{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2021:XIDZBYLFVUFY65Q46OIG3KL6TM","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":"1f41e99b411d635b461853284c2d0ab2f1a011ea4b5a28f4351b37b040f58fa0","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2021-05-28T08:07:03Z","title_canon_sha256":"d7ce7bb93a99e318818fc52cf9ac911b2be9b7dd8635e5885dd966897f599f07"},"schema_version":"1.0","source":{"id":"2105.13657","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2105.13657","created_at":"2026-07-05T04:12:01Z"},{"alias_kind":"arxiv_version","alias_value":"2105.13657v2","created_at":"2026-07-05T04:12:01Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2105.13657","created_at":"2026-07-05T04:12:01Z"},{"alias_kind":"pith_short_12","alias_value":"XIDZBYLFVUFY","created_at":"2026-07-05T04:12:01Z"},{"alias_kind":"pith_short_16","alias_value":"XIDZBYLFVUFY65Q4","created_at":"2026-07-05T04:12:01Z"},{"alias_kind":"pith_short_8","alias_value":"XIDZBYLF","created_at":"2026-07-05T04:12:01Z"}],"graph_snapshots":[{"event_id":"sha256:17d66a7290ba817564d4fbf0e0ce65b22c662b51b2afda576b612399325fd75a","target":"graph","created_at":"2026-07-05T04:12:01Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2105.13657/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"In this paper, we introduce the notion of completely non-trivial module of a Lie conformal algebra. By this notion, we classify all finite irreducible modules of a class of $\\mathbb{Z}^+$-graded Lie conformal algebras $\\mathcal{L}=\\bigoplus_{i=0}^{\\infty} \\mathbb{C}[\\partial]L_i$ satisfying $ [{L_0}_\\lambda L_0]=(\\partial+2\\lambda)L_0,$ and $[{L_1}_\\lambda L_i]\\neq 0$ for any $i\\in \\mathbb{Z}^+$. These Lie conformal algebras include Block type Lie conformal algebra $\\mathcal{B}(p)$ and map Virasoro Lie conformal algebra $\\mathcal{V}(\\mathbb{C}[T])=Vir\\otimes \\mathbb{C}[T]$. As a result, we sho","authors_text":"Maosen Xu, Yanyong Hong","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2021-05-28T08:07:03Z","title":"Finite irreducible modules of a class of $\\mathbb{Z}^+$-graded Lie conformal algebras"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2105.13657","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":"sha256:0337be8950b66f0f15708d94f573cad2759fb65d645af06f8e82b2f5600cbbd6","target":"record","created_at":"2026-07-05T04:12:01Z","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":"1f41e99b411d635b461853284c2d0ab2f1a011ea4b5a28f4351b37b040f58fa0","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2021-05-28T08:07:03Z","title_canon_sha256":"d7ce7bb93a99e318818fc52cf9ac911b2be9b7dd8635e5885dd966897f599f07"},"schema_version":"1.0","source":{"id":"2105.13657","kind":"arxiv","version":2}},"canonical_sha256":"ba0790e165ad0b8f761cf3906da97e9b34acb7906a1fcb09f91d2d58ce327d14","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ba0790e165ad0b8f761cf3906da97e9b34acb7906a1fcb09f91d2d58ce327d14","first_computed_at":"2026-07-05T04:12:01.631865Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T04:12:01.631865Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ePGUG8mIYHYFxaeDvaVp96pU72KqYcAW3zbrl8tJ5uV9onj4MVabJ4sqSihw5M47GDF27x8sOgw/1CmiTVDmCg==","signature_status":"signed_v1","signed_at":"2026-07-05T04:12:01.632271Z","signed_message":"canonical_sha256_bytes"},"source_id":"2105.13657","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0337be8950b66f0f15708d94f573cad2759fb65d645af06f8e82b2f5600cbbd6","sha256:17d66a7290ba817564d4fbf0e0ce65b22c662b51b2afda576b612399325fd75a"],"state_sha256":"902bdb3d5a4f0139b3f55de5c507ca8095bddca24e92d5458af6ddde296cf933"}