{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:CPFWZJYTAQRH5VB66WUKPDQ7YT","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":"ddaf8413d8f45f7cc7d1b87fdf7efb8272dc07a1049cbb5a94d136c2fc0a70c1","cross_cats_sorted":["math.CA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.MS","submitted_at":"2016-08-14T23:17:03Z","title_canon_sha256":"a22ea062a5838e835659357424808f06282c7396f3918eff73957a6a932e82c3"},"schema_version":"1.0","source":{"id":"1608.04152","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1608.04152","created_at":"2026-05-18T01:09:04Z"},{"alias_kind":"arxiv_version","alias_value":"1608.04152v1","created_at":"2026-05-18T01:09:04Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1608.04152","created_at":"2026-05-18T01:09:04Z"},{"alias_kind":"pith_short_12","alias_value":"CPFWZJYTAQRH","created_at":"2026-05-18T12:30:09Z"},{"alias_kind":"pith_short_16","alias_value":"CPFWZJYTAQRH5VB6","created_at":"2026-05-18T12:30:09Z"},{"alias_kind":"pith_short_8","alias_value":"CPFWZJYT","created_at":"2026-05-18T12:30:09Z"}],"graph_snapshots":[{"event_id":"sha256:1f8d00b4a70eeb18eeeecd6f276ebba4209df4fee5c9c0a13e107d76c19222a2","target":"graph","created_at":"2026-05-18T01:09:04Z","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":"An algorithm for computing the incomplete gamma function $\\gamma^*(a,z)$ for real values of the parameter $a$ and negative real values of the argument $z$ is presented. The algorithm combines the use of series expansions, Poincar\\'e-type expansions, uniform asymptotic expansions and recurrence relations, depending on the parameter region. A relative accuracy $\\sim 10^{-13}$ in the parameter region $(a,z) \\in [-500,\\,500] \\times [-500,\\,0)$ can be obtained when computing the function $\\gamma^*(a,z)$ with the Fortran 90 module IncgamNEG implementing the algorithm.","authors_text":"A. Gil, D. Ruiz-Antol\\'in, J. Segura, N. M. Temme","cross_cats":["math.CA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.MS","submitted_at":"2016-08-14T23:17:03Z","title":"Computation of the incomplete gamma function for negative values of the argument"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1608.04152","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:a183f1f07c3845a37e6ced66de264eeea6700b3514e7b7d9e4c2870fd7eb65d9","target":"record","created_at":"2026-05-18T01:09:04Z","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":"ddaf8413d8f45f7cc7d1b87fdf7efb8272dc07a1049cbb5a94d136c2fc0a70c1","cross_cats_sorted":["math.CA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.MS","submitted_at":"2016-08-14T23:17:03Z","title_canon_sha256":"a22ea062a5838e835659357424808f06282c7396f3918eff73957a6a932e82c3"},"schema_version":"1.0","source":{"id":"1608.04152","kind":"arxiv","version":1}},"canonical_sha256":"13cb6ca71304227ed43ef5a8a78e1fc4fb98cace2d1b01f97475f8671a6796e5","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"13cb6ca71304227ed43ef5a8a78e1fc4fb98cace2d1b01f97475f8671a6796e5","first_computed_at":"2026-05-18T01:09:04.170045Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:09:04.170045Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Mc+E4nvV0P+XEe6x1grAS2GP4qTLqvsudQ7DQMVRXm02qGisqhbwrtnLA3ATArhDpm2n/vbeAkx4dGvfAQzUBA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:09:04.170429Z","signed_message":"canonical_sha256_bytes"},"source_id":"1608.04152","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a183f1f07c3845a37e6ced66de264eeea6700b3514e7b7d9e4c2870fd7eb65d9","sha256:1f8d00b4a70eeb18eeeecd6f276ebba4209df4fee5c9c0a13e107d76c19222a2"],"state_sha256":"99f7003aa2371a163e7f77bac41a575e3a2da71ae9b12928a7547b17757a8732"}