{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:WXYK4TSKVCATZHZTOBZZODGJR2","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":"400c367fdee60939377f5cccbf3060bd749496ab66ded265c923a0d1a0537beb","cross_cats_sorted":["math.CO","math.QA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2017-03-02T03:33:11Z","title_canon_sha256":"0c646581cbedb15e0a080a173f45c3fa25c5cd8d881078ad3d7c82961e4f58ca"},"schema_version":"1.0","source":{"id":"1703.00602","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1703.00602","created_at":"2026-07-05T01:09:37Z"},{"alias_kind":"arxiv_version","alias_value":"1703.00602v3","created_at":"2026-07-05T01:09:37Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1703.00602","created_at":"2026-07-05T01:09:37Z"},{"alias_kind":"pith_short_12","alias_value":"WXYK4TSKVCAT","created_at":"2026-07-05T01:09:37Z"},{"alias_kind":"pith_short_16","alias_value":"WXYK4TSKVCATZHZT","created_at":"2026-07-05T01:09:37Z"},{"alias_kind":"pith_short_8","alias_value":"WXYK4TSK","created_at":"2026-07-05T01:09:37Z"}],"graph_snapshots":[{"event_id":"sha256:e7670c4c82ebf188e505cd6b3f0b62d60ed991521015e011caff025f11502fde","target":"graph","created_at":"2026-07-05T01:09:37Z","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/1703.00602/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"The existence of the $\\imath$-canonical basis (also known as the $\\imath$-divided powers) for the coideal subalgebra of the quantum $\\mathfrak{sl}_2$ were established by Bao and Wang, with conjectural explicit formulae. In this paper we prove the conjectured formulae of these $\\imath$-divided powers. This is achieved by first establishing closed formulae of the $\\imath$-divided powers in basis for quantum $\\mathfrak{sl}_2$ and then formulae for the $\\imath$-canonical basis in terms of Lusztig's divided powers in each finite-dimensional simple module of quantum $\\mathfrak{sl}_2$. These formulae","authors_text":"Collin Berman, Weiqiang Wang","cross_cats":["math.CO","math.QA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2017-03-02T03:33:11Z","title":"Formulae of $\\imath$-divided powers in ${\\mathbf U}_q(\\mathfrak{sl}_2)$"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1703.00602","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":"sha256:7be18509bf9f0081d0c319353f7115b3e58f8ce1592047e204c6528abe40196c","target":"record","created_at":"2026-07-05T01:09:37Z","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":"400c367fdee60939377f5cccbf3060bd749496ab66ded265c923a0d1a0537beb","cross_cats_sorted":["math.CO","math.QA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2017-03-02T03:33:11Z","title_canon_sha256":"0c646581cbedb15e0a080a173f45c3fa25c5cd8d881078ad3d7c82961e4f58ca"},"schema_version":"1.0","source":{"id":"1703.00602","kind":"arxiv","version":3}},"canonical_sha256":"b5f0ae4e4aa8813c9f337073970cc98e847e4aef1596df397b52525da7bf4c4a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b5f0ae4e4aa8813c9f337073970cc98e847e4aef1596df397b52525da7bf4c4a","first_computed_at":"2026-07-05T01:09:37.463226Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T01:09:37.463226Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"fdNLtriikVbg+bzCnHh05+QExW9w6rwd3ZTsXkhY6WZUShJBpmwiX51GF0Bae2DjTMg35BQA3NOr0tCEdOPFCQ==","signature_status":"signed_v1","signed_at":"2026-07-05T01:09:37.463728Z","signed_message":"canonical_sha256_bytes"},"source_id":"1703.00602","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:7be18509bf9f0081d0c319353f7115b3e58f8ce1592047e204c6528abe40196c","sha256:e7670c4c82ebf188e505cd6b3f0b62d60ed991521015e011caff025f11502fde"],"state_sha256":"a0e320fec7013ff9bd76112b9e608a2f42492e007492d7e75abe5b6ab1e28e22"}