{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:YM33ITJQ7IS5JENIYPPLBJYKIQ","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"ae1c044da532c3b5b3051c9f03cd2173bee63b3765523a630040e3b1329d34c7","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2017-11-03T00:41:56Z","title_canon_sha256":"367088a189dd1b2563acbe96fa35c921611be374f24233f2f1aa6d258979cf9c"},"schema_version":"1.0","source":{"id":"1711.00985","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1711.00985","created_at":"2026-05-18T00:31:18Z"},{"alias_kind":"arxiv_version","alias_value":"1711.00985v2","created_at":"2026-05-18T00:31:18Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1711.00985","created_at":"2026-05-18T00:31:18Z"},{"alias_kind":"pith_short_12","alias_value":"YM33ITJQ7IS5","created_at":"2026-05-18T12:31:56Z"},{"alias_kind":"pith_short_16","alias_value":"YM33ITJQ7IS5JENI","created_at":"2026-05-18T12:31:56Z"},{"alias_kind":"pith_short_8","alias_value":"YM33ITJQ","created_at":"2026-05-18T12:31:56Z"}],"graph_snapshots":[{"event_id":"sha256:208ae758b19d1b8486992ab4a84300a098234d5d77ac9420eb6fe636b67de6f6","target":"graph","created_at":"2026-05-18T00:31:18Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"In this paper, we study Virasoro vertex algebras and affine vertex algebras over a general field of characteristic $p>2$. More specifically, we study certain quotients of the universal Virasoro and affine vertex algebras by ideals related to the $p$-centers of the Virasoro algebra and affine Lie algebras. Among the main results, we classify their irreducible $\\mathbb{N}$-graded modules by explicitly determining their Zhu algebras and show that these vertex algebras have only finitely many irreducible $\\mathbb{N}$-graded modules and they are $C_2$-cofinite.","authors_text":"Haisheng Li, Qiang Mu, Xiangyu Jiao","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2017-11-03T00:41:56Z","title":"Modular Virasoro Vertex Algebras and Affine Vertex Algebras"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1711.00985","kind":"arxiv","version":2},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:d9cd429c272b5602b62a2583dc2b892afa22f0fa736f7eb77537c7a4a4b46ae1","target":"record","created_at":"2026-05-18T00:31:18Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"ae1c044da532c3b5b3051c9f03cd2173bee63b3765523a630040e3b1329d34c7","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2017-11-03T00:41:56Z","title_canon_sha256":"367088a189dd1b2563acbe96fa35c921611be374f24233f2f1aa6d258979cf9c"},"schema_version":"1.0","source":{"id":"1711.00985","kind":"arxiv","version":2}},"canonical_sha256":"c337b44d30fa25d491a8c3deb0a70a441e633d185af2d17afab994456764914f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c337b44d30fa25d491a8c3deb0a70a441e633d185af2d17afab994456764914f","first_computed_at":"2026-05-18T00:31:18.332951Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:31:18.332951Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"O59GAAy2AODDoZgfPVQ+Kwj5xfRK7VFJ3OCSd+yhAvo0xzaf3wbN2ohpA/A8HHCqN/pr4brs5As2h4n3h4hxBA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:31:18.333554Z","signed_message":"canonical_sha256_bytes"},"source_id":"1711.00985","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d9cd429c272b5602b62a2583dc2b892afa22f0fa736f7eb77537c7a4a4b46ae1","sha256:208ae758b19d1b8486992ab4a84300a098234d5d77ac9420eb6fe636b67de6f6"],"state_sha256":"f57ab6eb57925db9fb311d950696cbd8f8bdb35dbe716ff0afb7c8e7d04b8b68"}