{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2019:S3O6HZ2JYVBYHM57ZY4R3J4ENZ","short_pith_number":"pith:S3O6HZ2J","schema_version":"1.0","canonical_sha256":"96dde3e749c54383b3bfce391da7846e4ead7c445ecf5564591d184da7d416df","source":{"kind":"arxiv","id":"1910.01263","version":3},"attestation_state":"computed","paper":{"title":"Hall algebras and quantum symmetric pairs III: Quiver varieties","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG"],"primary_cat":"math.RT","authors_text":"Ming Lu, Weiqiang Wang","submitted_at":"2019-10-03T00:51:02Z","abstract_excerpt":"The $\\imath$quiver algebras were introduced recently by the authors to provide a Hall algebra realization of universal $\\imath$quantum groups, which is a generalization of Bridgeland's Hall algebra construction for (Drinfeld doubles of) quantum groups; here an $\\imath$quantum group and a corresponding Drinfeld-Jimbo quantum group form a quantum symmetric pair. In this paper, the Dynkin $\\imath$quiver algebras are shown to arise as new examples of singular Nakajima-Keller-Scherotzke categories. Then we provide a geometric construction of the universal $\\imath$quantum groups and their ``dual can"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1910.01263","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2019-10-03T00:51:02Z","cross_cats_sorted":["math.AG"],"title_canon_sha256":"c132ce2011a0ad9be4a8a431fe87e1d1b00378422d8732d80f6eb16fc12b05a7","abstract_canon_sha256":"2b5bafa74b5dadd09334bedc648597aa3637d490192fe7c3e346bea12d3b0f6d"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T03:57:23.025964Z","signature_b64":"FFsuNzCQeTwmLP0fF+8EXBVgROYzLyG6hNRnUeQ0QDtl5G/xlmgcBxRCBtlMuXz7cE1QpO/JiWZmro3HAnEuAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"96dde3e749c54383b3bfce391da7846e4ead7c445ecf5564591d184da7d416df","last_reissued_at":"2026-07-05T03:57:23.025505Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T03:57:23.025505Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Hall algebras and quantum symmetric pairs III: Quiver varieties","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG"],"primary_cat":"math.RT","authors_text":"Ming Lu, Weiqiang Wang","submitted_at":"2019-10-03T00:51:02Z","abstract_excerpt":"The $\\imath$quiver algebras were introduced recently by the authors to provide a Hall algebra realization of universal $\\imath$quantum groups, which is a generalization of Bridgeland's Hall algebra construction for (Drinfeld doubles of) quantum groups; here an $\\imath$quantum group and a corresponding Drinfeld-Jimbo quantum group form a quantum symmetric pair. In this paper, the Dynkin $\\imath$quiver algebras are shown to arise as new examples of singular Nakajima-Keller-Scherotzke categories. Then we provide a geometric construction of the universal $\\imath$quantum groups and their ``dual can"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1910.01263","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/1910.01263/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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1910.01263","created_at":"2026-07-05T03:57:23.025563+00:00"},{"alias_kind":"arxiv_version","alias_value":"1910.01263v3","created_at":"2026-07-05T03:57:23.025563+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1910.01263","created_at":"2026-07-05T03:57:23.025563+00:00"},{"alias_kind":"pith_short_12","alias_value":"S3O6HZ2JYVBY","created_at":"2026-07-05T03:57:23.025563+00:00"},{"alias_kind":"pith_short_16","alias_value":"S3O6HZ2JYVBYHM57","created_at":"2026-07-05T03:57:23.025563+00:00"},{"alias_kind":"pith_short_8","alias_value":"S3O6HZ2J","created_at":"2026-07-05T03:57:23.025563+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/S3O6HZ2JYVBYHM57ZY4R3J4ENZ","json":"https://pith.science/pith/S3O6HZ2JYVBYHM57ZY4R3J4ENZ.json","graph_json":"https://pith.science/api/pith-number/S3O6HZ2JYVBYHM57ZY4R3J4ENZ/graph.json","events_json":"https://pith.science/api/pith-number/S3O6HZ2JYVBYHM57ZY4R3J4ENZ/events.json","paper":"https://pith.science/paper/S3O6HZ2J"},"agent_actions":{"view_html":"https://pith.science/pith/S3O6HZ2JYVBYHM57ZY4R3J4ENZ","download_json":"https://pith.science/pith/S3O6HZ2JYVBYHM57ZY4R3J4ENZ.json","view_paper":"https://pith.science/paper/S3O6HZ2J","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1910.01263&json=true","fetch_graph":"https://pith.science/api/pith-number/S3O6HZ2JYVBYHM57ZY4R3J4ENZ/graph.json","fetch_events":"https://pith.science/api/pith-number/S3O6HZ2JYVBYHM57ZY4R3J4ENZ/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/S3O6HZ2JYVBYHM57ZY4R3J4ENZ/action/timestamp_anchor","attest_storage":"https://pith.science/pith/S3O6HZ2JYVBYHM57ZY4R3J4ENZ/action/storage_attestation","attest_author":"https://pith.science/pith/S3O6HZ2JYVBYHM57ZY4R3J4ENZ/action/author_attestation","sign_citation":"https://pith.science/pith/S3O6HZ2JYVBYHM57ZY4R3J4ENZ/action/citation_signature","submit_replication":"https://pith.science/pith/S3O6HZ2JYVBYHM57ZY4R3J4ENZ/action/replication_record"}},"created_at":"2026-07-05T03:57:23.025563+00:00","updated_at":"2026-07-05T03:57:23.025563+00:00"}