{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2014:QGLN3MMXFIACME3JFSJUVKCYQD","short_pith_number":"pith:QGLN3MMX","schema_version":"1.0","canonical_sha256":"8196ddb1972a002613692c934aa85880d150a925311fdb4385318cbbe26b7d68","source":{"kind":"arxiv","id":"1403.7182","version":2},"attestation_state":"computed","paper":{"title":"Exponential asymptotics and problems with coalescing singularities","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Philippe H. Trinh, S. Jonathan Chapman","submitted_at":"2014-03-27T19:28:12Z","abstract_excerpt":"Problems in exponential asymptotics are typically characterized by divergence of the associated asymptotic expansion in the form of a factorial divided by a power. In this paper, we demonstrate that in certain classes of problems that involve coalescing singularities, a more general type of exponential-over-power divergence must be used. As a model example, we study the water waves produced by flow past an obstruction such as a surface-piercing ship. In the low speed or low Froude limit, the resultant water waves are exponentially small, and their formation is attributed to the singularities i"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1403.7182","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2014-03-27T19:28:12Z","cross_cats_sorted":[],"title_canon_sha256":"19ff8787f431a9f4ea255d8e16c4ea335131e03a133ae2400884f63473ec6d32","abstract_canon_sha256":"13b3e960acb5e9f503666284b794d81fdde2226824da941d8777fd8e6e4713a9"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:43:49.958784Z","signature_b64":"cTC0Lpj8/VRkREQfsIIQzkK0Dlj9+xX42bXvSCw7Zu+SFB0jUXTZjmgENJFuuVNyh6uWHAp057ihiPyAtVw8AQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"8196ddb1972a002613692c934aa85880d150a925311fdb4385318cbbe26b7d68","last_reissued_at":"2026-05-18T01:43:49.958073Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:43:49.958073Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Exponential asymptotics and problems with coalescing singularities","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Philippe H. Trinh, S. Jonathan Chapman","submitted_at":"2014-03-27T19:28:12Z","abstract_excerpt":"Problems in exponential asymptotics are typically characterized by divergence of the associated asymptotic expansion in the form of a factorial divided by a power. In this paper, we demonstrate that in certain classes of problems that involve coalescing singularities, a more general type of exponential-over-power divergence must be used. As a model example, we study the water waves produced by flow past an obstruction such as a surface-piercing ship. In the low speed or low Froude limit, the resultant water waves are exponentially small, and their formation is attributed to the singularities i"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1403.7182","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"aliases":[{"alias_kind":"arxiv","alias_value":"1403.7182","created_at":"2026-05-18T01:43:49.958183+00:00"},{"alias_kind":"arxiv_version","alias_value":"1403.7182v2","created_at":"2026-05-18T01:43:49.958183+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1403.7182","created_at":"2026-05-18T01:43:49.958183+00:00"},{"alias_kind":"pith_short_12","alias_value":"QGLN3MMXFIAC","created_at":"2026-05-18T12:28:46.137349+00:00"},{"alias_kind":"pith_short_16","alias_value":"QGLN3MMXFIACME3J","created_at":"2026-05-18T12:28:46.137349+00:00"},{"alias_kind":"pith_short_8","alias_value":"QGLN3MMX","created_at":"2026-05-18T12:28:46.137349+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/QGLN3MMXFIACME3JFSJUVKCYQD","json":"https://pith.science/pith/QGLN3MMXFIACME3JFSJUVKCYQD.json","graph_json":"https://pith.science/api/pith-number/QGLN3MMXFIACME3JFSJUVKCYQD/graph.json","events_json":"https://pith.science/api/pith-number/QGLN3MMXFIACME3JFSJUVKCYQD/events.json","paper":"https://pith.science/paper/QGLN3MMX"},"agent_actions":{"view_html":"https://pith.science/pith/QGLN3MMXFIACME3JFSJUVKCYQD","download_json":"https://pith.science/pith/QGLN3MMXFIACME3JFSJUVKCYQD.json","view_paper":"https://pith.science/paper/QGLN3MMX","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1403.7182&json=true","fetch_graph":"https://pith.science/api/pith-number/QGLN3MMXFIACME3JFSJUVKCYQD/graph.json","fetch_events":"https://pith.science/api/pith-number/QGLN3MMXFIACME3JFSJUVKCYQD/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/QGLN3MMXFIACME3JFSJUVKCYQD/action/timestamp_anchor","attest_storage":"https://pith.science/pith/QGLN3MMXFIACME3JFSJUVKCYQD/action/storage_attestation","attest_author":"https://pith.science/pith/QGLN3MMXFIACME3JFSJUVKCYQD/action/author_attestation","sign_citation":"https://pith.science/pith/QGLN3MMXFIACME3JFSJUVKCYQD/action/citation_signature","submit_replication":"https://pith.science/pith/QGLN3MMXFIACME3JFSJUVKCYQD/action/replication_record"}},"created_at":"2026-05-18T01:43:49.958183+00:00","updated_at":"2026-05-18T01:43:49.958183+00:00"}