{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2005:LJ2HZNATCULIAGSEW5S2BXIFA2","short_pith_number":"pith:LJ2HZNAT","canonical_record":{"source":{"id":"math-ph/0511055","kind":"arxiv","version":3},"metadata":{"license":"","primary_cat":"math-ph","submitted_at":"2005-11-16T20:33:34Z","cross_cats_sorted":["math.MP","nlin.SI"],"title_canon_sha256":"bb058bc64ffa3321fffb06fa52fc1e713624ec1694f8227254dcc50c0f56297b","abstract_canon_sha256":"9eb03625eb13bb8920071f9d14c14931dfd13814aa04971fd1d42a2abe8e8b39"},"schema_version":"1.0"},"canonical_sha256":"5a747cb4131516801a44b765a0dd0506818871c6aa7782bad72633e2bb88783d","source":{"kind":"arxiv","id":"math-ph/0511055","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"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2005:LJ2HZNATCULIAGSEW5S2BXIFA2","target":"record","payload":{"canonical_record":{"source":{"id":"math-ph/0511055","kind":"arxiv","version":3},"metadata":{"license":"","primary_cat":"math-ph","submitted_at":"2005-11-16T20:33:34Z","cross_cats_sorted":["math.MP","nlin.SI"],"title_canon_sha256":"bb058bc64ffa3321fffb06fa52fc1e713624ec1694f8227254dcc50c0f56297b","abstract_canon_sha256":"9eb03625eb13bb8920071f9d14c14931dfd13814aa04971fd1d42a2abe8e8b39"},"schema_version":"1.0"},"canonical_sha256":"5a747cb4131516801a44b765a0dd0506818871c6aa7782bad72633e2bb88783d","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:24:09.250387Z","signature_b64":"Hp8Wuf1880pTsmBddrfu8rkxZeOl7Mr7IWQbNK3i0/WR4BTIF6wa9T2vlN5tMbSUUpcz4QQP1ZWccp+whH0SBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5a747cb4131516801a44b765a0dd0506818871c6aa7782bad72633e2bb88783d","last_reissued_at":"2026-05-18T01:24:09.249643Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:24:09.249643Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"math-ph/0511055","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:24:09Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"nQANX9Gb4XdDARVX5DM50UUljkUzeQjFB+uE9ZanBQ35Fy0Ew8xTUR4+cHz2q1u6AiNrwekjnd7g9Wg0DSlrDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-04T15:04:13.348425Z"},"content_sha256":"e69808e3afea1f81a767aac97f900e30d8506c8d2b903c578ccca3dbc4705b5e","schema_version":"1.0","event_id":"sha256:e69808e3afea1f81a767aac97f900e30d8506c8d2b903c578ccca3dbc4705b5e"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2005:LJ2HZNATCULIAGSEW5S2BXIFA2","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Finite vs. affine W-algebras","license":"","headline":"","cross_cats":["math.MP","nlin.SI"],"primary_cat":"math-ph","authors_text":"Alberto De Sole, Victor Kac","submitted_at":"2005-11-16T20:33:34Z","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"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math-ph/0511055","kind":"arxiv","version":3},"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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:24:09Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"x1FXqCd8j4qz32kKCX+7TnAWsxrJCjZlOanAuUG2WDVOjN5FgBy0JHePd3FkN+lD31SDGDAvtXgzTNHFm5oQCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-04T15:04:13.349080Z"},"content_sha256":"d00c75fbf5b0864345e4df8f532fd84963e0cf728a370fba443fc9e82beddf2b","schema_version":"1.0","event_id":"sha256:d00c75fbf5b0864345e4df8f532fd84963e0cf728a370fba443fc9e82beddf2b"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/LJ2HZNATCULIAGSEW5S2BXIFA2/bundle.json","state_url":"https://pith.science/pith/LJ2HZNATCULIAGSEW5S2BXIFA2/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/LJ2HZNATCULIAGSEW5S2BXIFA2/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-06-04T15:04:13Z","links":{"resolver":"https://pith.science/pith/LJ2HZNATCULIAGSEW5S2BXIFA2","bundle":"https://pith.science/pith/LJ2HZNATCULIAGSEW5S2BXIFA2/bundle.json","state":"https://pith.science/pith/LJ2HZNATCULIAGSEW5S2BXIFA2/state.json","well_known_bundle":"https://pith.science/.well-known/pith/LJ2HZNATCULIAGSEW5S2BXIFA2/bundle.json"},"state":{"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"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"azjzWXMtc5So+tGCSKspay5Yp+08Jvz7aNVLvJHSGxLrRwEifqQHUl+mzSAnm84XiKePPgsoNWfuorrqfJfPAg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-04T15:04:13.351914Z","bundle_sha256":"9d46134fd0cf0a042e439fcd92b2db27863020a9662548868cdf4e3a79d392bb"}}