{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:JMGCJLIUTZ2Z3CYCADB4TJGEVS","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":"891b9321d41b7a7e5ff458cf55bc29f66c3d84140e021c25769d0a5caba11684","cross_cats_sorted":["gr-qc","hep-ph","hep-th"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"astro-ph.CO","submitted_at":"2017-07-11T19:15:41Z","title_canon_sha256":"85537c606a7787d960f4facb091933a7fbc4501953c314c492dd1f74e4af0506"},"schema_version":"1.0","source":{"id":"1707.03439","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1707.03439","created_at":"2026-05-18T00:29:29Z"},{"alias_kind":"arxiv_version","alias_value":"1707.03439v2","created_at":"2026-05-18T00:29:29Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1707.03439","created_at":"2026-05-18T00:29:29Z"},{"alias_kind":"pith_short_12","alias_value":"JMGCJLIUTZ2Z","created_at":"2026-05-18T12:31:24Z"},{"alias_kind":"pith_short_16","alias_value":"JMGCJLIUTZ2Z3CYC","created_at":"2026-05-18T12:31:24Z"},{"alias_kind":"pith_short_8","alias_value":"JMGCJLIU","created_at":"2026-05-18T12:31:24Z"}],"graph_snapshots":[{"event_id":"sha256:c7b611d8a2e7d7021569af97c119948465578179c5e5b083db8671d91c0fe740","target":"graph","created_at":"2026-05-18T00:29:29Z","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":"To derive a power spectrum for energy density inhomogeneities in a closed universe, we study a spatially-closed inflation-modified hot big bang model whose evolutionary history is divided into three epochs: an early slowly-rolling scalar field inflation epoch and the usual radiation and non-relativistic matter epochs. (For our purposes it is not necessary to consider a final dark energy dominated epoch.) We derive general solutions of the relativistic linear perturbation equations in each epoch. The constants of integration in the inflation epoch solutions are determined from de Sitter invaria","authors_text":"Bharat Ratra","cross_cats":["gr-qc","hep-ph","hep-th"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"astro-ph.CO","submitted_at":"2017-07-11T19:15:41Z","title":"Inflation in a closed universe"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1707.03439","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":"sha256:1d47206c64ab0f638c899f681e1d4179a930e9be0ec1c8f1881c6f992e432457","target":"record","created_at":"2026-05-18T00:29:29Z","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":"891b9321d41b7a7e5ff458cf55bc29f66c3d84140e021c25769d0a5caba11684","cross_cats_sorted":["gr-qc","hep-ph","hep-th"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"astro-ph.CO","submitted_at":"2017-07-11T19:15:41Z","title_canon_sha256":"85537c606a7787d960f4facb091933a7fbc4501953c314c492dd1f74e4af0506"},"schema_version":"1.0","source":{"id":"1707.03439","kind":"arxiv","version":2}},"canonical_sha256":"4b0c24ad149e759d8b0200c3c9a4c4acb536f79a8494627d44e88d2fe0622fe1","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"4b0c24ad149e759d8b0200c3c9a4c4acb536f79a8494627d44e88d2fe0622fe1","first_computed_at":"2026-05-18T00:29:29.902795Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:29:29.902795Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"JV+t11iECq9JGZPIb4f8XpTdeY+//ytE7rKXot+3xrEFtc3P8jLcgk4RQeL2+MhVPubfjOkkqaylFS6HFVU5Aw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:29:29.903534Z","signed_message":"canonical_sha256_bytes"},"source_id":"1707.03439","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1d47206c64ab0f638c899f681e1d4179a930e9be0ec1c8f1881c6f992e432457","sha256:c7b611d8a2e7d7021569af97c119948465578179c5e5b083db8671d91c0fe740"],"state_sha256":"d0d04adcf513f37c932c24cdd551a1a0621d67f3edd947de4e5d9370efe3a75d"}