{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2024:GV6JRRUCT7DBXYNYJXQQEOMINN","short_pith_number":"pith:GV6JRRUC","schema_version":"1.0","canonical_sha256":"357c98c6829fc61be1b84de10239886b6d9d011c597a913d3ea98c237d155d9d","source":{"kind":"arxiv","id":"2407.17016","version":2},"attestation_state":"computed","paper":{"title":"$q$-deformed Griffiths polynomials of Racah type","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.MP"],"primary_cat":"math-ph","authors_text":"Eric Ragoucy, Julien Gaboriaud, Luc Frappat, Nicolas Crampe","submitted_at":"2024-07-24T05:50:21Z","abstract_excerpt":"New bivariate Griffiths polynomials of $q$-Racah type are introduced and characterized. They generalize the polynomials orthogonal on the multinomial distribution introduced by R. Griffiths fifty years ago. They also correspond to a $q$-deformation of the Griffiths polynomials of Racah type introduced previously by the authors and collaborators. The latter are recovered from the former by a $q\\to1$ limit. We show that these new polynomials are bispectral and biorthogonal. We also exhibit some symmetry relations that are essential in the proof of the bispectrality property."},"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":"2407.17016","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math-ph","submitted_at":"2024-07-24T05:50:21Z","cross_cats_sorted":["math.MP"],"title_canon_sha256":"7f066f5d5c3268adfa628e43558b12904994a1551605f47bde324a5a4fb2dcae","abstract_canon_sha256":"c1594492dd758ae0b343277d779010e0152a3ff49ce519b42798ebd8e637c4f9"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T09:25:45.530703Z","signature_b64":"dF9WKHIeP6k7dOR8PsxrPHEjYnXbf2Xa05S7xDnLaPwsCo7fVAQSJHyUMZ2sNZwzVfrM5gisymRErU9fACZaBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"357c98c6829fc61be1b84de10239886b6d9d011c597a913d3ea98c237d155d9d","last_reissued_at":"2026-07-05T09:25:45.530093Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T09:25:45.530093Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"$q$-deformed Griffiths polynomials of Racah type","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.MP"],"primary_cat":"math-ph","authors_text":"Eric Ragoucy, Julien Gaboriaud, Luc Frappat, Nicolas Crampe","submitted_at":"2024-07-24T05:50:21Z","abstract_excerpt":"New bivariate Griffiths polynomials of $q$-Racah type are introduced and characterized. They generalize the polynomials orthogonal on the multinomial distribution introduced by R. Griffiths fifty years ago. They also correspond to a $q$-deformation of the Griffiths polynomials of Racah type introduced previously by the authors and collaborators. The latter are recovered from the former by a $q\\to1$ limit. We show that these new polynomials are bispectral and biorthogonal. We also exhibit some symmetry relations that are essential in the proof of the bispectrality property."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2407.17016","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2407.17016/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2407.17016","created_at":"2026-07-05T09:25:45.530159+00:00"},{"alias_kind":"arxiv_version","alias_value":"2407.17016v2","created_at":"2026-07-05T09:25:45.530159+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2407.17016","created_at":"2026-07-05T09:25:45.530159+00:00"},{"alias_kind":"pith_short_12","alias_value":"GV6JRRUCT7DB","created_at":"2026-07-05T09:25:45.530159+00:00"},{"alias_kind":"pith_short_16","alias_value":"GV6JRRUCT7DBXYNY","created_at":"2026-07-05T09:25:45.530159+00:00"},{"alias_kind":"pith_short_8","alias_value":"GV6JRRUC","created_at":"2026-07-05T09:25:45.530159+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"2504.20802","citing_title":"Contiguity relations for finite families of orthogonal polynomials in the Askey scheme","ref_index":9,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/GV6JRRUCT7DBXYNYJXQQEOMINN","json":"https://pith.science/pith/GV6JRRUCT7DBXYNYJXQQEOMINN.json","graph_json":"https://pith.science/api/pith-number/GV6JRRUCT7DBXYNYJXQQEOMINN/graph.json","events_json":"https://pith.science/api/pith-number/GV6JRRUCT7DBXYNYJXQQEOMINN/events.json","paper":"https://pith.science/paper/GV6JRRUC"},"agent_actions":{"view_html":"https://pith.science/pith/GV6JRRUCT7DBXYNYJXQQEOMINN","download_json":"https://pith.science/pith/GV6JRRUCT7DBXYNYJXQQEOMINN.json","view_paper":"https://pith.science/paper/GV6JRRUC","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2407.17016&json=true","fetch_graph":"https://pith.science/api/pith-number/GV6JRRUCT7DBXYNYJXQQEOMINN/graph.json","fetch_events":"https://pith.science/api/pith-number/GV6JRRUCT7DBXYNYJXQQEOMINN/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/GV6JRRUCT7DBXYNYJXQQEOMINN/action/timestamp_anchor","attest_storage":"https://pith.science/pith/GV6JRRUCT7DBXYNYJXQQEOMINN/action/storage_attestation","attest_author":"https://pith.science/pith/GV6JRRUCT7DBXYNYJXQQEOMINN/action/author_attestation","sign_citation":"https://pith.science/pith/GV6JRRUCT7DBXYNYJXQQEOMINN/action/citation_signature","submit_replication":"https://pith.science/pith/GV6JRRUCT7DBXYNYJXQQEOMINN/action/replication_record"}},"created_at":"2026-07-05T09:25:45.530159+00:00","updated_at":"2026-07-05T09:25:45.530159+00:00"}