{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:1992:ICNKTIZIGKATUB3FVB6QVX2ZNN","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":"5b56de5093b6ec00f3402be453676635c343e36137ba5bae6890eeb548c09359","cross_cats_sorted":[],"license":"","primary_cat":"hep-ph","submitted_at":"1992-11-09T15:55:00Z","title_canon_sha256":"b8ca1baef78e95b125265beb4ac9acf8d08248de7e5865b5053d521d11acd348"},"schema_version":"1.0","source":{"id":"hep-ph/9211231","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"hep-ph/9211231","created_at":"2026-07-04T15:55:17Z"},{"alias_kind":"arxiv_version","alias_value":"hep-ph/9211231v1","created_at":"2026-07-04T15:55:17Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.hep-ph/9211231","created_at":"2026-07-04T15:55:17Z"},{"alias_kind":"pith_short_12","alias_value":"ICNKTIZIGKAT","created_at":"2026-07-04T15:55:17Z"},{"alias_kind":"pith_short_16","alias_value":"ICNKTIZIGKATUB3F","created_at":"2026-07-04T15:55:17Z"},{"alias_kind":"pith_short_8","alias_value":"ICNKTIZI","created_at":"2026-07-04T15:55:17Z"}],"graph_snapshots":[{"event_id":"sha256:d512535bd0d1ddb947f791d5b296e0915441792f197ad654f1ce26f2aa621962","target":"graph","created_at":"2026-07-04T15:55:17Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/hep-ph/9211231/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We derive an equation for the evolution of the number density of a massive particle species in the early Universe, which correctly accounts for the Fermi-Dirac (FD) statistics. The FD-corrections are sizable and potentially important if the decoupling from the thermal equilibrium takes place at temperatures of the order of, or less than the mass of the particle. This is the case e.g.\\ for a few MeV tau neutrino with the ordinary weak interactions.","authors_text":"A. D. Dolgov, K. Kainulainen","cross_cats":[],"headline":"","license":"","primary_cat":"hep-ph","submitted_at":"1992-11-09T15:55:00Z","title":"Fermi-Dirac corrections to relic abundances"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"hep-ph/9211231","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:e86d1cf642a2b72a18a709d9c28711254ee74ad719db0b60e8bb72936ed7e382","target":"record","created_at":"2026-07-04T15:55:17Z","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":"5b56de5093b6ec00f3402be453676635c343e36137ba5bae6890eeb548c09359","cross_cats_sorted":[],"license":"","primary_cat":"hep-ph","submitted_at":"1992-11-09T15:55:00Z","title_canon_sha256":"b8ca1baef78e95b125265beb4ac9acf8d08248de7e5865b5053d521d11acd348"},"schema_version":"1.0","source":{"id":"hep-ph/9211231","kind":"arxiv","version":1}},"canonical_sha256":"409aa9a32832813a0765a87d0adf596b46a1770683ecbbc165b3ca7b5ab54702","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"409aa9a32832813a0765a87d0adf596b46a1770683ecbbc165b3ca7b5ab54702","first_computed_at":"2026-07-04T15:55:17.230004Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-04T15:55:17.230004Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"w2R5LSrsfClvBauUEqY9u85mrUqY6XugGXd1uhk2+Y23By9xXXU8hw/UdThcFXtpGdH9RKJptGuCthxjgXFUBQ==","signature_status":"signed_v1","signed_at":"2026-07-04T15:55:17.230426Z","signed_message":"canonical_sha256_bytes"},"source_id":"hep-ph/9211231","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e86d1cf642a2b72a18a709d9c28711254ee74ad719db0b60e8bb72936ed7e382","sha256:d512535bd0d1ddb947f791d5b296e0915441792f197ad654f1ce26f2aa621962"],"state_sha256":"e25ae7c40a84cefd234f9f7f03947435530309154a81da17289fccd9e5d1ed2d"}