{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2024:TOK7CIAI6ENYXJIHJR5KBR45JQ","short_pith_number":"pith:TOK7CIAI","schema_version":"1.0","canonical_sha256":"9b95f12008f11b8ba5074c7aa0c79d4c00535202c8718bcbf9207c7ea2b12d06","source":{"kind":"arxiv","id":"2403.05167","version":2},"attestation_state":"computed","paper":{"title":"Quantum duality principle and quantum symmetric pairs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.RT"],"primary_cat":"math.QA","authors_text":"Jinfeng Song","submitted_at":"2024-03-08T09:13:27Z","abstract_excerpt":"The quantum duality principal (QDP) by Drinfeld predicts a connection between the quantized universial enveloping algebras and the quantized coordinate algebras, where the underlying classical objects are related by the duality in Poisson geometry. The current paper gives an explicit formulization of the QDP for quantum symmetric pairs.\n  Let $\\mathfrak{g}$ be a complex semi-simple Lie algebra, equipped with the standard Lie bialgebra structure. Let $\\theta$ be a Lie algebra involution on $\\mathfrak{g}$ and denote by $\\mathfrak{k}=\\mathfrak{g}^\\theta$ the fixed point subalgebra. The quantum sy"},"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":"2403.05167","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2024-03-08T09:13:27Z","cross_cats_sorted":["math.RT"],"title_canon_sha256":"92b1fb678ac12f3e64f803dcda72825dd39a0399d6c4d81f0173a0bf5ebc6b19","abstract_canon_sha256":"f7c78a6d97ba86343fcd589743d3e8cebcc043e7939449b50a372c39a2d1f603"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T09:10:45.896431Z","signature_b64":"cOC00RjtE2e0TgqzZ+lelPvltMkrazayk04GXrCn5tl0cStT6am6/WdM/EwN8jJKw28mGK0kz5JqakEhzBi/Cw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9b95f12008f11b8ba5074c7aa0c79d4c00535202c8718bcbf9207c7ea2b12d06","last_reissued_at":"2026-07-05T09:10:45.896021Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T09:10:45.896021Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Quantum duality principle and quantum symmetric pairs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.RT"],"primary_cat":"math.QA","authors_text":"Jinfeng Song","submitted_at":"2024-03-08T09:13:27Z","abstract_excerpt":"The quantum duality principal (QDP) by Drinfeld predicts a connection between the quantized universial enveloping algebras and the quantized coordinate algebras, where the underlying classical objects are related by the duality in Poisson geometry. The current paper gives an explicit formulization of the QDP for quantum symmetric pairs.\n  Let $\\mathfrak{g}$ be a complex semi-simple Lie algebra, equipped with the standard Lie bialgebra structure. Let $\\theta$ be a Lie algebra involution on $\\mathfrak{g}$ and denote by $\\mathfrak{k}=\\mathfrak{g}^\\theta$ the fixed point subalgebra. The quantum sy"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2403.05167","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/2403.05167/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":"2403.05167","created_at":"2026-07-05T09:10:45.896084+00:00"},{"alias_kind":"arxiv_version","alias_value":"2403.05167v2","created_at":"2026-07-05T09:10:45.896084+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2403.05167","created_at":"2026-07-05T09:10:45.896084+00:00"},{"alias_kind":"pith_short_12","alias_value":"TOK7CIAI6ENY","created_at":"2026-07-05T09:10:45.896084+00:00"},{"alias_kind":"pith_short_16","alias_value":"TOK7CIAI6ENYXJIH","created_at":"2026-07-05T09:10:45.896084+00:00"},{"alias_kind":"pith_short_8","alias_value":"TOK7CIAI","created_at":"2026-07-05T09:10:45.896084+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"2507.09456","citing_title":"Braid group symmetries on Poisson algebras arising from quantum symmetric pairs","ref_index":37,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/TOK7CIAI6ENYXJIHJR5KBR45JQ","json":"https://pith.science/pith/TOK7CIAI6ENYXJIHJR5KBR45JQ.json","graph_json":"https://pith.science/api/pith-number/TOK7CIAI6ENYXJIHJR5KBR45JQ/graph.json","events_json":"https://pith.science/api/pith-number/TOK7CIAI6ENYXJIHJR5KBR45JQ/events.json","paper":"https://pith.science/paper/TOK7CIAI"},"agent_actions":{"view_html":"https://pith.science/pith/TOK7CIAI6ENYXJIHJR5KBR45JQ","download_json":"https://pith.science/pith/TOK7CIAI6ENYXJIHJR5KBR45JQ.json","view_paper":"https://pith.science/paper/TOK7CIAI","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2403.05167&json=true","fetch_graph":"https://pith.science/api/pith-number/TOK7CIAI6ENYXJIHJR5KBR45JQ/graph.json","fetch_events":"https://pith.science/api/pith-number/TOK7CIAI6ENYXJIHJR5KBR45JQ/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/TOK7CIAI6ENYXJIHJR5KBR45JQ/action/timestamp_anchor","attest_storage":"https://pith.science/pith/TOK7CIAI6ENYXJIHJR5KBR45JQ/action/storage_attestation","attest_author":"https://pith.science/pith/TOK7CIAI6ENYXJIHJR5KBR45JQ/action/author_attestation","sign_citation":"https://pith.science/pith/TOK7CIAI6ENYXJIHJR5KBR45JQ/action/citation_signature","submit_replication":"https://pith.science/pith/TOK7CIAI6ENYXJIHJR5KBR45JQ/action/replication_record"}},"created_at":"2026-07-05T09:10:45.896084+00:00","updated_at":"2026-07-05T09:10:45.896084+00:00"}