{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:JMGCJLIUTZ2Z3CYCADB4TJGEVS","short_pith_number":"pith:JMGCJLIU","canonical_record":{"source":{"id":"1707.03439","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"astro-ph.CO","submitted_at":"2017-07-11T19:15:41Z","cross_cats_sorted":["gr-qc","hep-ph","hep-th"],"title_canon_sha256":"85537c606a7787d960f4facb091933a7fbc4501953c314c492dd1f74e4af0506","abstract_canon_sha256":"891b9321d41b7a7e5ff458cf55bc29f66c3d84140e021c25769d0a5caba11684"},"schema_version":"1.0"},"canonical_sha256":"4b0c24ad149e759d8b0200c3c9a4c4acb536f79a8494627d44e88d2fe0622fe1","source":{"kind":"arxiv","id":"1707.03439","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"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:JMGCJLIUTZ2Z3CYCADB4TJGEVS","target":"record","payload":{"canonical_record":{"source":{"id":"1707.03439","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"astro-ph.CO","submitted_at":"2017-07-11T19:15:41Z","cross_cats_sorted":["gr-qc","hep-ph","hep-th"],"title_canon_sha256":"85537c606a7787d960f4facb091933a7fbc4501953c314c492dd1f74e4af0506","abstract_canon_sha256":"891b9321d41b7a7e5ff458cf55bc29f66c3d84140e021c25769d0a5caba11684"},"schema_version":"1.0"},"canonical_sha256":"4b0c24ad149e759d8b0200c3c9a4c4acb536f79a8494627d44e88d2fe0622fe1","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:29:29.903534Z","signature_b64":"JV+t11iECq9JGZPIb4f8XpTdeY+//ytE7rKXot+3xrEFtc3P8jLcgk4RQeL2+MhVPubfjOkkqaylFS6HFVU5Aw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4b0c24ad149e759d8b0200c3c9a4c4acb536f79a8494627d44e88d2fe0622fe1","last_reissued_at":"2026-05-18T00:29:29.902795Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:29:29.902795Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1707.03439","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:29:29Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"dOg9fSFUqGAmzhmW+ohAGphf+mSaTTUwemL0pU87y2goYCjBnbpQhimllsKLYf2zhrrAViGuQ3z1aRG/OJRPDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-16T12:03:15.820312Z"},"content_sha256":"1d47206c64ab0f638c899f681e1d4179a930e9be0ec1c8f1881c6f992e432457","schema_version":"1.0","event_id":"sha256:1d47206c64ab0f638c899f681e1d4179a930e9be0ec1c8f1881c6f992e432457"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:JMGCJLIUTZ2Z3CYCADB4TJGEVS","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Inflation in a closed universe","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["gr-qc","hep-ph","hep-th"],"primary_cat":"astro-ph.CO","authors_text":"Bharat Ratra","submitted_at":"2017-07-11T19:15:41Z","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"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1707.03439","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:29:29Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"7rG+a9qE0WFkkZLxOR55toLEf3akJmjYpt1ZkKcSdiHk/YJaEO9wZhLsnEKwUDvqYzNK2sSfOWtA8qrLrjAzCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-16T12:03:15.821218Z"},"content_sha256":"c7b611d8a2e7d7021569af97c119948465578179c5e5b083db8671d91c0fe740","schema_version":"1.0","event_id":"sha256:c7b611d8a2e7d7021569af97c119948465578179c5e5b083db8671d91c0fe740"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/JMGCJLIUTZ2Z3CYCADB4TJGEVS/bundle.json","state_url":"https://pith.science/pith/JMGCJLIUTZ2Z3CYCADB4TJGEVS/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/JMGCJLIUTZ2Z3CYCADB4TJGEVS/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-08-16T12:03:15Z","links":{"resolver":"https://pith.science/pith/JMGCJLIUTZ2Z3CYCADB4TJGEVS","bundle":"https://pith.science/pith/JMGCJLIUTZ2Z3CYCADB4TJGEVS/bundle.json","state":"https://pith.science/pith/JMGCJLIUTZ2Z3CYCADB4TJGEVS/state.json","well_known_bundle":"https://pith.science/.well-known/pith/JMGCJLIUTZ2Z3CYCADB4TJGEVS/bundle.json"},"state":{"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"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"jPsnTVvx3aGKjkLQ5b/o1KqoNE3hx5Y6WrMbIiXaccxW06pRJgoSVn9f4OvQ284AlXvGcxWTdPp9cA2h9qwTAA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-16T12:03:15.828368Z","bundle_sha256":"5b594fecc9c592e5b8e67401e443cc6838b2a00fc0b2a91b6ed9c1d583104fa6"}}