{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:OY22LLWBL7N54HATLXEGCFSQVY","short_pith_number":"pith:OY22LLWB","canonical_record":{"source":{"id":"1406.1628","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2014-06-06T10:15:05Z","cross_cats_sorted":[],"title_canon_sha256":"ab631933eb7772c1d56bb11d9b3600abe24706c3556c1d23b37de30792577aff","abstract_canon_sha256":"fd8110ad452caa574d233f6d31cd1f8eb7ef1995e323d9a52c381ca14c82dc70"},"schema_version":"1.0"},"canonical_sha256":"7635a5aec15fdbde1c135dc8611650ae012542b9b16a1fedd527f294988bf183","source":{"kind":"arxiv","id":"1406.1628","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1406.1628","created_at":"2026-05-18T02:50:22Z"},{"alias_kind":"arxiv_version","alias_value":"1406.1628v1","created_at":"2026-05-18T02:50:22Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1406.1628","created_at":"2026-05-18T02:50:22Z"},{"alias_kind":"pith_short_12","alias_value":"OY22LLWBL7N5","created_at":"2026-05-18T12:28:43Z"},{"alias_kind":"pith_short_16","alias_value":"OY22LLWBL7N54HAT","created_at":"2026-05-18T12:28:43Z"},{"alias_kind":"pith_short_8","alias_value":"OY22LLWB","created_at":"2026-05-18T12:28:43Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:OY22LLWBL7N54HATLXEGCFSQVY","target":"record","payload":{"canonical_record":{"source":{"id":"1406.1628","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2014-06-06T10:15:05Z","cross_cats_sorted":[],"title_canon_sha256":"ab631933eb7772c1d56bb11d9b3600abe24706c3556c1d23b37de30792577aff","abstract_canon_sha256":"fd8110ad452caa574d233f6d31cd1f8eb7ef1995e323d9a52c381ca14c82dc70"},"schema_version":"1.0"},"canonical_sha256":"7635a5aec15fdbde1c135dc8611650ae012542b9b16a1fedd527f294988bf183","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:50:22.005140Z","signature_b64":"Hs1AB8OHcVS1pYTIXcwlpeXaueJKYyS0JqvKKxeHPjPpPHjVPh9U22xWHZNcbueF+5U8cF8UZLmIdPS5HmaxBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7635a5aec15fdbde1c135dc8611650ae012542b9b16a1fedd527f294988bf183","last_reissued_at":"2026-05-18T02:50:22.004483Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:50:22.004483Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1406.1628","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":"2026-05-18T02:50:22Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"7J+aVt4o6YcgjWn8TMcaOlBzuiCMdxjdOVxsEI6F7GUCOW+5RBXEtYbn0k/sFEZCGWb/SOcEe91FAFi5jLREBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T19:00:37.897896Z"},"content_sha256":"924090d14325f53c3305160b4af91f04a17e679bb0ded8eeadb7fc4026bdaf1f","schema_version":"1.0","event_id":"sha256:924090d14325f53c3305160b4af91f04a17e679bb0ded8eeadb7fc4026bdaf1f"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:OY22LLWBL7N54HATLXEGCFSQVY","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Some transformation formulas associated with Askey-Wilson polynomials and Lassalle's formulas for Macdonald-Koornwinder polynomials","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"A. Hoshino, J. Shiraishi, M. Noumi","submitted_at":"2014-06-06T10:15:05Z","abstract_excerpt":"We present a fourfold series expansion representing the Askey-Wilson polynomials. To obtain the result, a sequential use is made of several summation and transformation formulas for the basic hypergeometric series, including the Verma's q-extension of the Field and Wimp expansion, Andrews' terminating q-analogue of Watson's 3F2 sum, Singh's quadratic transformation. As an application, we present an explicit formula for the Koornwinder polynomial of type BCn (n in Z_>0) with one row diagram. When the parameters are specialized, we recover Lassalle's formula for Macdonald polynomials of type Bn,"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1406.1628","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":"2026-05-18T02:50:22Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"2DbBF4imiOOfduPmgNX/8XJ0A79oFG9PuYK+n8Esgb+GwY8kdVc5csB2GNlVAiXnsxGUYHCIDOSC2cXmBDF6Cw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T19:00:37.898243Z"},"content_sha256":"d1a02bb001797c9928b8304a4a27a32473aa2064091c0f130e4a67b197612747","schema_version":"1.0","event_id":"sha256:d1a02bb001797c9928b8304a4a27a32473aa2064091c0f130e4a67b197612747"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/OY22LLWBL7N54HATLXEGCFSQVY/bundle.json","state_url":"https://pith.science/pith/OY22LLWBL7N54HATLXEGCFSQVY/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/OY22LLWBL7N54HATLXEGCFSQVY/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":"2026-06-01T19:00:37Z","links":{"resolver":"https://pith.science/pith/OY22LLWBL7N54HATLXEGCFSQVY","bundle":"https://pith.science/pith/OY22LLWBL7N54HATLXEGCFSQVY/bundle.json","state":"https://pith.science/pith/OY22LLWBL7N54HATLXEGCFSQVY/state.json","well_known_bundle":"https://pith.science/.well-known/pith/OY22LLWBL7N54HATLXEGCFSQVY/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:OY22LLWBL7N54HATLXEGCFSQVY","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":"fd8110ad452caa574d233f6d31cd1f8eb7ef1995e323d9a52c381ca14c82dc70","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2014-06-06T10:15:05Z","title_canon_sha256":"ab631933eb7772c1d56bb11d9b3600abe24706c3556c1d23b37de30792577aff"},"schema_version":"1.0","source":{"id":"1406.1628","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1406.1628","created_at":"2026-05-18T02:50:22Z"},{"alias_kind":"arxiv_version","alias_value":"1406.1628v1","created_at":"2026-05-18T02:50:22Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1406.1628","created_at":"2026-05-18T02:50:22Z"},{"alias_kind":"pith_short_12","alias_value":"OY22LLWBL7N5","created_at":"2026-05-18T12:28:43Z"},{"alias_kind":"pith_short_16","alias_value":"OY22LLWBL7N54HAT","created_at":"2026-05-18T12:28:43Z"},{"alias_kind":"pith_short_8","alias_value":"OY22LLWB","created_at":"2026-05-18T12:28:43Z"}],"graph_snapshots":[{"event_id":"sha256:d1a02bb001797c9928b8304a4a27a32473aa2064091c0f130e4a67b197612747","target":"graph","created_at":"2026-05-18T02:50:22Z","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":"We present a fourfold series expansion representing the Askey-Wilson polynomials. To obtain the result, a sequential use is made of several summation and transformation formulas for the basic hypergeometric series, including the Verma's q-extension of the Field and Wimp expansion, Andrews' terminating q-analogue of Watson's 3F2 sum, Singh's quadratic transformation. As an application, we present an explicit formula for the Koornwinder polynomial of type BCn (n in Z_>0) with one row diagram. When the parameters are specialized, we recover Lassalle's formula for Macdonald polynomials of type Bn,","authors_text":"A. Hoshino, J. Shiraishi, M. Noumi","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2014-06-06T10:15:05Z","title":"Some transformation formulas associated with Askey-Wilson polynomials and Lassalle's formulas for Macdonald-Koornwinder polynomials"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1406.1628","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":"sha256:924090d14325f53c3305160b4af91f04a17e679bb0ded8eeadb7fc4026bdaf1f","target":"record","created_at":"2026-05-18T02:50:22Z","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":"fd8110ad452caa574d233f6d31cd1f8eb7ef1995e323d9a52c381ca14c82dc70","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2014-06-06T10:15:05Z","title_canon_sha256":"ab631933eb7772c1d56bb11d9b3600abe24706c3556c1d23b37de30792577aff"},"schema_version":"1.0","source":{"id":"1406.1628","kind":"arxiv","version":1}},"canonical_sha256":"7635a5aec15fdbde1c135dc8611650ae012542b9b16a1fedd527f294988bf183","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"7635a5aec15fdbde1c135dc8611650ae012542b9b16a1fedd527f294988bf183","first_computed_at":"2026-05-18T02:50:22.004483Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:50:22.004483Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Hs1AB8OHcVS1pYTIXcwlpeXaueJKYyS0JqvKKxeHPjPpPHjVPh9U22xWHZNcbueF+5U8cF8UZLmIdPS5HmaxBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T02:50:22.005140Z","signed_message":"canonical_sha256_bytes"},"source_id":"1406.1628","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:924090d14325f53c3305160b4af91f04a17e679bb0ded8eeadb7fc4026bdaf1f","sha256:d1a02bb001797c9928b8304a4a27a32473aa2064091c0f130e4a67b197612747"],"state_sha256":"2de24d93c0e9a051287099824e2d27304a40419438098bd7ae655bb1a6a46056"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"hXb1Ud/CfcxoF02KtKRqcW7AGbYmTZlNE0+iEj4FUa3JSwMjVN2yIawSVeBfR1dv8OwWptZKKkacfQLh3cWtDg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-01T19:00:37.900251Z","bundle_sha256":"5da0330d9fb0fba5d2a2cbf8e8bf8cee3365e6162df9078e37d9d6e60a3c8905"}}