{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:SRREZOQN5T6QESLVQ27YRHORSV","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":"68b1b3a9aed5e45a23ff7ab319fb894179a93ae1baab4851c320badbee2b29bb","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2017-01-16T06:14:34Z","title_canon_sha256":"bf4ab7aa508f5fe523bd545de831d694b35751c038c42b8fc775130520f29e61"},"schema_version":"1.0","source":{"id":"1701.04179","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1701.04179","created_at":"2026-05-18T00:52:47Z"},{"alias_kind":"arxiv_version","alias_value":"1701.04179v1","created_at":"2026-05-18T00:52:47Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1701.04179","created_at":"2026-05-18T00:52:47Z"},{"alias_kind":"pith_short_12","alias_value":"SRREZOQN5T6Q","created_at":"2026-05-18T12:31:43Z"},{"alias_kind":"pith_short_16","alias_value":"SRREZOQN5T6QESLV","created_at":"2026-05-18T12:31:43Z"},{"alias_kind":"pith_short_8","alias_value":"SRREZOQN","created_at":"2026-05-18T12:31:43Z"}],"graph_snapshots":[{"event_id":"sha256:9a411808c957ad81a411cffa149dde88d0c0746a918d4ee2d488682fe15036b4","target":"graph","created_at":"2026-05-18T00:52:47Z","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":"Consider an abstract operator $L$ which acts on monomials $x^n$ according to $L x^n= \\lambda_n x^n + \\nu_n x^{n-2}$ for $\\lambda_n$ and $\\nu_n$ some coefficients. Let $P_n(x)$ be eigenpolynomials of degree $n$ of $L$: $L P_n(x) = \\lambda_n P_n(x)$. A classification of all the cases for which the polynomials $P_n(x)$ are orthogonal is provided. A general derivation of the algebras explaining the bispectrality of the polynomials is given. The resulting algebras prove to be central extensions of the Askey-Wilson algebra and its degenerate cases.","authors_text":"Alexei Zhedanov, Guo-Fu Yu, Luc Vinet, Satoshi Tsujimoto","cross_cats":["math-ph","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2017-01-16T06:14:34Z","title":"Symmetric abstract hypergeometric polynomials"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1701.04179","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":"sha256:33056f1083e09e8fa66b56629dd3f57dd898bb9a17435b74710f656e9dc5d41b","target":"record","created_at":"2026-05-18T00:52:47Z","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":"68b1b3a9aed5e45a23ff7ab319fb894179a93ae1baab4851c320badbee2b29bb","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2017-01-16T06:14:34Z","title_canon_sha256":"bf4ab7aa508f5fe523bd545de831d694b35751c038c42b8fc775130520f29e61"},"schema_version":"1.0","source":{"id":"1701.04179","kind":"arxiv","version":1}},"canonical_sha256":"94624cba0decfd02497586bf889dd195559f79a837780f28e4c03f078eb5938f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"94624cba0decfd02497586bf889dd195559f79a837780f28e4c03f078eb5938f","first_computed_at":"2026-05-18T00:52:47.600838Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:52:47.600838Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"SM9cne4QB8Z/yK5Dm5sE2OcWzXxCtz4oavBbqCNily7Ut4AAD+yY6cnn6d+cSixlguos0CeiBSaAjOHdtTSCCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:52:47.601537Z","signed_message":"canonical_sha256_bytes"},"source_id":"1701.04179","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:33056f1083e09e8fa66b56629dd3f57dd898bb9a17435b74710f656e9dc5d41b","sha256:9a411808c957ad81a411cffa149dde88d0c0746a918d4ee2d488682fe15036b4"],"state_sha256":"8d39c32a1a32982023c5fa8cd72d86eeee3bebc1e3dab5522c5ea5e38b6c9832"}