{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2013:PUIPSZCT5OGMIZ4D5M7L7XIN4V","short_pith_number":"pith:PUIPSZCT","schema_version":"1.0","canonical_sha256":"7d10f96453eb8cc46783eb3ebfdd0de546810dc58cbb72769fb3d837adca29e3","source":{"kind":"arxiv","id":"1311.0608","version":1},"attestation_state":"computed","paper":{"title":"The commutant of $L_{\\widehat{\\frak{sl}}_{2}}(n,0)$ in the vertex operator algebra $L_{\\widehat{\\frak{sl}}_{2}}(1,0)^{\\otimes n}$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.QA","authors_text":"Cuipo (Cuibo) Jiang, Zongzhu Lin","submitted_at":"2013-11-04T08:52:36Z","abstract_excerpt":"We study the commutant $L_{\\widehat{\\frak{sl}}_{2}}(n,0)^c$ of $L_{\\widehat{\\frak{sl}}_{2}}(n,0)$ in the vertex operator algebra $L_{\\widehat{\\frak{sl}}_{2}}(1,0)^{\\otimes n}$, for $n\\geq 2$. The main results include a complete classification of all irreducible $L_{\\widehat{\\frak{sl}}_{2}}(n,0)^c$-modules and a proof that $L_{\\widehat{\\frak{sl}}_{2}}(n,0)^c$ is a rational vertex operator algebra. As a consequence, every irreducible $L_{\\widehat{\\frak{sl}}_{2}}(n,0)^c$-module arises from the coset construction as conjectured in \\cite{LS}."},"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":"1311.0608","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2013-11-04T08:52:36Z","cross_cats_sorted":[],"title_canon_sha256":"d43aa7b99ee4a9f2b06299064360d838186a3c4b5cb4992c87ea4cdfcd83f485","abstract_canon_sha256":"46909bb3556cca7bdd97cf134623149f71e9970e91b56a087ba7279731eca2d7"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:08:05.353482Z","signature_b64":"MxAKDzDaBsmWwzQu3jyCYT1CNuykTLJwEpXxem68s49YUlg4b+e0I7El1Z3qm0q7KbDqdvm9xAe3CHMrUzUgAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7d10f96453eb8cc46783eb3ebfdd0de546810dc58cbb72769fb3d837adca29e3","last_reissued_at":"2026-05-18T03:08:05.353007Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:08:05.353007Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The commutant of $L_{\\widehat{\\frak{sl}}_{2}}(n,0)$ in the vertex operator algebra $L_{\\widehat{\\frak{sl}}_{2}}(1,0)^{\\otimes n}$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.QA","authors_text":"Cuipo (Cuibo) Jiang, Zongzhu Lin","submitted_at":"2013-11-04T08:52:36Z","abstract_excerpt":"We study the commutant $L_{\\widehat{\\frak{sl}}_{2}}(n,0)^c$ of $L_{\\widehat{\\frak{sl}}_{2}}(n,0)$ in the vertex operator algebra $L_{\\widehat{\\frak{sl}}_{2}}(1,0)^{\\otimes n}$, for $n\\geq 2$. The main results include a complete classification of all irreducible $L_{\\widehat{\\frak{sl}}_{2}}(n,0)^c$-modules and a proof that $L_{\\widehat{\\frak{sl}}_{2}}(n,0)^c$ is a rational vertex operator algebra. As a consequence, every irreducible $L_{\\widehat{\\frak{sl}}_{2}}(n,0)^c$-module arises from the coset construction as conjectured in \\cite{LS}."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1311.0608","kind":"arxiv","version":1},"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":"1311.0608","created_at":"2026-05-18T03:08:05.353073+00:00"},{"alias_kind":"arxiv_version","alias_value":"1311.0608v1","created_at":"2026-05-18T03:08:05.353073+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1311.0608","created_at":"2026-05-18T03:08:05.353073+00:00"},{"alias_kind":"pith_short_12","alias_value":"PUIPSZCT5OGM","created_at":"2026-05-18T12:27:57.521954+00:00"},{"alias_kind":"pith_short_16","alias_value":"PUIPSZCT5OGMIZ4D","created_at":"2026-05-18T12:27:57.521954+00:00"},{"alias_kind":"pith_short_8","alias_value":"PUIPSZCT","created_at":"2026-05-18T12:27:57.521954+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"2608.11308","citing_title":"A Comment On Topological Degeneracy In Gauged WZW Models","ref_index":251,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/PUIPSZCT5OGMIZ4D5M7L7XIN4V","json":"https://pith.science/pith/PUIPSZCT5OGMIZ4D5M7L7XIN4V.json","graph_json":"https://pith.science/api/pith-number/PUIPSZCT5OGMIZ4D5M7L7XIN4V/graph.json","events_json":"https://pith.science/api/pith-number/PUIPSZCT5OGMIZ4D5M7L7XIN4V/events.json","paper":"https://pith.science/paper/PUIPSZCT"},"agent_actions":{"view_html":"https://pith.science/pith/PUIPSZCT5OGMIZ4D5M7L7XIN4V","download_json":"https://pith.science/pith/PUIPSZCT5OGMIZ4D5M7L7XIN4V.json","view_paper":"https://pith.science/paper/PUIPSZCT","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1311.0608&json=true","fetch_graph":"https://pith.science/api/pith-number/PUIPSZCT5OGMIZ4D5M7L7XIN4V/graph.json","fetch_events":"https://pith.science/api/pith-number/PUIPSZCT5OGMIZ4D5M7L7XIN4V/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/PUIPSZCT5OGMIZ4D5M7L7XIN4V/action/timestamp_anchor","attest_storage":"https://pith.science/pith/PUIPSZCT5OGMIZ4D5M7L7XIN4V/action/storage_attestation","attest_author":"https://pith.science/pith/PUIPSZCT5OGMIZ4D5M7L7XIN4V/action/author_attestation","sign_citation":"https://pith.science/pith/PUIPSZCT5OGMIZ4D5M7L7XIN4V/action/citation_signature","submit_replication":"https://pith.science/pith/PUIPSZCT5OGMIZ4D5M7L7XIN4V/action/replication_record"}},"created_at":"2026-05-18T03:08:05.353073+00:00","updated_at":"2026-05-18T03:08:05.353073+00:00"}