{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2007:R77ZI67NVVYTSIBFCUHSIGXSEZ","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":"8573ec98df9c18146271799d217972ead0fc2081d8e7c3fc349c3b2f8a467991","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2007-07-23T18:17:10Z","title_canon_sha256":"64ce82bf6fc6351bb91761367acd3fadbd0b1dbb760317dbe1b38a8ef8c003fa"},"schema_version":"1.0","source":{"id":"0707.3387","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0707.3387","created_at":"2026-05-18T03:51:46Z"},{"alias_kind":"arxiv_version","alias_value":"0707.3387v2","created_at":"2026-05-18T03:51:46Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0707.3387","created_at":"2026-05-18T03:51:46Z"},{"alias_kind":"pith_short_12","alias_value":"R77ZI67NVVYT","created_at":"2026-05-18T12:25:56Z"},{"alias_kind":"pith_short_16","alias_value":"R77ZI67NVVYTSIBF","created_at":"2026-05-18T12:25:56Z"},{"alias_kind":"pith_short_8","alias_value":"R77ZI67N","created_at":"2026-05-18T12:25:56Z"}],"graph_snapshots":[{"event_id":"sha256:22a9df21f93fc82b99da93bf08d4ee852aaca1d923fc4cd9a290e76e2d44bdfd","target":"graph","created_at":"2026-05-18T03:51:46Z","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":"In this paper we present the equations of the evolution of the universe in $D$ spatial dimensions, as a generalization of the work of Lima \\citep{lima}. We discuss the Friedmann-Robertson-Walker cosmological equations in $D$ spatial dimensions for a simple fluid with equation of state $p=\\omega_{D}\\rho$. It is possible to reduce the multidimensional equations to the equation of a point particle system subject to a linear force. This force can be expressed as an oscillator equation, anti-oscillator or a free particle equation, depending on the $k$ parameter of the spatial curvature. An interest","authors_text":"R. F. L. Holanda, S. H. Pereira","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2007-07-23T18:17:10Z","title":"On the dynamics of the universe in $D$ spatial dimensions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0707.3387","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:b122f53cafa5edb812f69b55f9bd3fc52cefe5869376c95ca43b8cbbbcb5ae1a","target":"record","created_at":"2026-05-18T03:51:46Z","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":"8573ec98df9c18146271799d217972ead0fc2081d8e7c3fc349c3b2f8a467991","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2007-07-23T18:17:10Z","title_canon_sha256":"64ce82bf6fc6351bb91761367acd3fadbd0b1dbb760317dbe1b38a8ef8c003fa"},"schema_version":"1.0","source":{"id":"0707.3387","kind":"arxiv","version":2}},"canonical_sha256":"8fff947bedad71392025150f241af2264143dc8d7857ea73d79c21e99af4705b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"8fff947bedad71392025150f241af2264143dc8d7857ea73d79c21e99af4705b","first_computed_at":"2026-05-18T03:51:46.103585Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:51:46.103585Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"e5uwyhH8XRy5mPNXPq3DzUku7J6JrFeGo3u/9hahFgczneT4plQhIxcmkRa+z3gTm0VS7kLnjrYPs8gaELrkDA==","signature_status":"signed_v1","signed_at":"2026-05-18T03:51:46.104100Z","signed_message":"canonical_sha256_bytes"},"source_id":"0707.3387","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b122f53cafa5edb812f69b55f9bd3fc52cefe5869376c95ca43b8cbbbcb5ae1a","sha256:22a9df21f93fc82b99da93bf08d4ee852aaca1d923fc4cd9a290e76e2d44bdfd"],"state_sha256":"6518421e6adf7adb6f49a33e0027325d20ccf060e7266e1307afc97934ecee2d"}