{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:F7TZDDM3E6HITEKNUO266NP4UZ","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":"ec79b10e11d7fe3ea1bae5edbcd2330c2501d2696b7589829c4e249ebdf9c9f3","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2013-10-01T07:22:04Z","title_canon_sha256":"d69f5b9efc1b16ce9645761d0e8b50b613b69916413c191d7f3c691999a183c3"},"schema_version":"1.0","source":{"id":"1310.0166","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1310.0166","created_at":"2026-05-18T01:36:21Z"},{"alias_kind":"arxiv_version","alias_value":"1310.0166v2","created_at":"2026-05-18T01:36:21Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1310.0166","created_at":"2026-05-18T01:36:21Z"},{"alias_kind":"pith_short_12","alias_value":"F7TZDDM3E6HI","created_at":"2026-05-18T12:27:45Z"},{"alias_kind":"pith_short_16","alias_value":"F7TZDDM3E6HITEKN","created_at":"2026-05-18T12:27:45Z"},{"alias_kind":"pith_short_8","alias_value":"F7TZDDM3","created_at":"2026-05-18T12:27:45Z"}],"graph_snapshots":[{"event_id":"sha256:8eb71b84fa4d446e72af7f43b67e7cab590c568914f2942008d94650913a36d3","target":"graph","created_at":"2026-05-18T01:36:21Z","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":"In (Boyd, Proc. R. Soc. Lond. A 447 (1994) 609--630), W. G. C. Boyd derived a resurgence representation for the gamma function, exploiting the reformulation of the method of steepest descents by M. Berry and C. Howls (Berry and Howls, Proc. R. Soc. Lond. A 434 (1991) 657--675). Using this representation, he was able to derive a number of properties of the asymptotic expansion for the gamma function, including explicit and realistic error bounds, the smooth transition of the Stokes discontinuities, and asymptotics for the late coefficients. The main aim of this paper is to modify the resurgence","authors_text":"Gerg\\H{o} Nemes","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2013-10-01T07:22:04Z","title":"Error bounds and exponential improvements for the asymptotic expansions of the gamma function and its reciprocal"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1310.0166","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":"sha256:7b230c7d98f96978a764ffad5957a02d7e0151425e6e9c2ff01c1cf8f6a418ad","target":"record","created_at":"2026-05-18T01:36:21Z","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":"ec79b10e11d7fe3ea1bae5edbcd2330c2501d2696b7589829c4e249ebdf9c9f3","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2013-10-01T07:22:04Z","title_canon_sha256":"d69f5b9efc1b16ce9645761d0e8b50b613b69916413c191d7f3c691999a183c3"},"schema_version":"1.0","source":{"id":"1310.0166","kind":"arxiv","version":2}},"canonical_sha256":"2fe7918d9b278e89914da3b5ef35fca646ec0f3c2e887b219c3450d9c1dd248c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"2fe7918d9b278e89914da3b5ef35fca646ec0f3c2e887b219c3450d9c1dd248c","first_computed_at":"2026-05-18T01:36:21.001097Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:36:21.001097Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"q6INQpC1hleF6Gl9jYwV7IK5VS3DBRCgQhGdSNbxiNt3wwBW4RebELWT33uADE2NEv9RA0L+XzE1m6j5SVrMCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:36:21.001667Z","signed_message":"canonical_sha256_bytes"},"source_id":"1310.0166","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:7b230c7d98f96978a764ffad5957a02d7e0151425e6e9c2ff01c1cf8f6a418ad","sha256:8eb71b84fa4d446e72af7f43b67e7cab590c568914f2942008d94650913a36d3"],"state_sha256":"87c336668740acd526ec02951821e2fc0f5a58eff3730c85f673340180c268b8"}