{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2009:75BIBYGDAVQEFSY4JK5PJYLMPR","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":"34f46aeb03751b149ec13236b185278ed770ae7a216f2fbed77ff02a95a12ce8","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"astro-ph.CO","submitted_at":"2009-10-01T10:21:37Z","title_canon_sha256":"607553e961b5bcf417b78962899b3a3ead09587e8916acb02b13ae8bf7616a03"},"schema_version":"1.0","source":{"id":"0910.0126","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0910.0126","created_at":"2026-05-18T04:38:48Z"},{"alias_kind":"arxiv_version","alias_value":"0910.0126v2","created_at":"2026-05-18T04:38:48Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0910.0126","created_at":"2026-05-18T04:38:48Z"},{"alias_kind":"pith_short_12","alias_value":"75BIBYGDAVQE","created_at":"2026-05-18T12:25:58Z"},{"alias_kind":"pith_short_16","alias_value":"75BIBYGDAVQEFSY4","created_at":"2026-05-18T12:25:58Z"},{"alias_kind":"pith_short_8","alias_value":"75BIBYGD","created_at":"2026-05-18T12:25:58Z"}],"graph_snapshots":[{"event_id":"sha256:71def7cceb659d291e61d77d0ea7583b678868a0f807fb6ae482a2012c2ed2fb","target":"graph","created_at":"2026-05-18T04:38:48Z","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":"We investigate a spherical overdensity model for the non-clustering dark energy (DE) with the constant equation of state, w in a flat universe. In this case, the exact solution for the evolution of the scale factor is obtained for general w. We also obtain the exact (when w = - 1/3) and the approximate (when w neq -1/3) solutions for the ratio of the overdensity radius to its value at the turnaround epoch (y) for general cosmological parameters. Also the exact and approximate solutions of the overdensity at the turnaround epoch (zeta) are obtained for general w. Thus, we are able to obtain the","authors_text":"Kin-Wang Ng, Seokcheon Lee","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"astro-ph.CO","submitted_at":"2009-10-01T10:21:37Z","title":"Spherical collapse model with non-clustering dark energy"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0910.0126","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":"sha256:1e36dc3452b523c581236cf29eda61deba9e3e74d9b0644daf25a53e52303639","target":"record","created_at":"2026-05-18T04:38:48Z","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":"34f46aeb03751b149ec13236b185278ed770ae7a216f2fbed77ff02a95a12ce8","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"astro-ph.CO","submitted_at":"2009-10-01T10:21:37Z","title_canon_sha256":"607553e961b5bcf417b78962899b3a3ead09587e8916acb02b13ae8bf7616a03"},"schema_version":"1.0","source":{"id":"0910.0126","kind":"arxiv","version":2}},"canonical_sha256":"ff4280e0c3056042cb1c4abaf4e16c7c617af8997087d4e79b4568b0d090964b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ff4280e0c3056042cb1c4abaf4e16c7c617af8997087d4e79b4568b0d090964b","first_computed_at":"2026-05-18T04:38:48.615051Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:38:48.615051Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"IcK5wS4jjIlYjzoR4IKSsod4AiKEoJ0NDPHhMP0KXvFHp4vw4cUzY7GNr7F7aYcb6ileF4OKI3KL35zvJxiZDg==","signature_status":"signed_v1","signed_at":"2026-05-18T04:38:48.615506Z","signed_message":"canonical_sha256_bytes"},"source_id":"0910.0126","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1e36dc3452b523c581236cf29eda61deba9e3e74d9b0644daf25a53e52303639","sha256:71def7cceb659d291e61d77d0ea7583b678868a0f807fb6ae482a2012c2ed2fb"],"state_sha256":"4df2be433318007c8ae68c5e60413d402cc1acf62a7215157fa9c9d66c64f522"}