{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2016:VXDJA5FM7E2YNEALZBQE2ULP3X","short_pith_number":"pith:VXDJA5FM","schema_version":"1.0","canonical_sha256":"adc69074acf93586900bc8604d516fddcabb64911b7f1e20a6af370b47bce200","source":{"kind":"arxiv","id":"1607.00271","version":3},"attestation_state":"computed","paper":{"title":"A cluster realization of $U_q(\\mathfrak{sl_n})$ from quantum character varieties","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.CO","math.MP","math.RT"],"primary_cat":"math.QA","authors_text":"Alexander Shapiro, Gus Schrader","submitted_at":"2016-07-01T14:54:55Z","abstract_excerpt":"We construct an injective algebra homomorphism of the quantum group $U_q(\\mathfrak{sl}_{n+1})$ into a quantum cluster algebra $\\mathbf{L}_n$ associated to the moduli space of framed $PGL_{n+1}$-local systems on a marked punctured disk. We obtain a description of the coproduct of $U_q(\\mathfrak{sl}_{n+1})$ in terms of the corresponding quantum cluster algebra associated to the marked twice punctured disk, and express the action of the $R$-matrix in terms of a mapping class group element corresponding to the half-Dehn twist rotating one puncture about the other. As a consequence, we realize the "},"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":"1607.00271","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2016-07-01T14:54:55Z","cross_cats_sorted":["math-ph","math.CO","math.MP","math.RT"],"title_canon_sha256":"0381eff561fa10137950b6ba9acf73b15e15ee9efcb7a25c087ce770885ee230","abstract_canon_sha256":"55b794aa73fc304cdcfb4ffc290cd7e99d57193b3e97f462e717255ebfd36984"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:56:39.177001Z","signature_b64":"B6nUA8iBJFoyPEiLKuwjAQ9Zn8bM6aa20V2U6OPYpyy4LPUFabVOOtwX3/5HDR9FBbM6fAT0Ckg4YHRxrYCgAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"adc69074acf93586900bc8604d516fddcabb64911b7f1e20a6af370b47bce200","last_reissued_at":"2026-05-17T23:56:39.176353Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:56:39.176353Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A cluster realization of $U_q(\\mathfrak{sl_n})$ from quantum character varieties","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.CO","math.MP","math.RT"],"primary_cat":"math.QA","authors_text":"Alexander Shapiro, Gus Schrader","submitted_at":"2016-07-01T14:54:55Z","abstract_excerpt":"We construct an injective algebra homomorphism of the quantum group $U_q(\\mathfrak{sl}_{n+1})$ into a quantum cluster algebra $\\mathbf{L}_n$ associated to the moduli space of framed $PGL_{n+1}$-local systems on a marked punctured disk. We obtain a description of the coproduct of $U_q(\\mathfrak{sl}_{n+1})$ in terms of the corresponding quantum cluster algebra associated to the marked twice punctured disk, and express the action of the $R$-matrix in terms of a mapping class group element corresponding to the half-Dehn twist rotating one puncture about the other. As a consequence, we realize the "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1607.00271","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1607.00271","created_at":"2026-05-17T23:56:39.176455+00:00"},{"alias_kind":"arxiv_version","alias_value":"1607.00271v3","created_at":"2026-05-17T23:56:39.176455+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1607.00271","created_at":"2026-05-17T23:56:39.176455+00:00"},{"alias_kind":"pith_short_12","alias_value":"VXDJA5FM7E2Y","created_at":"2026-05-18T12:30:48.956258+00:00"},{"alias_kind":"pith_short_16","alias_value":"VXDJA5FM7E2YNEAL","created_at":"2026-05-18T12:30:48.956258+00:00"},{"alias_kind":"pith_short_8","alias_value":"VXDJA5FM","created_at":"2026-05-18T12:30:48.956258+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"2509.02354","citing_title":"The holonomy braiding for $\\mathcal{U}_\\xi(\\mathfrak{sl}_2)$ in terms of geometric quantum dilogarithms","ref_index":30,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/VXDJA5FM7E2YNEALZBQE2ULP3X","json":"https://pith.science/pith/VXDJA5FM7E2YNEALZBQE2ULP3X.json","graph_json":"https://pith.science/api/pith-number/VXDJA5FM7E2YNEALZBQE2ULP3X/graph.json","events_json":"https://pith.science/api/pith-number/VXDJA5FM7E2YNEALZBQE2ULP3X/events.json","paper":"https://pith.science/paper/VXDJA5FM"},"agent_actions":{"view_html":"https://pith.science/pith/VXDJA5FM7E2YNEALZBQE2ULP3X","download_json":"https://pith.science/pith/VXDJA5FM7E2YNEALZBQE2ULP3X.json","view_paper":"https://pith.science/paper/VXDJA5FM","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1607.00271&json=true","fetch_graph":"https://pith.science/api/pith-number/VXDJA5FM7E2YNEALZBQE2ULP3X/graph.json","fetch_events":"https://pith.science/api/pith-number/VXDJA5FM7E2YNEALZBQE2ULP3X/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/VXDJA5FM7E2YNEALZBQE2ULP3X/action/timestamp_anchor","attest_storage":"https://pith.science/pith/VXDJA5FM7E2YNEALZBQE2ULP3X/action/storage_attestation","attest_author":"https://pith.science/pith/VXDJA5FM7E2YNEALZBQE2ULP3X/action/author_attestation","sign_citation":"https://pith.science/pith/VXDJA5FM7E2YNEALZBQE2ULP3X/action/citation_signature","submit_replication":"https://pith.science/pith/VXDJA5FM7E2YNEALZBQE2ULP3X/action/replication_record"}},"created_at":"2026-05-17T23:56:39.176455+00:00","updated_at":"2026-05-17T23:56:39.176455+00:00"}