{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:V5EKSZQ6ZTA3LSMUTAQ6564PIW","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":"081033024a0a8b40b759cc561a579f1b3c566cd02862d3ad2fdc64b2e8492523","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2017-10-27T10:56:33Z","title_canon_sha256":"58d8599bd71121ce91fc8aac63a7c638e2ad16bb423fb4d109656f15a515b745"},"schema_version":"1.0","source":{"id":"1710.10073","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1710.10073","created_at":"2026-05-18T00:18:09Z"},{"alias_kind":"arxiv_version","alias_value":"1710.10073v2","created_at":"2026-05-18T00:18:09Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1710.10073","created_at":"2026-05-18T00:18:09Z"},{"alias_kind":"pith_short_12","alias_value":"V5EKSZQ6ZTA3","created_at":"2026-05-18T12:31:49Z"},{"alias_kind":"pith_short_16","alias_value":"V5EKSZQ6ZTA3LSMU","created_at":"2026-05-18T12:31:49Z"},{"alias_kind":"pith_short_8","alias_value":"V5EKSZQ6","created_at":"2026-05-18T12:31:49Z"}],"graph_snapshots":[{"event_id":"sha256:8071da9cabff1a3400133c49c05e72d3056424297726a8a7d5a3b1f06a33ab29","target":"graph","created_at":"2026-05-18T00:18:09Z","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 derive the first exact, rigorous but practical, globally valid remainder terms for asymptotic expansions about saddles and contour endpoints of arbitrary order degeneracy derived from the method of steepest descents. The exact remainder terms lead naturally to sharper novel asymptotic bounds for truncated expansions that are a significant improvement over the previous best existing bounds for quadratic saddles derived two decades ago. We also develop a comprehensive hyperasymptotic theory, whereby the remainder terms are iteratively re-expanded about adjacent saddle points to achieve better","authors_text":"Adri B. Olde Daalhuis, Christopher J. Howls, Gerg\\H{o} Nemes, Thomas Bennett","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2017-10-27T10:56:33Z","title":"Globally exact asymptotics for integrals with arbitrary order saddles"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1710.10073","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:f41f0920531b0b54d585a60b8de8472ab791b9bf76bd547044bf0847aa20b959","target":"record","created_at":"2026-05-18T00:18:09Z","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":"081033024a0a8b40b759cc561a579f1b3c566cd02862d3ad2fdc64b2e8492523","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2017-10-27T10:56:33Z","title_canon_sha256":"58d8599bd71121ce91fc8aac63a7c638e2ad16bb423fb4d109656f15a515b745"},"schema_version":"1.0","source":{"id":"1710.10073","kind":"arxiv","version":2}},"canonical_sha256":"af48a9661eccc1b5c9949821eefb8f45b58e473b5050976b0513fdb4ca2db882","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"af48a9661eccc1b5c9949821eefb8f45b58e473b5050976b0513fdb4ca2db882","first_computed_at":"2026-05-18T00:18:09.399374Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:18:09.399374Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"RLe2UoISVV4ZLSdn+MOri4hIp0uoPuXpaUxgmrwBUiPZqzWFg9aXpHqCWYN8SQT5LHlnMcJJ3g+IdCzc4X8RBg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:18:09.399942Z","signed_message":"canonical_sha256_bytes"},"source_id":"1710.10073","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f41f0920531b0b54d585a60b8de8472ab791b9bf76bd547044bf0847aa20b959","sha256:8071da9cabff1a3400133c49c05e72d3056424297726a8a7d5a3b1f06a33ab29"],"state_sha256":"2719f6e39436e92efd7e1b6390409d6b5d9c6afeb769b5a2a68883172690ee1d"}