{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:JJDGSJSGUVLVOTQ2AWUKLIONZF","short_pith_number":"pith:JJDGSJSG","schema_version":"1.0","canonical_sha256":"4a46692646a557574e1a05a8a5a1cdc961142692fce78fa5e9bbd7321027f97b","source":{"kind":"arxiv","id":"1509.08719","version":4},"attestation_state":"computed","paper":{"title":"Center of the universal Askey--Wilson algebra at roots of unity","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.QA","authors_text":"Hau-wen Huang","submitted_at":"2015-09-29T12:42:34Z","abstract_excerpt":"Inspired by a profound observation on the Racah--Wigner coefficients of $U_q(\\mathfrak{sl}_2)$, the Askey--Wilson algebras were introduced in the early 1990s. A universal analog $\\triangle_q$ of the Askey--Wilson algebras was recently studied. For $q$ not a root of unity, it is known that $Z(\\triangle_q)$ is isomorphic to the polynomial ring of four variables. A presentation for $Z(\\triangle_q)$ at $q$ a root of unity is displayed in this paper. As an application, a presentation for the center of the double affine Hecke algebra of type $(C_1^\\vee,C_1)$ at roots of unity is obtained."},"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":"1509.08719","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2015-09-29T12:42:34Z","cross_cats_sorted":[],"title_canon_sha256":"59ab64dce33633af82a44c348ddfec2a4adbaf35e275ff0e42b26b19e4c87640","abstract_canon_sha256":"2df2d6ec6b07faa89f463570bdef84204c8a4bbe848093735ebdc5d6063b0521"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:29:21.377011Z","signature_b64":"aybcMkKMaJ9x1HnuB+fMayLI7AfBfRMsLea0a0JwK4VsWiK+qlazFB/KNOXXZftmZxSssuk7o6qPO/QO+m9BCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4a46692646a557574e1a05a8a5a1cdc961142692fce78fa5e9bbd7321027f97b","last_reissued_at":"2026-05-18T00:29:21.376212Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:29:21.376212Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Center of the universal Askey--Wilson algebra at roots of unity","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.QA","authors_text":"Hau-wen Huang","submitted_at":"2015-09-29T12:42:34Z","abstract_excerpt":"Inspired by a profound observation on the Racah--Wigner coefficients of $U_q(\\mathfrak{sl}_2)$, the Askey--Wilson algebras were introduced in the early 1990s. A universal analog $\\triangle_q$ of the Askey--Wilson algebras was recently studied. For $q$ not a root of unity, it is known that $Z(\\triangle_q)$ is isomorphic to the polynomial ring of four variables. A presentation for $Z(\\triangle_q)$ at $q$ a root of unity is displayed in this paper. As an application, a presentation for the center of the double affine Hecke algebra of type $(C_1^\\vee,C_1)$ at roots of unity is obtained."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1509.08719","kind":"arxiv","version":4},"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":"1509.08719","created_at":"2026-05-18T00:29:21.376362+00:00"},{"alias_kind":"arxiv_version","alias_value":"1509.08719v4","created_at":"2026-05-18T00:29:21.376362+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1509.08719","created_at":"2026-05-18T00:29:21.376362+00:00"},{"alias_kind":"pith_short_12","alias_value":"JJDGSJSGUVLV","created_at":"2026-05-18T12:29:27.538025+00:00"},{"alias_kind":"pith_short_16","alias_value":"JJDGSJSGUVLVOTQ2","created_at":"2026-05-18T12:29:27.538025+00:00"},{"alias_kind":"pith_short_8","alias_value":"JJDGSJSG","created_at":"2026-05-18T12:29:27.538025+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/JJDGSJSGUVLVOTQ2AWUKLIONZF","json":"https://pith.science/pith/JJDGSJSGUVLVOTQ2AWUKLIONZF.json","graph_json":"https://pith.science/api/pith-number/JJDGSJSGUVLVOTQ2AWUKLIONZF/graph.json","events_json":"https://pith.science/api/pith-number/JJDGSJSGUVLVOTQ2AWUKLIONZF/events.json","paper":"https://pith.science/paper/JJDGSJSG"},"agent_actions":{"view_html":"https://pith.science/pith/JJDGSJSGUVLVOTQ2AWUKLIONZF","download_json":"https://pith.science/pith/JJDGSJSGUVLVOTQ2AWUKLIONZF.json","view_paper":"https://pith.science/paper/JJDGSJSG","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1509.08719&json=true","fetch_graph":"https://pith.science/api/pith-number/JJDGSJSGUVLVOTQ2AWUKLIONZF/graph.json","fetch_events":"https://pith.science/api/pith-number/JJDGSJSGUVLVOTQ2AWUKLIONZF/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/JJDGSJSGUVLVOTQ2AWUKLIONZF/action/timestamp_anchor","attest_storage":"https://pith.science/pith/JJDGSJSGUVLVOTQ2AWUKLIONZF/action/storage_attestation","attest_author":"https://pith.science/pith/JJDGSJSGUVLVOTQ2AWUKLIONZF/action/author_attestation","sign_citation":"https://pith.science/pith/JJDGSJSGUVLVOTQ2AWUKLIONZF/action/citation_signature","submit_replication":"https://pith.science/pith/JJDGSJSGUVLVOTQ2AWUKLIONZF/action/replication_record"}},"created_at":"2026-05-18T00:29:21.376362+00:00","updated_at":"2026-05-18T00:29:21.376362+00:00"}