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We first construct an $(r+1)$-toroidal vertex algebra $V(T,0)$ and show that the category of restricted $L_{r}(\\hat{\\frak{g}})$-modules is canonically isomorphic to that of $V(T,0)$-modules.Let $c$ denote the standard central element of $\\hat{\\frak{g}}$ and set $S"},"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":"1408.0579","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2014-08-04T04:07:11Z","cross_cats_sorted":["math.RT"],"title_canon_sha256":"3ab5676cb51cd54dcddc034c2a66132577416d150c2c020acbe2072962781197","abstract_canon_sha256":"6e76091617e171f7284f71893f5b87d713e28068f8d79167fa4f3816ae18e543"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:45:56.752531Z","signature_b64":"8WBLITnj6jDDTZdd0aeFBSwTe/lho8sIC+G4BaBSp2I1kseiE29WaP3BEv3zTVBaOTPFlrYJfW+tUj+tnd9UBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f477999196b107f5f035cec2f134d9db82043ac8a506903131752e4af7ef245b","last_reissued_at":"2026-05-18T02:45:56.752054Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:45:56.752054Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Simple Toroidal Vertex Algebras and Their Irreducible Modules","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.RT"],"primary_cat":"math.QA","authors_text":"Fei Kong, Haisheng Li, Qing Wang, Shaobin Tan","submitted_at":"2014-08-04T04:07:11Z","abstract_excerpt":"In this paper, we continue the study on toroidal vertex algebras initiated in \\cite{LTW}, to study concrete toroidal vertex algebras associated to toroidal Lie algebra $L_{r}(\\hat{\\frak{g}})=\\hat{\\frak{g}}\\otimes L_r$, where $\\hat{\\frak{g}}$ is an untwisted affine Lie algebra and $L_r=$\\mathbb{C}[t_{1}^{\\pm 1},\\ldots,t_{r}^{\\pm 1}]$. We first construct an $(r+1)$-toroidal vertex algebra $V(T,0)$ and show that the category of restricted $L_{r}(\\hat{\\frak{g}})$-modules is canonically isomorphic to that of $V(T,0)$-modules.Let $c$ denote the standard central element of $\\hat{\\frak{g}}$ and set $S"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1408.0579","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":"1408.0579","created_at":"2026-05-18T02:45:56.752127+00:00"},{"alias_kind":"arxiv_version","alias_value":"1408.0579v1","created_at":"2026-05-18T02:45:56.752127+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1408.0579","created_at":"2026-05-18T02:45:56.752127+00:00"},{"alias_kind":"pith_short_12","alias_value":"6R3ZTEMWWED7","created_at":"2026-05-18T12:28:16.859392+00:00"},{"alias_kind":"pith_short_16","alias_value":"6R3ZTEMWWED7L4BV","created_at":"2026-05-18T12:28:16.859392+00:00"},{"alias_kind":"pith_short_8","alias_value":"6R3ZTEMW","created_at":"2026-05-18T12:28:16.859392+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/6R3ZTEMWWED7L4BVZ3BPCNGZ3O","json":"https://pith.science/pith/6R3ZTEMWWED7L4BVZ3BPCNGZ3O.json","graph_json":"https://pith.science/api/pith-number/6R3ZTEMWWED7L4BVZ3BPCNGZ3O/graph.json","events_json":"https://pith.science/api/pith-number/6R3ZTEMWWED7L4BVZ3BPCNGZ3O/events.json","paper":"https://pith.science/paper/6R3ZTEMW"},"agent_actions":{"view_html":"https://pith.science/pith/6R3ZTEMWWED7L4BVZ3BPCNGZ3O","download_json":"https://pith.science/pith/6R3ZTEMWWED7L4BVZ3BPCNGZ3O.json","view_paper":"https://pith.science/paper/6R3ZTEMW","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1408.0579&json=true","fetch_graph":"https://pith.science/api/pith-number/6R3ZTEMWWED7L4BVZ3BPCNGZ3O/graph.json","fetch_events":"https://pith.science/api/pith-number/6R3ZTEMWWED7L4BVZ3BPCNGZ3O/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/6R3ZTEMWWED7L4BVZ3BPCNGZ3O/action/timestamp_anchor","attest_storage":"https://pith.science/pith/6R3ZTEMWWED7L4BVZ3BPCNGZ3O/action/storage_attestation","attest_author":"https://pith.science/pith/6R3ZTEMWWED7L4BVZ3BPCNGZ3O/action/author_attestation","sign_citation":"https://pith.science/pith/6R3ZTEMWWED7L4BVZ3BPCNGZ3O/action/citation_signature","submit_replication":"https://pith.science/pith/6R3ZTEMWWED7L4BVZ3BPCNGZ3O/action/replication_record"}},"created_at":"2026-05-18T02:45:56.752127+00:00","updated_at":"2026-05-18T02:45:56.752127+00:00"}