{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:XF4KQBITNYVT62DHOT3C3XE4NZ","short_pith_number":"pith:XF4KQBIT","schema_version":"1.0","canonical_sha256":"b978a805136e2b3f686774f62ddc9c6e5009c009e70035d4fcd06f319dac6f49","source":{"kind":"arxiv","id":"1511.05215","version":1},"attestation_state":"computed","paper":{"title":"The para-Racah polynomials","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Alexei Zhedanov, Jean-Michel Lemay, Luc Vinet","submitted_at":"2015-11-16T23:23:28Z","abstract_excerpt":"New bispectral polynomials orthogonal on a quadratic bi-lattice are obtained from a truncation of Wilson polynomials. Recurrence relation and difference equation are provided. The recurrence coefficients can be encoded in a perturbed persymmetric Jacobi matrix. The orthogonality relation and an explicit expression in terms of hypergeometric functions are also given. Special cases and connections with the para-Krawtchouk polynomials and the dual-Hahn polynomials are also discussed."},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1511.05215","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2015-11-16T23:23:28Z","cross_cats_sorted":[],"title_canon_sha256":"ab10704e3138651c59c40b0f1dacf944d9a863165623ab640dcec66176e27fe2","abstract_canon_sha256":"5b0155de87b0feb9d395aa07d8173796c7365cad92a35f2e47919797386deffc"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:26:49.755031Z","signature_b64":"7ZMK2UMDXR38qom0zp0vbewTzSyXCN2UsJ5dFbngDiAII6nXBbwFkGfgfvhN+4NyxLb2rJSDTPpoEIpGCg36DQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b978a805136e2b3f686774f62ddc9c6e5009c009e70035d4fcd06f319dac6f49","last_reissued_at":"2026-05-18T01:26:49.754286Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:26:49.754286Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The para-Racah polynomials","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Alexei Zhedanov, Jean-Michel Lemay, Luc Vinet","submitted_at":"2015-11-16T23:23:28Z","abstract_excerpt":"New bispectral polynomials orthogonal on a quadratic bi-lattice are obtained from a truncation of Wilson polynomials. Recurrence relation and difference equation are provided. The recurrence coefficients can be encoded in a perturbed persymmetric Jacobi matrix. The orthogonality relation and an explicit expression in terms of hypergeometric functions are also given. Special cases and connections with the para-Krawtchouk polynomials and the dual-Hahn polynomials are also discussed."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1511.05215","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"aliases":[{"alias_kind":"arxiv","alias_value":"1511.05215","created_at":"2026-05-18T01:26:49.754425+00:00"},{"alias_kind":"arxiv_version","alias_value":"1511.05215v1","created_at":"2026-05-18T01:26:49.754425+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1511.05215","created_at":"2026-05-18T01:26:49.754425+00:00"},{"alias_kind":"pith_short_12","alias_value":"XF4KQBITNYVT","created_at":"2026-05-18T12:29:50.041715+00:00"},{"alias_kind":"pith_short_16","alias_value":"XF4KQBITNYVT62DH","created_at":"2026-05-18T12:29:50.041715+00:00"},{"alias_kind":"pith_short_8","alias_value":"XF4KQBIT","created_at":"2026-05-18T12:29:50.041715+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/XF4KQBITNYVT62DHOT3C3XE4NZ","json":"https://pith.science/pith/XF4KQBITNYVT62DHOT3C3XE4NZ.json","graph_json":"https://pith.science/api/pith-number/XF4KQBITNYVT62DHOT3C3XE4NZ/graph.json","events_json":"https://pith.science/api/pith-number/XF4KQBITNYVT62DHOT3C3XE4NZ/events.json","paper":"https://pith.science/paper/XF4KQBIT"},"agent_actions":{"view_html":"https://pith.science/pith/XF4KQBITNYVT62DHOT3C3XE4NZ","download_json":"https://pith.science/pith/XF4KQBITNYVT62DHOT3C3XE4NZ.json","view_paper":"https://pith.science/paper/XF4KQBIT","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1511.05215&json=true","fetch_graph":"https://pith.science/api/pith-number/XF4KQBITNYVT62DHOT3C3XE4NZ/graph.json","fetch_events":"https://pith.science/api/pith-number/XF4KQBITNYVT62DHOT3C3XE4NZ/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/XF4KQBITNYVT62DHOT3C3XE4NZ/action/timestamp_anchor","attest_storage":"https://pith.science/pith/XF4KQBITNYVT62DHOT3C3XE4NZ/action/storage_attestation","attest_author":"https://pith.science/pith/XF4KQBITNYVT62DHOT3C3XE4NZ/action/author_attestation","sign_citation":"https://pith.science/pith/XF4KQBITNYVT62DHOT3C3XE4NZ/action/citation_signature","submit_replication":"https://pith.science/pith/XF4KQBITNYVT62DHOT3C3XE4NZ/action/replication_record"}},"created_at":"2026-05-18T01:26:49.754425+00:00","updated_at":"2026-05-18T01:26:49.754425+00:00"}