{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:4MZ5WXVZSA2QVAKZ46F5SQ74PC","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":"88b8f0f1e52a329336980ef9276036aabab8332fd84e75d46f72240fd4681830","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2014-07-09T21:41:51Z","title_canon_sha256":"852965d5d0599d2fdfb54eabe1716d542956b6b1890f46aa2d9337b540e0be02"},"schema_version":"1.0","source":{"id":"1407.2644","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1407.2644","created_at":"2026-05-18T02:47:54Z"},{"alias_kind":"arxiv_version","alias_value":"1407.2644v1","created_at":"2026-05-18T02:47:54Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1407.2644","created_at":"2026-05-18T02:47:54Z"},{"alias_kind":"pith_short_12","alias_value":"4MZ5WXVZSA2Q","created_at":"2026-05-18T12:28:14Z"},{"alias_kind":"pith_short_16","alias_value":"4MZ5WXVZSA2QVAKZ","created_at":"2026-05-18T12:28:14Z"},{"alias_kind":"pith_short_8","alias_value":"4MZ5WXVZ","created_at":"2026-05-18T12:28:14Z"}],"graph_snapshots":[{"event_id":"sha256:80f6fd06d54860adf958d17e2e341cf36762e1e20458ce9dbbed1458e66f2c67","target":"graph","created_at":"2026-05-18T02:47:54Z","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":"In this paper we obtain $L^1$-weighted norms of classical orthogonal polynomials (Hermite, Laguerre and Jacobi polynomials) in terms of the zeros of these orthogonal polynomials; these expressions are usually known as quadrature rules. In particular these new formulae are useful to calculate directly some positive defined integrals as several examples show.","authors_text":"Luciano Abadias, Natalia Romero, Pedro J. Miana","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2014-07-09T21:41:51Z","title":"Quadrature rules for $L^1$-weighted norms of orthogonal polynomials"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1407.2644","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":"sha256:58208d3a0190794dccc61e0b2ee52732a95ec71174b2f73084e4762d0ecb0192","target":"record","created_at":"2026-05-18T02:47:54Z","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":"88b8f0f1e52a329336980ef9276036aabab8332fd84e75d46f72240fd4681830","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2014-07-09T21:41:51Z","title_canon_sha256":"852965d5d0599d2fdfb54eabe1716d542956b6b1890f46aa2d9337b540e0be02"},"schema_version":"1.0","source":{"id":"1407.2644","kind":"arxiv","version":1}},"canonical_sha256":"e333db5eb990350a8159e78bd943fc78b0630bfe7056d2d021e2e5d55a1560a2","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e333db5eb990350a8159e78bd943fc78b0630bfe7056d2d021e2e5d55a1560a2","first_computed_at":"2026-05-18T02:47:54.028573Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:47:54.028573Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"a/woIc2FYLUP1ag30or57LMgwQKCUDP4hAp/K3AUPySTRFVsLZ/vdG/6naawmQDjAJcw0OZPWlf5byOiLiqkBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T02:47:54.029002Z","signed_message":"canonical_sha256_bytes"},"source_id":"1407.2644","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:58208d3a0190794dccc61e0b2ee52732a95ec71174b2f73084e4762d0ecb0192","sha256:80f6fd06d54860adf958d17e2e341cf36762e1e20458ce9dbbed1458e66f2c67"],"state_sha256":"c41bdbcdfeda87e9fba8f5af040e61e9f88fd1a440f01b484523f79872234867"}