{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2019:JUJFPWMFFVQ33CHW35ZEDO7PMM","short_pith_number":"pith:JUJFPWMF","canonical_record":{"source":{"id":"1908.11654","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by-sa/4.0/","primary_cat":"math.QA","submitted_at":"2019-08-30T11:22:07Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"add84b76183407edd1ae970d6661253d65b98b5819aa9e2c1c1ab98168630110","abstract_canon_sha256":"16529b19f85c23d91e4f085e2adcec9996bb31cee5a0a57b79d672a2db7b1d11"},"schema_version":"1.0"},"canonical_sha256":"4d1257d9852d61bd88f6df7241bbef63217e2040ba071e51208103293eb784b7","source":{"kind":"arxiv","id":"1908.11654","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1908.11654","created_at":"2026-07-05T00:27:18Z"},{"alias_kind":"arxiv_version","alias_value":"1908.11654v2","created_at":"2026-07-05T00:27:18Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1908.11654","created_at":"2026-07-05T00:27:18Z"},{"alias_kind":"pith_short_12","alias_value":"JUJFPWMFFVQ3","created_at":"2026-07-05T00:27:18Z"},{"alias_kind":"pith_short_16","alias_value":"JUJFPWMFFVQ33CHW","created_at":"2026-07-05T00:27:18Z"},{"alias_kind":"pith_short_8","alias_value":"JUJFPWMF","created_at":"2026-07-05T00:27:18Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2019:JUJFPWMFFVQ33CHW35ZEDO7PMM","target":"record","payload":{"canonical_record":{"source":{"id":"1908.11654","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by-sa/4.0/","primary_cat":"math.QA","submitted_at":"2019-08-30T11:22:07Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"add84b76183407edd1ae970d6661253d65b98b5819aa9e2c1c1ab98168630110","abstract_canon_sha256":"16529b19f85c23d91e4f085e2adcec9996bb31cee5a0a57b79d672a2db7b1d11"},"schema_version":"1.0"},"canonical_sha256":"4d1257d9852d61bd88f6df7241bbef63217e2040ba071e51208103293eb784b7","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T00:27:18.347858Z","signature_b64":"B3VRqKbTCLypjlgenf9FXAg+knTXBc0xqWPhHruPfUmM7jhTB9UzrNNRxnnIp8HC4YEWad3Rlfht6Ik7JEHzBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4d1257d9852d61bd88f6df7241bbef63217e2040ba071e51208103293eb784b7","last_reissued_at":"2026-07-05T00:27:18.347439Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T00:27:18.347439Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1908.11654","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T00:27:18Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"91OWai6gfTfsPVWDP0EqH4i8uFSTgRmp9VOBSGqxTUdPUNO4oUho9YBwLiBIOCcuvkc+EjT9TQ/MN8I1pEw+AQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-16T13:09:42.053782Z"},"content_sha256":"3931e5ce43fe678593fcbf04b6b12fdc56cabce14ff1d02fbae161059efe005f","schema_version":"1.0","event_id":"sha256:3931e5ce43fe678593fcbf04b6b12fdc56cabce14ff1d02fbae161059efe005f"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2019:JUJFPWMFFVQ33CHW35ZEDO7PMM","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Higher Rank Relations for the Askey-Wilson and $q$-Bannai-Ito Algebra","license":"http://creativecommons.org/licenses/by-sa/4.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.QA","authors_text":"Hadewijch De Clercq","submitted_at":"2019-08-30T11:22:07Z","abstract_excerpt":"The higher rank Askey-Wilson algebra was recently constructed in the $n$-fold tensor product of $U_q(\\mathfrak{sl}_2)$. In this paper we prove a class of identities inside this algebra, which generalize the defining relations of the rank one Askey-Wilson algebra. We extend the known construction algorithm by several equivalent methods, using a novel coaction. These allow to simplify calculations significantly. At the same time, this provides a proof of the corresponding relations for the higher rank $q$-Bannai-Ito algebra."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1908.11654","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/1908.11654/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2026-07-05T00:27:18Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"WFvYf4zX0qmtk22FuE6ifhnALI3yUtcTd8QcpAJWKBJCl2NrWm/fzNp6CrYjdhBodc0eKhTEK/bMnlpbUF9ZBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-16T13:09:42.054335Z"},"content_sha256":"3aa7ed93da3164c9e88380bf4602b46252eb714d7d7c212442198b1b903a0e77","schema_version":"1.0","event_id":"sha256:3aa7ed93da3164c9e88380bf4602b46252eb714d7d7c212442198b1b903a0e77"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/JUJFPWMFFVQ33CHW35ZEDO7PMM/bundle.json","state_url":"https://pith.science/pith/JUJFPWMFFVQ33CHW35ZEDO7PMM/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/JUJFPWMFFVQ33CHW35ZEDO7PMM/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":"2026-08-16T13:09:42Z","links":{"resolver":"https://pith.science/pith/JUJFPWMFFVQ33CHW35ZEDO7PMM","bundle":"https://pith.science/pith/JUJFPWMFFVQ33CHW35ZEDO7PMM/bundle.json","state":"https://pith.science/pith/JUJFPWMFFVQ33CHW35ZEDO7PMM/state.json","well_known_bundle":"https://pith.science/.well-known/pith/JUJFPWMFFVQ33CHW35ZEDO7PMM/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:JUJFPWMFFVQ33CHW35ZEDO7PMM","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":"16529b19f85c23d91e4f085e2adcec9996bb31cee5a0a57b79d672a2db7b1d11","cross_cats_sorted":["math-ph","math.MP"],"license":"http://creativecommons.org/licenses/by-sa/4.0/","primary_cat":"math.QA","submitted_at":"2019-08-30T11:22:07Z","title_canon_sha256":"add84b76183407edd1ae970d6661253d65b98b5819aa9e2c1c1ab98168630110"},"schema_version":"1.0","source":{"id":"1908.11654","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1908.11654","created_at":"2026-07-05T00:27:18Z"},{"alias_kind":"arxiv_version","alias_value":"1908.11654v2","created_at":"2026-07-05T00:27:18Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1908.11654","created_at":"2026-07-05T00:27:18Z"},{"alias_kind":"pith_short_12","alias_value":"JUJFPWMFFVQ3","created_at":"2026-07-05T00:27:18Z"},{"alias_kind":"pith_short_16","alias_value":"JUJFPWMFFVQ33CHW","created_at":"2026-07-05T00:27:18Z"},{"alias_kind":"pith_short_8","alias_value":"JUJFPWMF","created_at":"2026-07-05T00:27:18Z"}],"graph_snapshots":[{"event_id":"sha256:3aa7ed93da3164c9e88380bf4602b46252eb714d7d7c212442198b1b903a0e77","target":"graph","created_at":"2026-07-05T00:27:18Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/1908.11654/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"The higher rank Askey-Wilson algebra was recently constructed in the $n$-fold tensor product of $U_q(\\mathfrak{sl}_2)$. In this paper we prove a class of identities inside this algebra, which generalize the defining relations of the rank one Askey-Wilson algebra. We extend the known construction algorithm by several equivalent methods, using a novel coaction. These allow to simplify calculations significantly. At the same time, this provides a proof of the corresponding relations for the higher rank $q$-Bannai-Ito algebra.","authors_text":"Hadewijch De Clercq","cross_cats":["math-ph","math.MP"],"headline":"","license":"http://creativecommons.org/licenses/by-sa/4.0/","primary_cat":"math.QA","submitted_at":"2019-08-30T11:22:07Z","title":"Higher Rank Relations for the Askey-Wilson and $q$-Bannai-Ito Algebra"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1908.11654","kind":"arxiv","version":2},"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":"sha256:3931e5ce43fe678593fcbf04b6b12fdc56cabce14ff1d02fbae161059efe005f","target":"record","created_at":"2026-07-05T00:27:18Z","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":"16529b19f85c23d91e4f085e2adcec9996bb31cee5a0a57b79d672a2db7b1d11","cross_cats_sorted":["math-ph","math.MP"],"license":"http://creativecommons.org/licenses/by-sa/4.0/","primary_cat":"math.QA","submitted_at":"2019-08-30T11:22:07Z","title_canon_sha256":"add84b76183407edd1ae970d6661253d65b98b5819aa9e2c1c1ab98168630110"},"schema_version":"1.0","source":{"id":"1908.11654","kind":"arxiv","version":2}},"canonical_sha256":"4d1257d9852d61bd88f6df7241bbef63217e2040ba071e51208103293eb784b7","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"4d1257d9852d61bd88f6df7241bbef63217e2040ba071e51208103293eb784b7","first_computed_at":"2026-07-05T00:27:18.347439Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T00:27:18.347439Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"B3VRqKbTCLypjlgenf9FXAg+knTXBc0xqWPhHruPfUmM7jhTB9UzrNNRxnnIp8HC4YEWad3Rlfht6Ik7JEHzBA==","signature_status":"signed_v1","signed_at":"2026-07-05T00:27:18.347858Z","signed_message":"canonical_sha256_bytes"},"source_id":"1908.11654","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3931e5ce43fe678593fcbf04b6b12fdc56cabce14ff1d02fbae161059efe005f","sha256:3aa7ed93da3164c9e88380bf4602b46252eb714d7d7c212442198b1b903a0e77"],"state_sha256":"77f8663bd040a0a6614a5737b5146c38eb067270a614389ea60bf82bcdc1755b"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"k01ew+JZWyh4IH/6upxOZD0aECQKDQ3hGGRG6u6z5VjHBIivsYdko4e3MU+GYIoP2ny1sBduhCZ/0Vb/9xYqDg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-16T13:09:42.058319Z","bundle_sha256":"e9ce215ebcefeae5257bca0c46023a8f9d15a201a85338f2bc7792c4eddb1a27"}}