{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:IEMD3SENJOUZFWR7TWL76JZQRW","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":"239613feec96cc84df8379a69ea4875323da051286bdcc1af93216a1f49adc62","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2015-12-28T09:37:52Z","title_canon_sha256":"64d416bafa78695230885b7bb03bc01468f31c168a22d3f09f0940027a08c4e8"},"schema_version":"1.0","source":{"id":"1512.08357","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1512.08357","created_at":"2026-05-18T01:09:55Z"},{"alias_kind":"arxiv_version","alias_value":"1512.08357v2","created_at":"2026-05-18T01:09:55Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1512.08357","created_at":"2026-05-18T01:09:55Z"},{"alias_kind":"pith_short_12","alias_value":"IEMD3SENJOUZ","created_at":"2026-05-18T12:29:25Z"},{"alias_kind":"pith_short_16","alias_value":"IEMD3SENJOUZFWR7","created_at":"2026-05-18T12:29:25Z"},{"alias_kind":"pith_short_8","alias_value":"IEMD3SEN","created_at":"2026-05-18T12:29:25Z"}],"graph_snapshots":[{"event_id":"sha256:3198acae0a57338972d99f25872a74f59025d122d8abd55090505df8f0503156","target":"graph","created_at":"2026-05-18T01:09:55Z","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 describe a method for calculating the roots of special functions satisfying second order linear ordinary differential equations. It exploits the recent observation that the solutions of a large class of such equations can be represented via nonoscillatory phase functions, even in the high-frequency regime. Our algorithm achieves near machine precision accuracy and the time required to compute one root of a solution is independent of the frequency of oscillations of that solution. Moreover, despite its great generality, our approach is competitive with specialized, state-of-the-art methods f","authors_text":"James Bremer","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2015-12-28T09:37:52Z","title":"On the numerical calculation of the roots of special functions satisfying second order ordinary differential equations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1512.08357","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":"sha256:1732d85cf3c09c401c1453de1980560073aed97533bd10f013540b6f9930a86b","target":"record","created_at":"2026-05-18T01:09:55Z","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":"239613feec96cc84df8379a69ea4875323da051286bdcc1af93216a1f49adc62","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2015-12-28T09:37:52Z","title_canon_sha256":"64d416bafa78695230885b7bb03bc01468f31c168a22d3f09f0940027a08c4e8"},"schema_version":"1.0","source":{"id":"1512.08357","kind":"arxiv","version":2}},"canonical_sha256":"41183dc88d4ba992da3f9d97ff27308db0dec2f1d3f9051c2b46c5314d78e249","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"41183dc88d4ba992da3f9d97ff27308db0dec2f1d3f9051c2b46c5314d78e249","first_computed_at":"2026-05-18T01:09:55.070928Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:09:55.070928Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"GSuAs03JXnoS1QUeA5Sn45gG9huMvkFVFZsLF2pABOLdSpjPbhax6jwVGVbbfGKDX98Rk7GfpbckAZxsJUvxAA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:09:55.071676Z","signed_message":"canonical_sha256_bytes"},"source_id":"1512.08357","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1732d85cf3c09c401c1453de1980560073aed97533bd10f013540b6f9930a86b","sha256:3198acae0a57338972d99f25872a74f59025d122d8abd55090505df8f0503156"],"state_sha256":"02d93b7e466f37dc4e91ab8333b63505aeb6f6da4d55df3af81c072459bf1f1a"}