{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2008:6W7XL4GHPNRDMNTCJGVIULDVBT","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":"ff2a4ad91fca367e1fec50a8ecda3015e9052fe86d6a33a68b5723e9d6993428","cross_cats_sorted":["astro-ph","math.GT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2008-12-22T06:07:39Z","title_canon_sha256":"9c263374c6b1236325b7b17835e44ee310e5ea3d7859c29f399f9eb116d270e3"},"schema_version":"1.0","source":{"id":"0812.4103","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0812.4103","created_at":"2026-05-18T02:15:04Z"},{"alias_kind":"arxiv_version","alias_value":"0812.4103v4","created_at":"2026-05-18T02:15:04Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0812.4103","created_at":"2026-05-18T02:15:04Z"},{"alias_kind":"pith_short_12","alias_value":"6W7XL4GHPNRD","created_at":"2026-05-18T12:25:56Z"},{"alias_kind":"pith_short_16","alias_value":"6W7XL4GHPNRDMNTC","created_at":"2026-05-18T12:25:56Z"},{"alias_kind":"pith_short_8","alias_value":"6W7XL4GH","created_at":"2026-05-18T12:25:56Z"}],"graph_snapshots":[{"event_id":"sha256:07757214c6547b1b7b449d9946212c6151a45c470da450dcbf98136de9e83af5","target":"graph","created_at":"2026-05-18T02:15:04Z","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":"This paper deals with two aspects of relativistic cosmologies with closed (compact and boundless) spatial sections. These spacetimes are based on the theory of General Relativity, and admit a foliation into space sections S(t), which are spacelike hypersurfaces satisfying the postulate of the closure of space: each S(t) is a 3-dimensional, closed Riemannian manifold. The discussed topics are: (1) A comparison, previously obtained, between Thurston's geometries and Bianchi-Kantowski-Sachs metrics for such 3-manifolds is here clarified and developed. (2) Some implications of global inhomogeneity","authors_text":"Helio V. Fagundes","cross_cats":["astro-ph","math.GT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2008-12-22T06:07:39Z","title":"Closed Spaces in Cosmology"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0812.4103","kind":"arxiv","version":4},"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:f08f31219d28c80c60229bd6bb86bc53af6fe75f31ca1a22dc993fad904beda7","target":"record","created_at":"2026-05-18T02:15:04Z","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":"ff2a4ad91fca367e1fec50a8ecda3015e9052fe86d6a33a68b5723e9d6993428","cross_cats_sorted":["astro-ph","math.GT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2008-12-22T06:07:39Z","title_canon_sha256":"9c263374c6b1236325b7b17835e44ee310e5ea3d7859c29f399f9eb116d270e3"},"schema_version":"1.0","source":{"id":"0812.4103","kind":"arxiv","version":4}},"canonical_sha256":"f5bf75f0c77b6236366249aa8a2c750cced595afa136931b3a1c790f98abd521","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f5bf75f0c77b6236366249aa8a2c750cced595afa136931b3a1c790f98abd521","first_computed_at":"2026-05-18T02:15:04.049377Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:15:04.049377Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Z9ap61PLAi9cJ8b2UsXniZuaklzs+0aJc8mdgImiuiGECs94DWxprvowe9xgKdjoW4ssV2E47uH4f+JnPrSKBw==","signature_status":"signed_v1","signed_at":"2026-05-18T02:15:04.049816Z","signed_message":"canonical_sha256_bytes"},"source_id":"0812.4103","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f08f31219d28c80c60229bd6bb86bc53af6fe75f31ca1a22dc993fad904beda7","sha256:07757214c6547b1b7b449d9946212c6151a45c470da450dcbf98136de9e83af5"],"state_sha256":"42694dab6cbf5ffd8e71df736f5a376102a821b4f0a9b967d9ee2f2f8717d942"}