{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:BYZ3NOUDGQD2KJH3VBSA52N7ML","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":"b90904426987bcb2909ac021c599ad3ab36e39b03c8c1707123d3e1200448351","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2014-03-07T09:54:14Z","title_canon_sha256":"042b13725f4dbfb97770aa27d0c3610f211875571e8a83082ec20330d0cb90e5"},"schema_version":"1.0","source":{"id":"1403.1700","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1403.1700","created_at":"2026-05-18T02:20:59Z"},{"alias_kind":"arxiv_version","alias_value":"1403.1700v1","created_at":"2026-05-18T02:20:59Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1403.1700","created_at":"2026-05-18T02:20:59Z"},{"alias_kind":"pith_short_12","alias_value":"BYZ3NOUDGQD2","created_at":"2026-05-18T12:28:22Z"},{"alias_kind":"pith_short_16","alias_value":"BYZ3NOUDGQD2KJH3","created_at":"2026-05-18T12:28:22Z"},{"alias_kind":"pith_short_8","alias_value":"BYZ3NOUD","created_at":"2026-05-18T12:28:22Z"}],"graph_snapshots":[{"event_id":"sha256:a4eb7ecca86a45ecce63595a45bc45c9c3eb62b32538251b429a9c253df73483","target":"graph","created_at":"2026-05-18T02:20:59Z","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":"We produce explicit generators of the classical W-algebras associated with the principal nilpotents in the simple Lie algebras of all classical types and in the exceptional Lie algebra of type $G_2$. The generators are given by determinant formulas in the context of the Poisson vertex algebras. We also show that the images of the W-algebra generators under the Chevalley-type isomorphism coincide with the elements defined via the corresponding Miura transformations.","authors_text":"A. I. Molev, E. Ragoucy","cross_cats":["math-ph","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2014-03-07T09:54:14Z","title":"Classical W-algebras in types A, B, C, D and G"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1403.1700","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:cb6756dc673c3b78ecb7cdee4396494fd00f0500bc27ec35696ce082988c90aa","target":"record","created_at":"2026-05-18T02:20:59Z","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":"b90904426987bcb2909ac021c599ad3ab36e39b03c8c1707123d3e1200448351","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2014-03-07T09:54:14Z","title_canon_sha256":"042b13725f4dbfb97770aa27d0c3610f211875571e8a83082ec20330d0cb90e5"},"schema_version":"1.0","source":{"id":"1403.1700","kind":"arxiv","version":1}},"canonical_sha256":"0e33b6ba833407a524fba8640ee9bf62db237dd7463144e8d5b9cb416ab42e04","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"0e33b6ba833407a524fba8640ee9bf62db237dd7463144e8d5b9cb416ab42e04","first_computed_at":"2026-05-18T02:20:59.452093Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:20:59.452093Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"LkCDlIUwkSyqmr6hNFthDSxsZpA2RJBfteEV+JmQYhQ774mZBLxt/8BOOHqrm2vyGdU0QnV0WmQvWFtP5DoECQ==","signature_status":"signed_v1","signed_at":"2026-05-18T02:20:59.452566Z","signed_message":"canonical_sha256_bytes"},"source_id":"1403.1700","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:cb6756dc673c3b78ecb7cdee4396494fd00f0500bc27ec35696ce082988c90aa","sha256:a4eb7ecca86a45ecce63595a45bc45c9c3eb62b32538251b429a9c253df73483"],"state_sha256":"63ac15d64ec9dd9098a0921fb56e38cd138f043d68361b60574c97f8a3161844"}