{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2012:BTUPTXABCTFYAST2UHFVWHPFVH","short_pith_number":"pith:BTUPTXAB","schema_version":"1.0","canonical_sha256":"0ce8f9dc0114cb804a7aa1cb5b1de5a9e5abbd0cf219bba07dcf416d335033bd","source":{"kind":"arxiv","id":"1212.1887","version":2},"attestation_state":"computed","paper":{"title":"A quadratic formula for basic hypergeometric series related to Askey-Wilson polynomials","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CA"],"primary_cat":"math.CO","authors_text":"Hiroyuki Tagawa, Jiang Zeng, Masao Ishikawa, Victor J. W. Guo","submitted_at":"2012-12-09T12:46:27Z","abstract_excerpt":"We prove a general quadratic formula for basic hypergeometric series, from which simple proofs of several recent determinant and Pfaffian formulas are obtained. A special case of the quadratic formula is actually related to a Gram determinant formula for Askey-Wilson polynomials. We also show how to derive a recent double-sum formula for the moments of Askey-Wilson polynomials from Newton's interpolation formula."},"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":"1212.1887","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2012-12-09T12:46:27Z","cross_cats_sorted":["math.CA"],"title_canon_sha256":"79313dcb51d178b645f1c0f89fba93315b19ae21e3224fb9a7b747aeae0b166e","abstract_canon_sha256":"abe8ee949c8d948a49dab3f68d2f300654c35424ab9fd2f6a13f2ee40d010621"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:16:17.074804Z","signature_b64":"Nb0BMcwNbi9a1AAjxRX7Yf8NujQkw+53/pUx0JJ0hh1GqeKesQJ7rRQfGTBprL2pnvo9vq9W5R6wNd6dlXpSAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0ce8f9dc0114cb804a7aa1cb5b1de5a9e5abbd0cf219bba07dcf416d335033bd","last_reissued_at":"2026-05-18T03:16:17.074070Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:16:17.074070Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A quadratic formula for basic hypergeometric series related to Askey-Wilson polynomials","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CA"],"primary_cat":"math.CO","authors_text":"Hiroyuki Tagawa, Jiang Zeng, Masao Ishikawa, Victor J. W. Guo","submitted_at":"2012-12-09T12:46:27Z","abstract_excerpt":"We prove a general quadratic formula for basic hypergeometric series, from which simple proofs of several recent determinant and Pfaffian formulas are obtained. A special case of the quadratic formula is actually related to a Gram determinant formula for Askey-Wilson polynomials. We also show how to derive a recent double-sum formula for the moments of Askey-Wilson polynomials from Newton's interpolation formula."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1212.1887","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":""},"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":"1212.1887","created_at":"2026-05-18T03:16:17.074197+00:00"},{"alias_kind":"arxiv_version","alias_value":"1212.1887v2","created_at":"2026-05-18T03:16:17.074197+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1212.1887","created_at":"2026-05-18T03:16:17.074197+00:00"},{"alias_kind":"pith_short_12","alias_value":"BTUPTXABCTFY","created_at":"2026-05-18T12:27:01.376967+00:00"},{"alias_kind":"pith_short_16","alias_value":"BTUPTXABCTFYAST2","created_at":"2026-05-18T12:27:01.376967+00:00"},{"alias_kind":"pith_short_8","alias_value":"BTUPTXAB","created_at":"2026-05-18T12:27:01.376967+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/BTUPTXABCTFYAST2UHFVWHPFVH","json":"https://pith.science/pith/BTUPTXABCTFYAST2UHFVWHPFVH.json","graph_json":"https://pith.science/api/pith-number/BTUPTXABCTFYAST2UHFVWHPFVH/graph.json","events_json":"https://pith.science/api/pith-number/BTUPTXABCTFYAST2UHFVWHPFVH/events.json","paper":"https://pith.science/paper/BTUPTXAB"},"agent_actions":{"view_html":"https://pith.science/pith/BTUPTXABCTFYAST2UHFVWHPFVH","download_json":"https://pith.science/pith/BTUPTXABCTFYAST2UHFVWHPFVH.json","view_paper":"https://pith.science/paper/BTUPTXAB","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1212.1887&json=true","fetch_graph":"https://pith.science/api/pith-number/BTUPTXABCTFYAST2UHFVWHPFVH/graph.json","fetch_events":"https://pith.science/api/pith-number/BTUPTXABCTFYAST2UHFVWHPFVH/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/BTUPTXABCTFYAST2UHFVWHPFVH/action/timestamp_anchor","attest_storage":"https://pith.science/pith/BTUPTXABCTFYAST2UHFVWHPFVH/action/storage_attestation","attest_author":"https://pith.science/pith/BTUPTXABCTFYAST2UHFVWHPFVH/action/author_attestation","sign_citation":"https://pith.science/pith/BTUPTXABCTFYAST2UHFVWHPFVH/action/citation_signature","submit_replication":"https://pith.science/pith/BTUPTXABCTFYAST2UHFVWHPFVH/action/replication_record"}},"created_at":"2026-05-18T03:16:17.074197+00:00","updated_at":"2026-05-18T03:16:17.074197+00:00"}