{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2020:XTU636T4THPYCVMHULR6JR4DRP","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":"2b4c7da96815b5d384b0c1c06b89af3b1413ec63aa3fc996f35ed14178d76bf3","cross_cats_sorted":["astro-ph.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2020-01-30T15:17:29Z","title_canon_sha256":"e9c4ce9b5b28f3a1cf4e44d8ce79ba176a980ec4cc98f9231e428e3f36c078c0"},"schema_version":"1.0","source":{"id":"2001.11387","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2001.11387","created_at":"2026-07-05T00:37:23Z"},{"alias_kind":"arxiv_version","alias_value":"2001.11387v1","created_at":"2026-07-05T00:37:23Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2001.11387","created_at":"2026-07-05T00:37:23Z"},{"alias_kind":"pith_short_12","alias_value":"XTU636T4THPY","created_at":"2026-07-05T00:37:23Z"},{"alias_kind":"pith_short_16","alias_value":"XTU636T4THPYCVMH","created_at":"2026-07-05T00:37:23Z"},{"alias_kind":"pith_short_8","alias_value":"XTU636T4","created_at":"2026-07-05T00:37:23Z"}],"graph_snapshots":[{"event_id":"sha256:b7d86bd909c1d1ddfebe0c7c95b50ce45170700193f9ca7b60c3573eaedcbc30","target":"graph","created_at":"2026-07-05T00:37:23Z","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/2001.11387/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"(There is no original abstract.) These are lecture notes from a 1971 summer school surveying the then known cosmological models in particular the properties of Bianchi cosmologies, and giving a pedagogical introduction to groups of isometries in spacetime and to the orthonormal tetrad method.","authors_text":"M.A.H. MacCallum","cross_cats":["astro-ph.CO"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2020-01-30T15:17:29Z","title":"Cosmological models from a geometric point of view"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2001.11387","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:e3bf0bcda7dfc2378de78f3be481a2e0f59a3fdd6341c66207e6bc7297b243e8","target":"record","created_at":"2026-07-05T00:37:23Z","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":"2b4c7da96815b5d384b0c1c06b89af3b1413ec63aa3fc996f35ed14178d76bf3","cross_cats_sorted":["astro-ph.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2020-01-30T15:17:29Z","title_canon_sha256":"e9c4ce9b5b28f3a1cf4e44d8ce79ba176a980ec4cc98f9231e428e3f36c078c0"},"schema_version":"1.0","source":{"id":"2001.11387","kind":"arxiv","version":1}},"canonical_sha256":"bce9edfa7c99df815587a2e3e4c7838bf11284b206e7477416f1e550e1c6a948","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"bce9edfa7c99df815587a2e3e4c7838bf11284b206e7477416f1e550e1c6a948","first_computed_at":"2026-07-05T00:37:23.498850Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T00:37:23.498850Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"gSj3+AGvNWLUzJdrzY85eO9H72Sm+L9j+H0PD5dHVXo1uf3MntNbguKsTTxfbr2B05+CtjzZ17AEFqgic3G4Aw==","signature_status":"signed_v1","signed_at":"2026-07-05T00:37:23.499481Z","signed_message":"canonical_sha256_bytes"},"source_id":"2001.11387","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e3bf0bcda7dfc2378de78f3be481a2e0f59a3fdd6341c66207e6bc7297b243e8","sha256:b7d86bd909c1d1ddfebe0c7c95b50ce45170700193f9ca7b60c3573eaedcbc30"],"state_sha256":"7ef4a4fcebab1a768f5b2e644524956bf6cab13c7f2703eb18e6b2d74d6f2846"}