{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2005:LJ2HZNATCULIAGSEW5S2BXIFA2","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":"9eb03625eb13bb8920071f9d14c14931dfd13814aa04971fd1d42a2abe8e8b39","cross_cats_sorted":["math.MP","nlin.SI"],"license":"","primary_cat":"math-ph","submitted_at":"2005-11-16T20:33:34Z","title_canon_sha256":"bb058bc64ffa3321fffb06fa52fc1e713624ec1694f8227254dcc50c0f56297b"},"schema_version":"1.0","source":{"id":"math-ph/0511055","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math-ph/0511055","created_at":"2026-05-18T01:24:09Z"},{"alias_kind":"arxiv_version","alias_value":"math-ph/0511055v3","created_at":"2026-05-18T01:24:09Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math-ph/0511055","created_at":"2026-05-18T01:24:09Z"},{"alias_kind":"pith_short_12","alias_value":"LJ2HZNATCULI","created_at":"2026-05-18T12:25:53Z"},{"alias_kind":"pith_short_16","alias_value":"LJ2HZNATCULIAGSE","created_at":"2026-05-18T12:25:53Z"},{"alias_kind":"pith_short_8","alias_value":"LJ2HZNAT","created_at":"2026-05-18T12:25:53Z"}],"graph_snapshots":[{"event_id":"sha256:d00c75fbf5b0864345e4df8f532fd84963e0cf728a370fba443fc9e82beddf2b","target":"graph","created_at":"2026-05-18T01:24:09Z","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 Section 1 we review various equivalent definitions of a vertex algebra V. The main novelty here is the definition in terms of an indefinite integral of the lambda-bracket. In Section 2 we construct, in the most general framework, the Zhu algebra Zhu_G V, an associative algebra which \"controls\" G-twisted representations of the vertex algebra V with a given Hamiltonian operator H. An important special case of this construction is the H-twisted Zhu algebra Zhu_H V. In Section 3 we review the theory of non-linear Lie conformal algebras (respectively non-linear Lie algebras). Their universal env","authors_text":"Alberto De Sole, Victor Kac","cross_cats":["math.MP","nlin.SI"],"headline":"","license":"","primary_cat":"math-ph","submitted_at":"2005-11-16T20:33:34Z","title":"Finite vs. affine W-algebras"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math-ph/0511055","kind":"arxiv","version":3},"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:e69808e3afea1f81a767aac97f900e30d8506c8d2b903c578ccca3dbc4705b5e","target":"record","created_at":"2026-05-18T01:24:09Z","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":"9eb03625eb13bb8920071f9d14c14931dfd13814aa04971fd1d42a2abe8e8b39","cross_cats_sorted":["math.MP","nlin.SI"],"license":"","primary_cat":"math-ph","submitted_at":"2005-11-16T20:33:34Z","title_canon_sha256":"bb058bc64ffa3321fffb06fa52fc1e713624ec1694f8227254dcc50c0f56297b"},"schema_version":"1.0","source":{"id":"math-ph/0511055","kind":"arxiv","version":3}},"canonical_sha256":"5a747cb4131516801a44b765a0dd0506818871c6aa7782bad72633e2bb88783d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"5a747cb4131516801a44b765a0dd0506818871c6aa7782bad72633e2bb88783d","first_computed_at":"2026-05-18T01:24:09.249643Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:24:09.249643Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Hp8Wuf1880pTsmBddrfu8rkxZeOl7Mr7IWQbNK3i0/WR4BTIF6wa9T2vlN5tMbSUUpcz4QQP1ZWccp+whH0SBw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:24:09.250387Z","signed_message":"canonical_sha256_bytes"},"source_id":"math-ph/0511055","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e69808e3afea1f81a767aac97f900e30d8506c8d2b903c578ccca3dbc4705b5e","sha256:d00c75fbf5b0864345e4df8f532fd84963e0cf728a370fba443fc9e82beddf2b"],"state_sha256":"b1cf6a73b3e52fea146a91780d451bbbe3d02daba258104516b81abce07a0628"}