{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2012:JWHRH5Y7GDXTG7UKUJJHQYYJO5","short_pith_number":"pith:JWHRH5Y7","schema_version":"1.0","canonical_sha256":"4d8f13f71f30ef337e8aa252786309777dd9e769503b5da54d0ae5ff1c273737","source":{"kind":"arxiv","id":"1207.6861","version":3},"attestation_state":"computed","paper":{"title":"Absence of Zeros and Asymptotic Error Estimates for Airy and Parabolic Cylinder Functions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.CA","authors_text":"Felix Finster, Joel Smoller","submitted_at":"2012-07-30T08:10:47Z","abstract_excerpt":"We derive WKB approximations for a class of Airy and parabolic cylinder functions in the complex plane, including quantitative error bounds. We prove that all zeros of the Airy function lie on a ray in the complex plane, and that the parabolic cylinder functions have no zeros. We also analyze the Airy and Airy-WKB limit of the parabolic cylinder functions."},"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":"1207.6861","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2012-07-30T08:10:47Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"f7465e6b4cdd450337da61df9a2d4d12fd19c25f5d52c6a50f334e3204cea147","abstract_canon_sha256":"b4ffc7a2bc361b4fd5b07c6bff71037d4f9f09fb5ba57a10ce183c37118a0411"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:13:56.276404Z","signature_b64":"T6tDPspisUmg8FSHSPaICAr078q4MswGuYJFQwBge5yUviSncxTMb8nqjUr3sJiicYVQ+A0zeBIhDALNtGGJAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4d8f13f71f30ef337e8aa252786309777dd9e769503b5da54d0ae5ff1c273737","last_reissued_at":"2026-05-18T03:13:56.275825Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:13:56.275825Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Absence of Zeros and Asymptotic Error Estimates for Airy and Parabolic Cylinder Functions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.CA","authors_text":"Felix Finster, Joel Smoller","submitted_at":"2012-07-30T08:10:47Z","abstract_excerpt":"We derive WKB approximations for a class of Airy and parabolic cylinder functions in the complex plane, including quantitative error bounds. We prove that all zeros of the Airy function lie on a ray in the complex plane, and that the parabolic cylinder functions have no zeros. We also analyze the Airy and Airy-WKB limit of the parabolic cylinder functions."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1207.6861","kind":"arxiv","version":3},"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":"1207.6861","created_at":"2026-05-18T03:13:56.275909+00:00"},{"alias_kind":"arxiv_version","alias_value":"1207.6861v3","created_at":"2026-05-18T03:13:56.275909+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1207.6861","created_at":"2026-05-18T03:13:56.275909+00:00"},{"alias_kind":"pith_short_12","alias_value":"JWHRH5Y7GDXT","created_at":"2026-05-18T12:27:11.947152+00:00"},{"alias_kind":"pith_short_16","alias_value":"JWHRH5Y7GDXTG7UK","created_at":"2026-05-18T12:27:11.947152+00:00"},{"alias_kind":"pith_short_8","alias_value":"JWHRH5Y7","created_at":"2026-05-18T12:27:11.947152+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/JWHRH5Y7GDXTG7UKUJJHQYYJO5","json":"https://pith.science/pith/JWHRH5Y7GDXTG7UKUJJHQYYJO5.json","graph_json":"https://pith.science/api/pith-number/JWHRH5Y7GDXTG7UKUJJHQYYJO5/graph.json","events_json":"https://pith.science/api/pith-number/JWHRH5Y7GDXTG7UKUJJHQYYJO5/events.json","paper":"https://pith.science/paper/JWHRH5Y7"},"agent_actions":{"view_html":"https://pith.science/pith/JWHRH5Y7GDXTG7UKUJJHQYYJO5","download_json":"https://pith.science/pith/JWHRH5Y7GDXTG7UKUJJHQYYJO5.json","view_paper":"https://pith.science/paper/JWHRH5Y7","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1207.6861&json=true","fetch_graph":"https://pith.science/api/pith-number/JWHRH5Y7GDXTG7UKUJJHQYYJO5/graph.json","fetch_events":"https://pith.science/api/pith-number/JWHRH5Y7GDXTG7UKUJJHQYYJO5/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/JWHRH5Y7GDXTG7UKUJJHQYYJO5/action/timestamp_anchor","attest_storage":"https://pith.science/pith/JWHRH5Y7GDXTG7UKUJJHQYYJO5/action/storage_attestation","attest_author":"https://pith.science/pith/JWHRH5Y7GDXTG7UKUJJHQYYJO5/action/author_attestation","sign_citation":"https://pith.science/pith/JWHRH5Y7GDXTG7UKUJJHQYYJO5/action/citation_signature","submit_replication":"https://pith.science/pith/JWHRH5Y7GDXTG7UKUJJHQYYJO5/action/replication_record"}},"created_at":"2026-05-18T03:13:56.275909+00:00","updated_at":"2026-05-18T03:13:56.275909+00:00"}