{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2008:2QJO47GVITNWVFFSCFC6STBZJF","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":"577659297cc179b77870af48a85bb86763bcf2686d9bc70c22a24269d2de317e","cross_cats_sorted":["cs.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2008-05-14T16:33:42Z","title_canon_sha256":"32f161fd9833d784ab5f1c3b50f67a54d3070bf9cc2d5671006b03a95ff58e60"},"schema_version":"1.0","source":{"id":"0805.2111","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0805.2111","created_at":"2026-06-03T22:06:06Z"},{"alias_kind":"arxiv_version","alias_value":"0805.2111v1","created_at":"2026-06-03T22:06:06Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0805.2111","created_at":"2026-06-03T22:06:06Z"},{"alias_kind":"pith_short_12","alias_value":"2QJO47GVITNW","created_at":"2026-06-03T22:06:06Z"},{"alias_kind":"pith_short_16","alias_value":"2QJO47GVITNWVFFS","created_at":"2026-06-03T22:06:06Z"},{"alias_kind":"pith_short_8","alias_value":"2QJO47GV","created_at":"2026-06-03T22:06:06Z"}],"graph_snapshots":[{"event_id":"sha256:479699944131a661f12920631eed03225f44306e9e0c4788751b2a13987ddd65","target":"graph","created_at":"2026-06-03T22:06:06Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/0805.2111/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"By using the three-term recurrence equation satisfied by a family of orthogonal polynomials, the Christoffel-Darboux-type bilinear generating function and their asymptotic expressions, we obtain quadrature formulas for integral transforms generated by the classical orthogonal polynomials. These integral transforms, related to the so-called Poisson integrals, correspond to a modified Fourier Transform in the case of the Hermite polynomials, a Bessel Transform in the case of the Laguerre polynomials and to an Appell Transform in the case of the Jacobi polynomials.","authors_text":"E. Coronado, Francisco Dominguez Mota, Rafael G. Campos","cross_cats":["cs.NA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2008-05-14T16:33:42Z","title":"Quadrature formulas for integrals transforms generated by orthogonal polynomials"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0805.2111","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:ddfe5adec495db605ab03e82023fd0dc12bf572a9a761c3092653964b3c077cf","target":"record","created_at":"2026-06-03T22:06:06Z","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":"577659297cc179b77870af48a85bb86763bcf2686d9bc70c22a24269d2de317e","cross_cats_sorted":["cs.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2008-05-14T16:33:42Z","title_canon_sha256":"32f161fd9833d784ab5f1c3b50f67a54d3070bf9cc2d5671006b03a95ff58e60"},"schema_version":"1.0","source":{"id":"0805.2111","kind":"arxiv","version":1}},"canonical_sha256":"d412ee7cd544db6a94b21145e94c39496703f3d811aa31efd05dff72c8c32a26","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d412ee7cd544db6a94b21145e94c39496703f3d811aa31efd05dff72c8c32a26","first_computed_at":"2026-06-03T22:06:06.138305Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-03T22:06:06.138305Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"52qerHLikQD4rh8hicQay7p0DpnBBlMG7jvE9nybWDq+e6n71gZH2verfDg50IAmBkuzFTBTIpfIEdFwVDaqDw==","signature_status":"signed_v1","signed_at":"2026-06-03T22:06:06.138829Z","signed_message":"canonical_sha256_bytes"},"source_id":"0805.2111","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ddfe5adec495db605ab03e82023fd0dc12bf572a9a761c3092653964b3c077cf","sha256:479699944131a661f12920631eed03225f44306e9e0c4788751b2a13987ddd65"],"state_sha256":"6a18455e6309df8346ff1282aa6618c89bbd235e6073a415aecf77c5aee3abd8"}