{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:3BPEWRHJPDDUMHZK23WFMEL2XE","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":"f9eaa9edd5a6c3fd64b6f4f5c722a42b79dde542ce1d9c475da9182f9a198dae","cross_cats_sorted":["gr-qc"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.gen-ph","submitted_at":"2014-12-17T12:20:01Z","title_canon_sha256":"8d24b35157f001015d2e7634a3a22fca047adaad0e381bdb13402868085c3841"},"schema_version":"1.0","source":{"id":"1412.6132","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1412.6132","created_at":"2026-05-18T01:36:34Z"},{"alias_kind":"arxiv_version","alias_value":"1412.6132v1","created_at":"2026-05-18T01:36:34Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1412.6132","created_at":"2026-05-18T01:36:34Z"},{"alias_kind":"pith_short_12","alias_value":"3BPEWRHJPDDU","created_at":"2026-05-18T12:28:11Z"},{"alias_kind":"pith_short_16","alias_value":"3BPEWRHJPDDUMHZK","created_at":"2026-05-18T12:28:11Z"},{"alias_kind":"pith_short_8","alias_value":"3BPEWRHJ","created_at":"2026-05-18T12:28:11Z"}],"graph_snapshots":[{"event_id":"sha256:2f8dea4cd97166810b2633c5f34d0e65d19b45c4d72a9a2d9616dd405966fdc1","target":"graph","created_at":"2026-05-18T01:36:34Z","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":"Recently we have found an analytic integration formula that describes the dependence of the luminosity distance on the redshift for the flat cosmological model with a non-zero cosmological constant. The purpose of this article is to search for a similar relation for the non-flat models. A Taylor series was used. The elliptic integral of the first kind can indeed be applied. The result shows that a combination of the numerical integration with the previous analytic formula can also be useful for the nearly flat cosmological models.","authors_text":"A. Meszaros, J. Ripa","cross_cats":["gr-qc"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.gen-ph","submitted_at":"2014-12-17T12:20:01Z","title":"On the relation between the non-flat cosmological models and the elliptic integral of first kind"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1412.6132","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":"sha256:2199e8a7ea474c3c4fc8aed578aa8d24ae1c228c1c1603badca2eb847e06638d","target":"record","created_at":"2026-05-18T01:36:34Z","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":"f9eaa9edd5a6c3fd64b6f4f5c722a42b79dde542ce1d9c475da9182f9a198dae","cross_cats_sorted":["gr-qc"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.gen-ph","submitted_at":"2014-12-17T12:20:01Z","title_canon_sha256":"8d24b35157f001015d2e7634a3a22fca047adaad0e381bdb13402868085c3841"},"schema_version":"1.0","source":{"id":"1412.6132","kind":"arxiv","version":1}},"canonical_sha256":"d85e4b44e978c7461f2ad6ec56117ab933660a920c913cb8e2ac95354fd865d8","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d85e4b44e978c7461f2ad6ec56117ab933660a920c913cb8e2ac95354fd865d8","first_computed_at":"2026-05-18T01:36:34.076850Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:36:34.076850Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"QXE0atghoNjMC9R9ZkNafKUA4EMGjpu7hTFKO28TbrvjDdu4+XiRYtYqku048whZEpA5JYuKveKJpA3mKWi1Dg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:36:34.077510Z","signed_message":"canonical_sha256_bytes"},"source_id":"1412.6132","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2199e8a7ea474c3c4fc8aed578aa8d24ae1c228c1c1603badca2eb847e06638d","sha256:2f8dea4cd97166810b2633c5f34d0e65d19b45c4d72a9a2d9616dd405966fdc1"],"state_sha256":"e586c72971f34373a958e66574c6bc49ee4a2fe207a75a6e93749ad77e2eb70e"}