{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:4XRQVIYWYQENLIKVBPQFBDFRLW","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":"6ed6ff7e3b1d4175d98236350d3dbed46e78288b89689b05ebea7320b65f2d6d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2019-04-02T18:53:42Z","title_canon_sha256":"37f15325ad2af7d38577539f6539dfb25df53ad61b06864e3ee6c7ecbcae1fc3"},"schema_version":"1.0","source":{"id":"1904.01621","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1904.01621","created_at":"2026-07-05T02:43:04Z"},{"alias_kind":"arxiv_version","alias_value":"1904.01621v2","created_at":"2026-07-05T02:43:04Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1904.01621","created_at":"2026-07-05T02:43:04Z"},{"alias_kind":"pith_short_12","alias_value":"4XRQVIYWYQEN","created_at":"2026-07-05T02:43:04Z"},{"alias_kind":"pith_short_16","alias_value":"4XRQVIYWYQENLIKV","created_at":"2026-07-05T02:43:04Z"},{"alias_kind":"pith_short_8","alias_value":"4XRQVIYW","created_at":"2026-07-05T02:43:04Z"}],"graph_snapshots":[{"event_id":"sha256:3217c75599525b95225d14f49ab12e94b808c006a8cf8836f494e5be514e5cf0","target":"graph","created_at":"2026-07-05T02:43:04Z","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/1904.01621/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Recently the authors initiated an $\\imath$Hall algebra approach to (universal) $\\imath$quantum groups arising from quantum symmetric pairs. In this paper we construct and study BGP type reflection functors which lead to isomorphisms of the $\\imath$Hall algebras associated to acyclic $\\imath$quivers. For Dynkin quivers, these symmetries on $\\imath$Hall algebras induce automorphisms of universal $\\imath$quantum groups, which are shown to satisfy the braid group relations associated to the restricted Weyl group of a symmetric pair; conjecturally these continue to hold for acyclic quivers/Kac-Mood","authors_text":"Ming Lu, Weiqiang Wang","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2019-04-02T18:53:42Z","title":"Hall algebras and quantum symmetric pairs II: reflection functors"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1904.01621","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":"sha256:861d9fd4d8671a47f917a11037f6e859f0e34b79fb6cfaf404b834eafe1d84a7","target":"record","created_at":"2026-07-05T02:43:04Z","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":"6ed6ff7e3b1d4175d98236350d3dbed46e78288b89689b05ebea7320b65f2d6d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2019-04-02T18:53:42Z","title_canon_sha256":"37f15325ad2af7d38577539f6539dfb25df53ad61b06864e3ee6c7ecbcae1fc3"},"schema_version":"1.0","source":{"id":"1904.01621","kind":"arxiv","version":2}},"canonical_sha256":"e5e30aa316c408d5a1550be0508cb15d90a34a02cc0b7c3f79c8486177814c6b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e5e30aa316c408d5a1550be0508cb15d90a34a02cc0b7c3f79c8486177814c6b","first_computed_at":"2026-07-05T02:43:04.946476Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T02:43:04.946476Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"MRMWlHYi9y56cZ99Akqx98hj3bCmUQI8Kh3BV58NNUUNSShVCeB6p8caSrZmKXEyHdJWojou21FLQKu2jK/8CQ==","signature_status":"signed_v1","signed_at":"2026-07-05T02:43:04.946885Z","signed_message":"canonical_sha256_bytes"},"source_id":"1904.01621","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:861d9fd4d8671a47f917a11037f6e859f0e34b79fb6cfaf404b834eafe1d84a7","sha256:3217c75599525b95225d14f49ab12e94b808c006a8cf8836f494e5be514e5cf0"],"state_sha256":"e768eed3d8d6b77e3cebbe00322278c030c02dd85584e7cfe6e8481732e4cd93"}