{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:TJFH3Y5IN36ZTD3JCTLK6WGZAG","short_pith_number":"pith:TJFH3Y5I","canonical_record":{"source":{"id":"1212.0077","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by-nc-sa/3.0/","primary_cat":"math.CA","submitted_at":"2012-12-01T07:15:25Z","cross_cats_sorted":["math-ph","math.MP","math.QA"],"title_canon_sha256":"5144404e3c9fab212fa132feeeedcebaeec8616a9e70a21d21724c9b45e5f2c9","abstract_canon_sha256":"e02ef621d56a8207239aee816d4be164886291ac0f2beeffc348952cf7c62e4b"},"schema_version":"1.0"},"canonical_sha256":"9a4a7de3a86efd998f6914d6af58d901a55af23e371d8882dafbb12622bcd026","source":{"kind":"arxiv","id":"1212.0077","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1212.0077","created_at":"2026-05-18T03:39:27Z"},{"alias_kind":"arxiv_version","alias_value":"1212.0077v1","created_at":"2026-05-18T03:39:27Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1212.0077","created_at":"2026-05-18T03:39:27Z"},{"alias_kind":"pith_short_12","alias_value":"TJFH3Y5IN36Z","created_at":"2026-05-18T12:27:23Z"},{"alias_kind":"pith_short_16","alias_value":"TJFH3Y5IN36ZTD3J","created_at":"2026-05-18T12:27:23Z"},{"alias_kind":"pith_short_8","alias_value":"TJFH3Y5I","created_at":"2026-05-18T12:27:23Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:TJFH3Y5IN36ZTD3JCTLK6WGZAG","target":"record","payload":{"canonical_record":{"source":{"id":"1212.0077","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by-nc-sa/3.0/","primary_cat":"math.CA","submitted_at":"2012-12-01T07:15:25Z","cross_cats_sorted":["math-ph","math.MP","math.QA"],"title_canon_sha256":"5144404e3c9fab212fa132feeeedcebaeec8616a9e70a21d21724c9b45e5f2c9","abstract_canon_sha256":"e02ef621d56a8207239aee816d4be164886291ac0f2beeffc348952cf7c62e4b"},"schema_version":"1.0"},"canonical_sha256":"9a4a7de3a86efd998f6914d6af58d901a55af23e371d8882dafbb12622bcd026","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:39:27.384240Z","signature_b64":"AXrk+ygC3OG/f382K4IO4lb4mo6WpQ6LYtUcnKZWlZauk8oWmHXM/xn5rmP99JrWcEW3VAbBlQXZCttPYFylAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9a4a7de3a86efd998f6914d6af58d901a55af23e371d8882dafbb12622bcd026","last_reissued_at":"2026-05-18T03:39:27.383591Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:39:27.383591Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1212.0077","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:39:27Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"+XKe8wAh5ZfZSZs3J8X/Ish9zgwBH1KCLPwKOg/ib4nxWe+3fNxJokp2hUVD9aEUlfKG1KnAR161QrCTZObwBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-05T14:13:45.142472Z"},"content_sha256":"7e5ad6f9d2b91f9aa23814669e9ce3f3040bb0c84f8518d1f6640bd65cc98dbd","schema_version":"1.0","event_id":"sha256:7e5ad6f9d2b91f9aa23814669e9ce3f3040bb0c84f8518d1f6640bd65cc98dbd"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:TJFH3Y5IN36ZTD3JCTLK6WGZAG","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Orthogonal Basic Hypergeometric Laurent Polynomials","license":"http://creativecommons.org/licenses/by-nc-sa/3.0/","headline":"","cross_cats":["math-ph","math.MP","math.QA"],"primary_cat":"math.CA","authors_text":"Dennis Stanton, Mourad E.H. Ismail","submitted_at":"2012-12-01T07:15:25Z","abstract_excerpt":"The Askey-Wilson polynomials are orthogonal polynomials in $x = \\cos \\theta$, which are given as a terminating $_4\\phi_3$ basic hypergeometric series. The non-symmetric Askey-Wilson polynomials are Laurent polynomials in $z=e^{i\\theta}$, which are given as a sum of two terminating $_4\\phi_3$'s. They satisfy a biorthogonality relation. In this paper new orthogonality relations for single $_4\\phi_3$'s which are Laurent polynomials in $z$ are given, which imply the non-symmetric Askey-Wilson biorthogonality. These results include discrete orthogonality relations. They can be considered as a class"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1212.0077","kind":"arxiv","version":1},"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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:39:27Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"8hPfL0X0ItEvMbwYZfu5bGk7xKeXpf93bzJ3h0FbTNgCHHldBN7IncN1zXA2dUVjnJQX8ijpG0iII5jy4PRaCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-05T14:13:45.142822Z"},"content_sha256":"5049abd1c2449ba3665593ae6837c693974c4cb15c57b44270e9735532bbebb0","schema_version":"1.0","event_id":"sha256:5049abd1c2449ba3665593ae6837c693974c4cb15c57b44270e9735532bbebb0"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/TJFH3Y5IN36ZTD3JCTLK6WGZAG/bundle.json","state_url":"https://pith.science/pith/TJFH3Y5IN36ZTD3JCTLK6WGZAG/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/TJFH3Y5IN36ZTD3JCTLK6WGZAG/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-06-05T14:13:45Z","links":{"resolver":"https://pith.science/pith/TJFH3Y5IN36ZTD3JCTLK6WGZAG","bundle":"https://pith.science/pith/TJFH3Y5IN36ZTD3JCTLK6WGZAG/bundle.json","state":"https://pith.science/pith/TJFH3Y5IN36ZTD3JCTLK6WGZAG/state.json","well_known_bundle":"https://pith.science/.well-known/pith/TJFH3Y5IN36ZTD3JCTLK6WGZAG/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:TJFH3Y5IN36ZTD3JCTLK6WGZAG","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":"e02ef621d56a8207239aee816d4be164886291ac0f2beeffc348952cf7c62e4b","cross_cats_sorted":["math-ph","math.MP","math.QA"],"license":"http://creativecommons.org/licenses/by-nc-sa/3.0/","primary_cat":"math.CA","submitted_at":"2012-12-01T07:15:25Z","title_canon_sha256":"5144404e3c9fab212fa132feeeedcebaeec8616a9e70a21d21724c9b45e5f2c9"},"schema_version":"1.0","source":{"id":"1212.0077","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1212.0077","created_at":"2026-05-18T03:39:27Z"},{"alias_kind":"arxiv_version","alias_value":"1212.0077v1","created_at":"2026-05-18T03:39:27Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1212.0077","created_at":"2026-05-18T03:39:27Z"},{"alias_kind":"pith_short_12","alias_value":"TJFH3Y5IN36Z","created_at":"2026-05-18T12:27:23Z"},{"alias_kind":"pith_short_16","alias_value":"TJFH3Y5IN36ZTD3J","created_at":"2026-05-18T12:27:23Z"},{"alias_kind":"pith_short_8","alias_value":"TJFH3Y5I","created_at":"2026-05-18T12:27:23Z"}],"graph_snapshots":[{"event_id":"sha256:5049abd1c2449ba3665593ae6837c693974c4cb15c57b44270e9735532bbebb0","target":"graph","created_at":"2026-05-18T03:39:27Z","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":"The Askey-Wilson polynomials are orthogonal polynomials in $x = \\cos \\theta$, which are given as a terminating $_4\\phi_3$ basic hypergeometric series. The non-symmetric Askey-Wilson polynomials are Laurent polynomials in $z=e^{i\\theta}$, which are given as a sum of two terminating $_4\\phi_3$'s. They satisfy a biorthogonality relation. In this paper new orthogonality relations for single $_4\\phi_3$'s which are Laurent polynomials in $z$ are given, which imply the non-symmetric Askey-Wilson biorthogonality. These results include discrete orthogonality relations. They can be considered as a class","authors_text":"Dennis Stanton, Mourad E.H. Ismail","cross_cats":["math-ph","math.MP","math.QA"],"headline":"","license":"http://creativecommons.org/licenses/by-nc-sa/3.0/","primary_cat":"math.CA","submitted_at":"2012-12-01T07:15:25Z","title":"Orthogonal Basic Hypergeometric Laurent Polynomials"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1212.0077","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":"sha256:7e5ad6f9d2b91f9aa23814669e9ce3f3040bb0c84f8518d1f6640bd65cc98dbd","target":"record","created_at":"2026-05-18T03:39:27Z","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":"e02ef621d56a8207239aee816d4be164886291ac0f2beeffc348952cf7c62e4b","cross_cats_sorted":["math-ph","math.MP","math.QA"],"license":"http://creativecommons.org/licenses/by-nc-sa/3.0/","primary_cat":"math.CA","submitted_at":"2012-12-01T07:15:25Z","title_canon_sha256":"5144404e3c9fab212fa132feeeedcebaeec8616a9e70a21d21724c9b45e5f2c9"},"schema_version":"1.0","source":{"id":"1212.0077","kind":"arxiv","version":1}},"canonical_sha256":"9a4a7de3a86efd998f6914d6af58d901a55af23e371d8882dafbb12622bcd026","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9a4a7de3a86efd998f6914d6af58d901a55af23e371d8882dafbb12622bcd026","first_computed_at":"2026-05-18T03:39:27.383591Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:39:27.383591Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"AXrk+ygC3OG/f382K4IO4lb4mo6WpQ6LYtUcnKZWlZauk8oWmHXM/xn5rmP99JrWcEW3VAbBlQXZCttPYFylAg==","signature_status":"signed_v1","signed_at":"2026-05-18T03:39:27.384240Z","signed_message":"canonical_sha256_bytes"},"source_id":"1212.0077","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:7e5ad6f9d2b91f9aa23814669e9ce3f3040bb0c84f8518d1f6640bd65cc98dbd","sha256:5049abd1c2449ba3665593ae6837c693974c4cb15c57b44270e9735532bbebb0"],"state_sha256":"5a418feb19e94833b08d5d8b5001c0653ea2f079e9f72cc786732d5670347e9c"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Hs/BY1PQwf15uBaqS5C/zSNLzK5kdaCZ1PcO0dvZG67+3ldSv2pR1weiKLyGLczyduVKIpgnmLPF8X/iCx6EBw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-05T14:13:45.144698Z","bundle_sha256":"fb4514455d5309528fe1e7addac827d8cd37f3df575e8aff84527a59d25014f6"}}