{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:ZDXHK5NYQLZSV2NZ5PWDGDM3JY","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":"fb8433992f648d98dbc2f9cbc60faa52305c67704dfac68c4988048050926671","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2017-12-22T09:52:48Z","title_canon_sha256":"1dd661a06445f851b890b91b1969f0421cbb72a40bcba35b63a967514a8c3bca"},"schema_version":"1.0","source":{"id":"1712.08371","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1712.08371","created_at":"2026-05-18T00:27:23Z"},{"alias_kind":"arxiv_version","alias_value":"1712.08371v1","created_at":"2026-05-18T00:27:23Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1712.08371","created_at":"2026-05-18T00:27:23Z"},{"alias_kind":"pith_short_12","alias_value":"ZDXHK5NYQLZS","created_at":"2026-05-18T12:31:59Z"},{"alias_kind":"pith_short_16","alias_value":"ZDXHK5NYQLZSV2NZ","created_at":"2026-05-18T12:31:59Z"},{"alias_kind":"pith_short_8","alias_value":"ZDXHK5NY","created_at":"2026-05-18T12:31:59Z"}],"graph_snapshots":[{"event_id":"sha256:5435fa093c31c648ea6f453c51622ff05727b0ae5167d4f233803ed59ed10e0c","target":"graph","created_at":"2026-05-18T00:27:23Z","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":"The asymptotic expansion of the Kummer function ${}_1F_1(a; b; z)$ is examined as $z\\to+\\infty$ on the Stokes line $\\arg\\,z=0$. The correct form of the subdominant algebraic contribution is obtained for non-integer $a$. Numerical results demonstrating the accuracy of the expansion are given.","authors_text":"R B Paris","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2017-12-22T09:52:48Z","title":"The expansion of the confluent hypergeometric function on the positive real axis"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1712.08371","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:d9fa964b9d5ec2ef55ffc4ccd9f05946b2f97e64e20e1548e137dceb91cc4a28","target":"record","created_at":"2026-05-18T00:27:23Z","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":"fb8433992f648d98dbc2f9cbc60faa52305c67704dfac68c4988048050926671","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2017-12-22T09:52:48Z","title_canon_sha256":"1dd661a06445f851b890b91b1969f0421cbb72a40bcba35b63a967514a8c3bca"},"schema_version":"1.0","source":{"id":"1712.08371","kind":"arxiv","version":1}},"canonical_sha256":"c8ee7575b882f32ae9b9ebec330d9b4e118b1cdbe3ae152587c2f753db7456ed","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c8ee7575b882f32ae9b9ebec330d9b4e118b1cdbe3ae152587c2f753db7456ed","first_computed_at":"2026-05-18T00:27:23.632832Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:27:23.632832Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"eKQUwpYbdAAYCOUyuhX4vzVgxQrnrHfZ/YDNz0EC+ZFNQAHBZqtfgiZWz1COf1cmJseeZqHsGKj9QPtrL4zeBA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:27:23.633304Z","signed_message":"canonical_sha256_bytes"},"source_id":"1712.08371","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d9fa964b9d5ec2ef55ffc4ccd9f05946b2f97e64e20e1548e137dceb91cc4a28","sha256:5435fa093c31c648ea6f453c51622ff05727b0ae5167d4f233803ed59ed10e0c"],"state_sha256":"270f9bf219477e1432cb603aee919afd655e984fa8fbda142c50cf63a8b31fb4"}