{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:5T6DAZM3LP3XHHSXZ243W4QLMR","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":"82b7d827dbe50eddb3336e51d6b1c1c9a99bdcbccc075a7d5c74763c827b6be6","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2012-10-26T13:08:18Z","title_canon_sha256":"d530dc7c9cf5dae29b8cc2ab27e0c0ee9aac647140a76dd67a8d4f1ca07ff424"},"schema_version":"1.0","source":{"id":"1210.7132","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1210.7132","created_at":"2026-05-18T03:42:12Z"},{"alias_kind":"arxiv_version","alias_value":"1210.7132v1","created_at":"2026-05-18T03:42:12Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1210.7132","created_at":"2026-05-18T03:42:12Z"},{"alias_kind":"pith_short_12","alias_value":"5T6DAZM3LP3X","created_at":"2026-05-18T12:26:56Z"},{"alias_kind":"pith_short_16","alias_value":"5T6DAZM3LP3XHHSX","created_at":"2026-05-18T12:26:56Z"},{"alias_kind":"pith_short_8","alias_value":"5T6DAZM3","created_at":"2026-05-18T12:26:56Z"}],"graph_snapshots":[{"event_id":"sha256:879344c3bbe07fb0ebef8e64191251f67e786a6d3acc47849ce522046462ada0","target":"graph","created_at":"2026-05-18T03:42:12Z","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":"A well-known theorem of Mathieu's states that a Harish-chandra module over the Virasoro algebra is either a highest weight module, a lowest weight module or a module of the intermediate series. It is proved in this paper that an analogous result also holds for the Lie algebra $\\BB$ related to Block type, with basis {L_{\\a,i},C|a,i\\in\\Z, i\\ge0} and relations [L_{\\a,i},L_{\\b,j}]=((i+1)\\b-(j+1)\\a)L_{\\a+\\b,i+j}+\\d_{\\a+\\b,0}\\d_{i+j,0}\\frac{\\a^3-\\a}{6}C, [C,L_{\\a,i}]=0.Namely, an irreducible quasifinite $\\BB$-module is either a highest weight module, a lowest weight module or a module of the interme","authors_text":"Chunguang Xia, Ying Xu, Yucai Su","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2012-10-26T13:08:18Z","title":"Classification of quasifinite representations of a Lie algebra related to Block type"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1210.7132","kind":"arxiv","version":1},"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:c1e5760a55b3b2550f0d8b86417ce5c10bda1809883c0cf60880a6c648848f1e","target":"record","created_at":"2026-05-18T03:42:12Z","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":"82b7d827dbe50eddb3336e51d6b1c1c9a99bdcbccc075a7d5c74763c827b6be6","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2012-10-26T13:08:18Z","title_canon_sha256":"d530dc7c9cf5dae29b8cc2ab27e0c0ee9aac647140a76dd67a8d4f1ca07ff424"},"schema_version":"1.0","source":{"id":"1210.7132","kind":"arxiv","version":1}},"canonical_sha256":"ecfc30659b5bf7739e57ceb9bb720b645a9ad77cc175d883770fbd77dafbea0f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ecfc30659b5bf7739e57ceb9bb720b645a9ad77cc175d883770fbd77dafbea0f","first_computed_at":"2026-05-18T03:42:12.633579Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:42:12.633579Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"BmtqC5DDQWwMP+HDnNoWhfnQ1OVNLVdO01+2XzT1jRM7NadppskYmjP+w+8AqNo/zRgWYfSQsxolkWc5qy5QCg==","signature_status":"signed_v1","signed_at":"2026-05-18T03:42:12.634374Z","signed_message":"canonical_sha256_bytes"},"source_id":"1210.7132","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c1e5760a55b3b2550f0d8b86417ce5c10bda1809883c0cf60880a6c648848f1e","sha256:879344c3bbe07fb0ebef8e64191251f67e786a6d3acc47849ce522046462ada0"],"state_sha256":"9851bf897719d033a9a165f3985510766150b1b41c6919d27ce4b4d18260deb8"}