{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:PI2QAKMYUFOCGA5Z236JXAJNYG","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":"d185aaf382f771ac949e70426ff403d00dd4e586602f3a7664d3b4372b7dcbb8","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2014-10-20T14:12:31Z","title_canon_sha256":"cec0b0711582619e9672633fccbf96f5b2d550caf89b7185c6a12747806c568f"},"schema_version":"1.0","source":{"id":"1410.5286","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1410.5286","created_at":"2026-05-18T02:39:46Z"},{"alias_kind":"arxiv_version","alias_value":"1410.5286v1","created_at":"2026-05-18T02:39:46Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1410.5286","created_at":"2026-05-18T02:39:46Z"},{"alias_kind":"pith_short_12","alias_value":"PI2QAKMYUFOC","created_at":"2026-05-18T12:28:43Z"},{"alias_kind":"pith_short_16","alias_value":"PI2QAKMYUFOCGA5Z","created_at":"2026-05-18T12:28:43Z"},{"alias_kind":"pith_short_8","alias_value":"PI2QAKMY","created_at":"2026-05-18T12:28:43Z"}],"graph_snapshots":[{"event_id":"sha256:2ea11cea16258d1cffb6b1a1ebac38ad8b51d8c9cd9e63d56d3e3ec92e0853ef","target":"graph","created_at":"2026-05-18T02:39:46Z","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":"A fast and accurate algorithm for the computation of Gauss-Hermite and generalized Gauss-Hermite quadrature nodes and weights is presented. The algorithm is based on Newton's method with carefully selected initial guesses for the nodes and a fast evaluation scheme for the associated orthogonal polynomial. In the Gauss-Hermite case the initial guesses and evaluation scheme rely on explicit asymptotic formulas. For generalized Gauss-Hermite, the initial guesses are furnished by sampling a certain equilibrium measure and the associated polynomial evaluated via a Riemann-Hilbert reformulation. In ","authors_text":"Alex Townsend, Sheehan Olver, Thomas Trogdon","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2014-10-20T14:12:31Z","title":"Fast computation of Gauss quadrature nodes and weights on the whole real line"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1410.5286","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":"sha256:8c8a9806194adc66c751202a0f0f964af8c3716392846f385360a1d5bf68497b","target":"record","created_at":"2026-05-18T02:39:46Z","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":"d185aaf382f771ac949e70426ff403d00dd4e586602f3a7664d3b4372b7dcbb8","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2014-10-20T14:12:31Z","title_canon_sha256":"cec0b0711582619e9672633fccbf96f5b2d550caf89b7185c6a12747806c568f"},"schema_version":"1.0","source":{"id":"1410.5286","kind":"arxiv","version":1}},"canonical_sha256":"7a35002998a15c2303b9d6fc9b812dc1be079dd997a5037f6be8df4855ecda30","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"7a35002998a15c2303b9d6fc9b812dc1be079dd997a5037f6be8df4855ecda30","first_computed_at":"2026-05-18T02:39:46.410769Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:39:46.410769Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"18p2UoCfcnwfL7s7eqvL/mPw2BVGh09xlyOsPlXwFTP2TKNiAFkEvrwSZ/82dp0ljyvvUMJp5UdGPof+Zs19Dw==","signature_status":"signed_v1","signed_at":"2026-05-18T02:39:46.411194Z","signed_message":"canonical_sha256_bytes"},"source_id":"1410.5286","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8c8a9806194adc66c751202a0f0f964af8c3716392846f385360a1d5bf68497b","sha256:2ea11cea16258d1cffb6b1a1ebac38ad8b51d8c9cd9e63d56d3e3ec92e0853ef"],"state_sha256":"f1c481df63070ebe0f7e7890f40b7783da65e9577a4cbfa8e61532a1daed9710"}