{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2008:KXGFCCGV4X2J436LFKRSIG64GN","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":"527c3b9dd2284c3d28bc44fa18caa643ecfe86de5d190f8da2de20bc45527bc7","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"astro-ph","submitted_at":"2008-12-22T17:55:24Z","title_canon_sha256":"5ce0957390c12d17c2f8f32cbb1c6fd5a508e4b6a63e8103790d2174f9b2c519"},"schema_version":"1.0","source":{"id":"0812.4104","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0812.4104","created_at":"2026-05-18T04:29:24Z"},{"alias_kind":"arxiv_version","alias_value":"0812.4104v1","created_at":"2026-05-18T04:29:24Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0812.4104","created_at":"2026-05-18T04:29:24Z"},{"alias_kind":"pith_short_12","alias_value":"KXGFCCGV4X2J","created_at":"2026-05-18T12:25:57Z"},{"alias_kind":"pith_short_16","alias_value":"KXGFCCGV4X2J436L","created_at":"2026-05-18T12:25:57Z"},{"alias_kind":"pith_short_8","alias_value":"KXGFCCGV","created_at":"2026-05-18T12:25:57Z"}],"graph_snapshots":[{"event_id":"sha256:01ddecbbc50f2898f4e6db2e135ef8b0aba34c1bd82e09fb1325be18feae9fe2","target":"graph","created_at":"2026-05-18T04:29:24Z","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 study the Wouthuysen-Field coupling at early universe with numerical solutions of the integrodifferential equation describing the kinetics of photons undergoing resonant scattering. The numerical solver is developed based on the weighted essentially non-oscillatory (WENO) scheme for the Boltzmann-like integrodifferential equation. We focus on the time evolution of the Wouthuysen-Field (W-F) coupling in relation to the 21 cm emission and absorption at the epoch of reionization. We show that a local Boltzmann distribution will be formed if photons with frequency \\sim \\nu_0 have undergone a te","authors_text":"(2) Department of Physics, (3) Mathematical, Brown University, Colorado School of Mines, Computer Science, C.-W. Shu (1), I. Roy (1), J.-M. Qiu (3), L.-Z. Fang (2) ((1) Division of Applied Mathematics, University of Arizona, USA, USA), W. Xu (2)","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"astro-ph","submitted_at":"2008-12-22T17:55:24Z","title":"Time evolution of Wouthuysen-Field coupling"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0812.4104","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":"sha256:49be97249f6dd723019077145628f022823d1fd68cffa7c4a3d2fef4a26cb465","target":"record","created_at":"2026-05-18T04:29:24Z","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":"527c3b9dd2284c3d28bc44fa18caa643ecfe86de5d190f8da2de20bc45527bc7","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"astro-ph","submitted_at":"2008-12-22T17:55:24Z","title_canon_sha256":"5ce0957390c12d17c2f8f32cbb1c6fd5a508e4b6a63e8103790d2174f9b2c519"},"schema_version":"1.0","source":{"id":"0812.4104","kind":"arxiv","version":1}},"canonical_sha256":"55cc5108d5e5f49e6fcb2aa3241bdc336ad750d1cbffe9408b37851f7dedfcd3","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"55cc5108d5e5f49e6fcb2aa3241bdc336ad750d1cbffe9408b37851f7dedfcd3","first_computed_at":"2026-05-18T04:29:24.309014Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:29:24.309014Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"5YFkXTkjHe6Sdbfa56mQUEyzPc6Yzj1MvyyKGF7W/v5QgcR/y32QozwNSiRIquZeHW6Js3Ty8+yTkzFX23CsCA==","signature_status":"signed_v1","signed_at":"2026-05-18T04:29:24.309448Z","signed_message":"canonical_sha256_bytes"},"source_id":"0812.4104","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:49be97249f6dd723019077145628f022823d1fd68cffa7c4a3d2fef4a26cb465","sha256:01ddecbbc50f2898f4e6db2e135ef8b0aba34c1bd82e09fb1325be18feae9fe2"],"state_sha256":"0c714625cd3134a9559c56778ab188c37e3acde6b84da2c9d3c81885994ab120"}