0bb6a3b7f80850341336b8823301805a7ce2c7fe47d3388eb4fb4a0a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c35d04fe0bb6a3b7f80850341336b8823301805a7ce2c7fe47d3388eb4fb4a0a","first_computed_at":"2026-07-04T16:55:16.030800Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-04T16:55:16.030800Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"zdOECEU3CyhwwAZpMeepbguJqMtEVjy650uMx+ICltzT6L2fRvIELYjYQix1GmnaFjJzWaXsnZVWEtPXxTiqCw==","signature_status":"signed_v1","signed_at":"2026-07-04T16:55:16.031141Z","signed_message":"canonical_sha256_bytes"},"source_id":"gr-qc/0507020","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1e91dc2bcedc7b4dabf353b0813d3e36cd25a151c1a5bcd4afd53e9ce3c08067","sha256:e16e4298ce93246e790b33fa3ec4d2820e8e40ccdb6bb17b839a439227b7f594"],"state_sha256":"a54ac0b7d8c30ef127e53652cb7048541a4d02862b2b58a66803326ed2139980"}