{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:RLFKP5ECBKHLZRXYNPUVX6FPIG","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":"b6a3682f2cd9e477699f5395b7601abcafce0520aa0cc9139e1492ddcf93be20","cross_cats_sorted":["gr-qc"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.ed-ph","submitted_at":"2011-12-19T12:37:13Z","title_canon_sha256":"35cf044606b5c0ff5774f1d7f3dbfb1b8a1bea5451483d572e3b8d5f7b29cbdf"},"schema_version":"1.0","source":{"id":"1112.4319","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1112.4319","created_at":"2026-05-18T03:45:23Z"},{"alias_kind":"arxiv_version","alias_value":"1112.4319v1","created_at":"2026-05-18T03:45:23Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1112.4319","created_at":"2026-05-18T03:45:23Z"},{"alias_kind":"pith_short_12","alias_value":"RLFKP5ECBKHL","created_at":"2026-05-18T12:26:41Z"},{"alias_kind":"pith_short_16","alias_value":"RLFKP5ECBKHLZRXY","created_at":"2026-05-18T12:26:41Z"},{"alias_kind":"pith_short_8","alias_value":"RLFKP5EC","created_at":"2026-05-18T12:26:41Z"}],"graph_snapshots":[{"event_id":"sha256:4e7fa4441a8a7677ae5a259f6e7a271af8670dd8ab1fb89a66f8ea89d393c1c9","target":"graph","created_at":"2026-05-18T03:45:23Z","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"},"paper":{"abstract_excerpt":"The evolution of spatially homogeneous and isotropic cosmological models containing a perfect fluid with equation of state p=w\\rho\\ and a cosmological constant \\Lambda\\ is investigated for arbitrary combinations of w and \\Lambda, using standard qualitative analysis borrowed from classical mechanics. This approach allows one to consider a large variety of situations, appreciating similarities and differences between models, without solving the Friedmann equation, and is suitable for an elementary course in cosmology.","authors_text":"Sebastiano Sonego, Vittorino Talamini","cross_cats":["gr-qc"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.ed-ph","submitted_at":"2011-12-19T12:37:13Z","title":"Qualitative study of perfect-fluid Friedmann-Lema\\^{\\i}tre-Robertson-Walker models with a cosmological constant"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1112.4319","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":"sha256:62ad13a9ac99774984ff6816b18197c1919429d30ec03b094c74978faf053604","target":"record","created_at":"2026-05-18T03:45:23Z","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":"b6a3682f2cd9e477699f5395b7601abcafce0520aa0cc9139e1492ddcf93be20","cross_cats_sorted":["gr-qc"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.ed-ph","submitted_at":"2011-12-19T12:37:13Z","title_canon_sha256":"35cf044606b5c0ff5774f1d7f3dbfb1b8a1bea5451483d572e3b8d5f7b29cbdf"},"schema_version":"1.0","source":{"id":"1112.4319","kind":"arxiv","version":1}},"canonical_sha256":"8acaa7f4820a8ebcc6f86be95bf8af418bbc85e4778265f3c1f056a861ef04c6","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"8acaa7f4820a8ebcc6f86be95bf8af418bbc85e4778265f3c1f056a861ef04c6","first_computed_at":"2026-05-18T03:45:23.113262Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:45:23.113262Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Ua7nmYY5r9MhRFudNmzEOoiVPnfj5QSjJcVvcfROVCop4E/2AstY0tvwhwPERkxAoEcTJt10D5dH2i9qJUBEBA==","signature_status":"signed_v1","signed_at":"2026-05-18T03:45:23.113941Z","signed_message":"canonical_sha256_bytes"},"source_id":"1112.4319","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:62ad13a9ac99774984ff6816b18197c1919429d30ec03b094c74978faf053604","sha256:4e7fa4441a8a7677ae5a259f6e7a271af8670dd8ab1fb89a66f8ea89d393c1c9"],"state_sha256":"91f4b99a487703ce396b3dd004a3e27da19c93737ea839bc29cc982bb1be905e"}