{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:1994:A2BLAYXBH33METPJLYEGQEDIHP","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":"17c7d573ec2cd724312db0e76469120ac78d169b1477d9ac5ba43f5bbd6b5135","cross_cats_sorted":[],"license":"","primary_cat":"math.CA","submitted_at":"1994-04-22T00:00:00Z","title_canon_sha256":"09f948dcb0988bd885b4796270ebe0ab205568c1acd1fc1e600e5c522462417d"},"schema_version":"1.0","source":{"id":"math/9404224","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/9404224","created_at":"2026-05-18T01:38:23Z"},{"alias_kind":"arxiv_version","alias_value":"math/9404224v1","created_at":"2026-05-18T01:38:23Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/9404224","created_at":"2026-05-18T01:38:23Z"},{"alias_kind":"pith_short_12","alias_value":"A2BLAYXBH33M","created_at":"2026-05-18T12:25:47Z"},{"alias_kind":"pith_short_16","alias_value":"A2BLAYXBH33METPJ","created_at":"2026-05-18T12:25:47Z"},{"alias_kind":"pith_short_8","alias_value":"A2BLAYXB","created_at":"2026-05-18T12:25:47Z"}],"graph_snapshots":[{"event_id":"sha256:b98e6ce92bb6163ea9e8e16b3c38b77fa69fd0a1c006932c7e952e2edf221da1","target":"graph","created_at":"2026-05-18T01:38:23Z","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":"Given a parametrised weight function $\\omega(x,\\mu)$ such that the quotients of its consecutive moments are M\\\"obius maps, it is possible to express the underlying biorthogonal polynomials in a closed form \\cite{IN2}. In the present paper we address ourselves to two related issues. Firstly, we demonstrate that, subject to additional assumptions, every such $\\omega$ obeys (in $x$) a linear differential equation whose solution is a generalized hypergeometric function. Secondly, using a generalization of standard divided differences, we present a new explicit representation of the underlying orth","authors_text":"Arieh Iserles, Syvert Paul N{\\o}rsett","cross_cats":[],"headline":"","license":"","primary_cat":"math.CA","submitted_at":"1994-04-22T00:00:00Z","title":"Explicit representations of biorthogonal polynomials"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/9404224","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":"sha256:09c5f25c17a2f6267cc377d749e147bfde50e4f7bf5b2f64caa0acf092947290","target":"record","created_at":"2026-05-18T01:38:23Z","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":"17c7d573ec2cd724312db0e76469120ac78d169b1477d9ac5ba43f5bbd6b5135","cross_cats_sorted":[],"license":"","primary_cat":"math.CA","submitted_at":"1994-04-22T00:00:00Z","title_canon_sha256":"09f948dcb0988bd885b4796270ebe0ab205568c1acd1fc1e600e5c522462417d"},"schema_version":"1.0","source":{"id":"math/9404224","kind":"arxiv","version":1}},"canonical_sha256":"0682b062e13ef6c24de95e086810683bf3a00ff63022b2087a4defbfbe4d08d1","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"0682b062e13ef6c24de95e086810683bf3a00ff63022b2087a4defbfbe4d08d1","first_computed_at":"2026-05-18T01:38:23.071630Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:38:23.071630Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"oxP15aWu+z+hsxqUfaqVzjN9IJfBRvcjHgYxBJ18bzQK3KwVdLN6sEOkdv7Ro2ZCow6ylBaOBzFYMmByXsWxBA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:38:23.072283Z","signed_message":"canonical_sha256_bytes"},"source_id":"math/9404224","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:09c5f25c17a2f6267cc377d749e147bfde50e4f7bf5b2f64caa0acf092947290","sha256:b98e6ce92bb6163ea9e8e16b3c38b77fa69fd0a1c006932c7e952e2edf221da1"],"state_sha256":"c8dde85bc70692e445d2b5b6024b16d44c8e3afddd28ed79b6deb83ece3beaaf"}