{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2019:27ODL5LHYCVHGW2345GFE5J2BB","short_pith_number":"pith:27ODL5LH","canonical_record":{"source":{"id":"1902.07682","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2019-02-20T17:55:37Z","cross_cats_sorted":["math.QA"],"title_canon_sha256":"682c58a4aa68fa5a7709045b720e78b65f51eee0f10df3940bea79cd670f61a0","abstract_canon_sha256":"4d3b60241d2f29b8bf10a43593db7994566317f7e342b9cb909d5cdef2227e88"},"schema_version":"1.0"},"canonical_sha256":"d7dc35f567c0aa735b5be74c52753a087b087acded146f91a13c2da438b0d35f","source":{"kind":"arxiv","id":"1902.07682","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1902.07682","created_at":"2026-05-17T23:42:42Z"},{"alias_kind":"arxiv_version","alias_value":"1902.07682v3","created_at":"2026-05-17T23:42:42Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1902.07682","created_at":"2026-05-17T23:42:42Z"},{"alias_kind":"pith_short_12","alias_value":"27ODL5LHYCVH","created_at":"2026-05-18T12:33:07Z"},{"alias_kind":"pith_short_16","alias_value":"27ODL5LHYCVHGW23","created_at":"2026-05-18T12:33:07Z"},{"alias_kind":"pith_short_8","alias_value":"27ODL5LH","created_at":"2026-05-18T12:33:07Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2019:27ODL5LHYCVHGW2345GFE5J2BB","target":"record","payload":{"canonical_record":{"source":{"id":"1902.07682","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2019-02-20T17:55:37Z","cross_cats_sorted":["math.QA"],"title_canon_sha256":"682c58a4aa68fa5a7709045b720e78b65f51eee0f10df3940bea79cd670f61a0","abstract_canon_sha256":"4d3b60241d2f29b8bf10a43593db7994566317f7e342b9cb909d5cdef2227e88"},"schema_version":"1.0"},"canonical_sha256":"d7dc35f567c0aa735b5be74c52753a087b087acded146f91a13c2da438b0d35f","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:42:42.291164Z","signature_b64":"2Bws+XWLQ19cRGxdbiSDvx5uFwAIBwTkngE5zksjR6yxayTxIpbVsgmHGcsmFB8e2lz5Ux95cw+8NwjpiPmaDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d7dc35f567c0aa735b5be74c52753a087b087acded146f91a13c2da438b0d35f","last_reissued_at":"2026-05-17T23:42:42.290453Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:42:42.290453Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1902.07682","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-17T23:42:42Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"XfKJcMvDcESk67orO+0NDwL8ONNO0gGCTHvKEUAHG3s+ydrBDyM9pQVWf1o0w+5q8N+dSJyNKSdi1GQ/OnFWCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-04T15:40:03.462209Z"},"content_sha256":"1bb34ef09df01dc39336e1e0c1492843bae8130b7bd674c8a3ea59319c15d5bb","schema_version":"1.0","event_id":"sha256:1bb34ef09df01dc39336e1e0c1492843bae8130b7bd674c8a3ea59319c15d5bb"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2019:27ODL5LHYCVHGW2345GFE5J2BB","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On $q$-Schur algebras corresponding to Hecke algebras of type B","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.QA"],"primary_cat":"math.RT","authors_text":"Chun-Ju Lai, Daniel K. Nakano, Ziqing Xiang","submitted_at":"2019-02-20T17:55:37Z","abstract_excerpt":"In this paper the authors investigate the $q$-Schur algebras of type B that were constructed earlier using coideal subalgebras for the quantum group of type A. The authors present a coordinate algebra type construction that allows us to realize these $q$-Schur algebras as the duals of the $d$th graded components of certain graded coalgebras. Under suitable conditions an isomorphism theorem is proved that demonstrates that the representation theory reduces to the $q$-Schur algebra of type A. This enables the authors to address the questions of cellularity, quasi-hereditariness and representatio"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1902.07682","kind":"arxiv","version":3},"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":"2026-05-17T23:42:42Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"2XfgEVIqgrZqe9I7GbiAGIGUaIxrN7OBQFptNU21z8yoXuNtI13L8si28ygxQPtOk85vOvNK54Rvxp1Z2oITCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-04T15:40:03.462591Z"},"content_sha256":"a8a5554c736673d934de3e8dfa611596968ecc33e24f0f8993d8916711a36369","schema_version":"1.0","event_id":"sha256:a8a5554c736673d934de3e8dfa611596968ecc33e24f0f8993d8916711a36369"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/27ODL5LHYCVHGW2345GFE5J2BB/bundle.json","state_url":"https://pith.science/pith/27ODL5LHYCVHGW2345GFE5J2BB/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/27ODL5LHYCVHGW2345GFE5J2BB/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":"2026-06-04T15:40:03Z","links":{"resolver":"https://pith.science/pith/27ODL5LHYCVHGW2345GFE5J2BB","bundle":"https://pith.science/pith/27ODL5LHYCVHGW2345GFE5J2BB/bundle.json","state":"https://pith.science/pith/27ODL5LHYCVHGW2345GFE5J2BB/state.json","well_known_bundle":"https://pith.science/.well-known/pith/27ODL5LHYCVHGW2345GFE5J2BB/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:27ODL5LHYCVHGW2345GFE5J2BB","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":"4d3b60241d2f29b8bf10a43593db7994566317f7e342b9cb909d5cdef2227e88","cross_cats_sorted":["math.QA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2019-02-20T17:55:37Z","title_canon_sha256":"682c58a4aa68fa5a7709045b720e78b65f51eee0f10df3940bea79cd670f61a0"},"schema_version":"1.0","source":{"id":"1902.07682","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1902.07682","created_at":"2026-05-17T23:42:42Z"},{"alias_kind":"arxiv_version","alias_value":"1902.07682v3","created_at":"2026-05-17T23:42:42Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1902.07682","created_at":"2026-05-17T23:42:42Z"},{"alias_kind":"pith_short_12","alias_value":"27ODL5LHYCVH","created_at":"2026-05-18T12:33:07Z"},{"alias_kind":"pith_short_16","alias_value":"27ODL5LHYCVHGW23","created_at":"2026-05-18T12:33:07Z"},{"alias_kind":"pith_short_8","alias_value":"27ODL5LH","created_at":"2026-05-18T12:33:07Z"}],"graph_snapshots":[{"event_id":"sha256:a8a5554c736673d934de3e8dfa611596968ecc33e24f0f8993d8916711a36369","target":"graph","created_at":"2026-05-17T23:42:42Z","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":"In this paper the authors investigate the $q$-Schur algebras of type B that were constructed earlier using coideal subalgebras for the quantum group of type A. The authors present a coordinate algebra type construction that allows us to realize these $q$-Schur algebras as the duals of the $d$th graded components of certain graded coalgebras. Under suitable conditions an isomorphism theorem is proved that demonstrates that the representation theory reduces to the $q$-Schur algebra of type A. This enables the authors to address the questions of cellularity, quasi-hereditariness and representatio","authors_text":"Chun-Ju Lai, Daniel K. Nakano, Ziqing Xiang","cross_cats":["math.QA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2019-02-20T17:55:37Z","title":"On $q$-Schur algebras corresponding to Hecke algebras of type B"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1902.07682","kind":"arxiv","version":3},"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":"sha256:1bb34ef09df01dc39336e1e0c1492843bae8130b7bd674c8a3ea59319c15d5bb","target":"record","created_at":"2026-05-17T23:42:42Z","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":"4d3b60241d2f29b8bf10a43593db7994566317f7e342b9cb909d5cdef2227e88","cross_cats_sorted":["math.QA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2019-02-20T17:55:37Z","title_canon_sha256":"682c58a4aa68fa5a7709045b720e78b65f51eee0f10df3940bea79cd670f61a0"},"schema_version":"1.0","source":{"id":"1902.07682","kind":"arxiv","version":3}},"canonical_sha256":"d7dc35f567c0aa735b5be74c52753a087b087acded146f91a13c2da438b0d35f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d7dc35f567c0aa735b5be74c52753a087b087acded146f91a13c2da438b0d35f","first_computed_at":"2026-05-17T23:42:42.290453Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:42:42.290453Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"2Bws+XWLQ19cRGxdbiSDvx5uFwAIBwTkngE5zksjR6yxayTxIpbVsgmHGcsmFB8e2lz5Ux95cw+8NwjpiPmaDQ==","signature_status":"signed_v1","signed_at":"2026-05-17T23:42:42.291164Z","signed_message":"canonical_sha256_bytes"},"source_id":"1902.07682","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1bb34ef09df01dc39336e1e0c1492843bae8130b7bd674c8a3ea59319c15d5bb","sha256:a8a5554c736673d934de3e8dfa611596968ecc33e24f0f8993d8916711a36369"],"state_sha256":"e6e541d2f11859400deed352024763fccd5fc785578a04bb99ad30c3dc73303c"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"J/6pYmDFNSibYuXpRHP//ooBh4j/3xtXmZ6Lxv8/cmdWscWm24IK5rk1W3nqm5OgXlh9SOqf7M9yEuAKlbOEBA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-04T15:40:03.466461Z","bundle_sha256":"f47a396edf0de09b0960923df082484736dfe55b2bbb37d5abdcd0053349f4e6"}}