{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:KSEYETYVEFAQZWXT2YVWLRSBNS","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":"74a8f3abd70e9d7d5178d1db2406278744b2a8c456d20e44d09f59f1a6703d5d","cross_cats_sorted":["math-ph","math.MP","math.QA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2017-02-15T14:41:08Z","title_canon_sha256":"4d8c380636004c274861e258ad056b4f6ae7a7d9b6b0961b1359540915a7cef9"},"schema_version":"1.0","source":{"id":"1702.04626","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1702.04626","created_at":"2026-05-18T00:27:36Z"},{"alias_kind":"arxiv_version","alias_value":"1702.04626v2","created_at":"2026-05-18T00:27:36Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1702.04626","created_at":"2026-05-18T00:27:36Z"},{"alias_kind":"pith_short_12","alias_value":"KSEYETYVEFAQ","created_at":"2026-05-18T12:31:28Z"},{"alias_kind":"pith_short_16","alias_value":"KSEYETYVEFAQZWXT","created_at":"2026-05-18T12:31:28Z"},{"alias_kind":"pith_short_8","alias_value":"KSEYETYV","created_at":"2026-05-18T12:31:28Z"}],"graph_snapshots":[{"event_id":"sha256:ab1e7dc12423ac4c16face8f4d99a836ee62f45cfa6a017205a518795481ea66","target":"graph","created_at":"2026-05-18T00:27:36Z","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":"Gasper & Rahman's multivariate $q$-Racah polynomials are shown to arise as connection coefficients between families of multivariate $q$-Hahn or $q$-Jacobi polynomials. The families of $q$-Hahn polynomials are constructed as nested Clebsch--Gordan coefficients for the positive-discrete series representations of the quantum algebra $su_q(1,1)$. This gives an interpretation of the multivariate $q$-Racah polynomials in terms of $3nj$ symbols. It is shown that the families of $q$-Hahn polynomials also arise in wavefunctions of $q$-deformed quantum Calogero--Gaudin superintegrable systems.","authors_text":"Luc Vinet, Plamen Iliev, Vincent X. Genest","cross_cats":["math-ph","math.MP","math.QA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2017-02-15T14:41:08Z","title":"Coupling coefficients of $su_q(1,1)$ and multivariate $q$-Racah polynomials"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1702.04626","kind":"arxiv","version":2},"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:cd98446e50e77cbea9499abb916f6e25739537f4156d86cae1f2478c7660591c","target":"record","created_at":"2026-05-18T00:27:36Z","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":"74a8f3abd70e9d7d5178d1db2406278744b2a8c456d20e44d09f59f1a6703d5d","cross_cats_sorted":["math-ph","math.MP","math.QA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2017-02-15T14:41:08Z","title_canon_sha256":"4d8c380636004c274861e258ad056b4f6ae7a7d9b6b0961b1359540915a7cef9"},"schema_version":"1.0","source":{"id":"1702.04626","kind":"arxiv","version":2}},"canonical_sha256":"5489824f1521410cdaf3d62b65c6416caceaf3aba1b47493ad55abc01311b28d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"5489824f1521410cdaf3d62b65c6416caceaf3aba1b47493ad55abc01311b28d","first_computed_at":"2026-05-18T00:27:36.373633Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:27:36.373633Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"pHQsHhNCX3UY0aLE/hoDv/jap5Rx6+XzGqPcJbOToVOsG07GNJLk6CRu9EQvUAa5tx/mOP0cYjzw8swxBsEUCA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:27:36.374285Z","signed_message":"canonical_sha256_bytes"},"source_id":"1702.04626","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:cd98446e50e77cbea9499abb916f6e25739537f4156d86cae1f2478c7660591c","sha256:ab1e7dc12423ac4c16face8f4d99a836ee62f45cfa6a017205a518795481ea66"],"state_sha256":"7efe7b50bef2ba77ed1adf1e2d4c20ef87af9bbca4aeee9666d3bcef90293392"}