{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2006:G6NLDCGQJ2EYIRJPZIWYIEDSZY","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":"12649f7e6691139b04402a72d4c728f4dc2aab49169ee3d3512c04002b9c6aa7","cross_cats_sorted":["hep-th"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2006-01-17T14:25:49Z","title_canon_sha256":"1a840654203fd4338d1f6af42764ff70d20d0cf154eaef3f18a9d057dea35694"},"schema_version":"1.0","source":{"id":"gr-qc/0601068","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"gr-qc/0601068","created_at":"2026-05-18T04:36:20Z"},{"alias_kind":"arxiv_version","alias_value":"gr-qc/0601068v2","created_at":"2026-05-18T04:36:20Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.gr-qc/0601068","created_at":"2026-05-18T04:36:20Z"},{"alias_kind":"pith_short_12","alias_value":"G6NLDCGQJ2EY","created_at":"2026-05-18T12:25:53Z"},{"alias_kind":"pith_short_16","alias_value":"G6NLDCGQJ2EYIRJP","created_at":"2026-05-18T12:25:53Z"},{"alias_kind":"pith_short_8","alias_value":"G6NLDCGQ","created_at":"2026-05-18T12:25:53Z"}],"graph_snapshots":[{"event_id":"sha256:eec04088b49d4bd012c7e22774f67fae7b72ec907143c2455f4b928f8a783f3d","target":"graph","created_at":"2026-05-18T04:36:20Z","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":"It is shown that four dimensional vacuum Einstein solutions simply embedded in five dimensions obey the Gauss-Bonnet-Einstein field equations: $G_{ab}+\\alpha GB_{ab}+\\delta^{55}_{ab}\\alpha\\exp(-2\\chi/\\sqrt{\\alpha})GB_4=0$ and the Pauli-Einstein equations $G_{ab}-3\\alpha P_{ab}/5=0$, and the Bach-Einstein equations $B_{ab}=0$. General equations are calculated for which these and similar results follow. It is briefly argued that such field equations could be significant on large distance scales.","authors_text":"Mark D. Roberts","cross_cats":["hep-th"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2006-01-17T14:25:49Z","title":"Quadratic field equations on the brane"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"gr-qc/0601068","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":"sha256:2d14f9665a509c16549bf3fcec23f16163178a6526b7a8e8e7d8d749a8836c32","target":"record","created_at":"2026-05-18T04:36:20Z","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":"12649f7e6691139b04402a72d4c728f4dc2aab49169ee3d3512c04002b9c6aa7","cross_cats_sorted":["hep-th"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2006-01-17T14:25:49Z","title_canon_sha256":"1a840654203fd4338d1f6af42764ff70d20d0cf154eaef3f18a9d057dea35694"},"schema_version":"1.0","source":{"id":"gr-qc/0601068","kind":"arxiv","version":2}},"canonical_sha256":"379ab188d04e8984452fca2d841072ce1b5f22c8c1458d250b18a791871b7f56","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"379ab188d04e8984452fca2d841072ce1b5f22c8c1458d250b18a791871b7f56","first_computed_at":"2026-05-18T04:36:20.109626Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:36:20.109626Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"XlquEhkN0v+trRn3W1G0Cw+xsSPMkhjJip3kpDA/vbTCS3ZTU8WLEQAJpuvk2qh6OqZDwndsyvLwC1+QUTviDw==","signature_status":"signed_v1","signed_at":"2026-05-18T04:36:20.110085Z","signed_message":"canonical_sha256_bytes"},"source_id":"gr-qc/0601068","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2d14f9665a509c16549bf3fcec23f16163178a6526b7a8e8e7d8d749a8836c32","sha256:eec04088b49d4bd012c7e22774f67fae7b72ec907143c2455f4b928f8a783f3d"],"state_sha256":"d9baaeafede0582d343d084ba326c58cf318d0c98bd988db24aa3016d240d29d"}