{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:1993:ELOCXAVMUQARWQSEVGD7NLXZB2","short_pith_number":"pith:ELOCXAVM","canonical_record":{"source":{"id":"hep-th/9307170","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"hep-th","submitted_at":"1993-07-28T10:20:14Z","cross_cats_sorted":[],"title_canon_sha256":"bcfc48bdf560a5619acb6aec6ee75a0128f17297138a8ac9ee432fc9d11c65e9","abstract_canon_sha256":"0bd3a13e9544f64bc13ffedaeaff649c9b5a3b39d94bd40b3646a1ba985ca644"},"schema_version":"1.0"},"canonical_sha256":"22dc2b82aca4011b4244a987f6aef90ea04e42246f941127944cce4a68d9dd82","source":{"kind":"arxiv","id":"hep-th/9307170","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"hep-th/9307170","created_at":"2026-05-18T01:06:04Z"},{"alias_kind":"arxiv_version","alias_value":"hep-th/9307170v1","created_at":"2026-05-18T01:06:04Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.hep-th/9307170","created_at":"2026-05-18T01:06:04Z"},{"alias_kind":"pith_short_12","alias_value":"ELOCXAVMUQAR","created_at":"2026-05-18T12:25:47Z"},{"alias_kind":"pith_short_16","alias_value":"ELOCXAVMUQARWQSE","created_at":"2026-05-18T12:25:47Z"},{"alias_kind":"pith_short_8","alias_value":"ELOCXAVM","created_at":"2026-05-18T12:25:47Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:1993:ELOCXAVMUQARWQSEVGD7NLXZB2","target":"record","payload":{"canonical_record":{"source":{"id":"hep-th/9307170","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"hep-th","submitted_at":"1993-07-28T10:20:14Z","cross_cats_sorted":[],"title_canon_sha256":"bcfc48bdf560a5619acb6aec6ee75a0128f17297138a8ac9ee432fc9d11c65e9","abstract_canon_sha256":"0bd3a13e9544f64bc13ffedaeaff649c9b5a3b39d94bd40b3646a1ba985ca644"},"schema_version":"1.0"},"canonical_sha256":"22dc2b82aca4011b4244a987f6aef90ea04e42246f941127944cce4a68d9dd82","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:06:04.821262Z","signature_b64":"sCu+myxr1dH1/IxWwi9PjVf/VB8PxOsUmRkseKnxncostvbfNkSb2/KtPibhciRm45TxG3ZvcNLGF0QfP1qdDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"22dc2b82aca4011b4244a987f6aef90ea04e42246f941127944cce4a68d9dd82","last_reissued_at":"2026-05-18T01:06:04.820544Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:06:04.820544Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"hep-th/9307170","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:06:04Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"VI9XPFHcohsc7iWaIL7FSP74fNrE0/UauDv/fOTMezliddfDQGWsIvKJGYFrzUYetDcJixeJSJQLx0+BI3g6Cg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T15:40:07.379224Z"},"content_sha256":"0bdb189c28edf2d85bee9f766eee90b137f9f00402e1c5d5fc279831a315e5c6","schema_version":"1.0","event_id":"sha256:0bdb189c28edf2d85bee9f766eee90b137f9f00402e1c5d5fc279831a315e5c6"},{"event_type":"graph_snapshot","subject_pith_number":"pith:1993:ELOCXAVMUQARWQSEVGD7NLXZB2","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Classification of Structure Constants for W-algebras from Highest Weights","license":"","headline":"","cross_cats":[],"primary_cat":"hep-th","authors_text":"K. Hornfeck","submitted_at":"1993-07-28T10:20:14Z","abstract_excerpt":"We show that the structure constants of W-algebras can be grouped according to the lowest (bosonic) spin(s) of the algebra. The structure constants in each group are described by a unique formula, depending on a functional parameter h(c) that is characteristic for each algebra. As examples we give the structure constants C_{33}^4 and C_{44}^4 for the algebras of type W(2,3,4,...) (that include the WA_{n-1}-algebras) and the structure constant C_{44}^4 for the algebras of type W(2,4,...), especially for all the algebras WD_n, WB(0,n), WB_n and WC_n. It also includes the bosonic projection of th"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"hep-th/9307170","kind":"arxiv","version":1},"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":"2026-05-18T01:06:04Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"JRWZi1RNDNqVFIXMTRhld7GVjuYIskPbIJTaZIzRddb2bIpp80o3hD8krEsbOhhd89jZIvk1XxAYZgGaBm7mDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T15:40:07.379591Z"},"content_sha256":"dbd505a25afadc4c1ea97c1a8ac0ea3a691e317cadfee305f3f5b9edaafa83e8","schema_version":"1.0","event_id":"sha256:dbd505a25afadc4c1ea97c1a8ac0ea3a691e317cadfee305f3f5b9edaafa83e8"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/ELOCXAVMUQARWQSEVGD7NLXZB2/bundle.json","state_url":"https://pith.science/pith/ELOCXAVMUQARWQSEVGD7NLXZB2/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/ELOCXAVMUQARWQSEVGD7NLXZB2/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":"2026-06-02T15:40:07Z","links":{"resolver":"https://pith.science/pith/ELOCXAVMUQARWQSEVGD7NLXZB2","bundle":"https://pith.science/pith/ELOCXAVMUQARWQSEVGD7NLXZB2/bundle.json","state":"https://pith.science/pith/ELOCXAVMUQARWQSEVGD7NLXZB2/state.json","well_known_bundle":"https://pith.science/.well-known/pith/ELOCXAVMUQARWQSEVGD7NLXZB2/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:1993:ELOCXAVMUQARWQSEVGD7NLXZB2","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":"0bd3a13e9544f64bc13ffedaeaff649c9b5a3b39d94bd40b3646a1ba985ca644","cross_cats_sorted":[],"license":"","primary_cat":"hep-th","submitted_at":"1993-07-28T10:20:14Z","title_canon_sha256":"bcfc48bdf560a5619acb6aec6ee75a0128f17297138a8ac9ee432fc9d11c65e9"},"schema_version":"1.0","source":{"id":"hep-th/9307170","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"hep-th/9307170","created_at":"2026-05-18T01:06:04Z"},{"alias_kind":"arxiv_version","alias_value":"hep-th/9307170v1","created_at":"2026-05-18T01:06:04Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.hep-th/9307170","created_at":"2026-05-18T01:06:04Z"},{"alias_kind":"pith_short_12","alias_value":"ELOCXAVMUQAR","created_at":"2026-05-18T12:25:47Z"},{"alias_kind":"pith_short_16","alias_value":"ELOCXAVMUQARWQSE","created_at":"2026-05-18T12:25:47Z"},{"alias_kind":"pith_short_8","alias_value":"ELOCXAVM","created_at":"2026-05-18T12:25:47Z"}],"graph_snapshots":[{"event_id":"sha256:dbd505a25afadc4c1ea97c1a8ac0ea3a691e317cadfee305f3f5b9edaafa83e8","target":"graph","created_at":"2026-05-18T01:06:04Z","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 show that the structure constants of W-algebras can be grouped according to the lowest (bosonic) spin(s) of the algebra. The structure constants in each group are described by a unique formula, depending on a functional parameter h(c) that is characteristic for each algebra. As examples we give the structure constants C_{33}^4 and C_{44}^4 for the algebras of type W(2,3,4,...) (that include the WA_{n-1}-algebras) and the structure constant C_{44}^4 for the algebras of type W(2,4,...), especially for all the algebras WD_n, WB(0,n), WB_n and WC_n. It also includes the bosonic projection of th","authors_text":"K. Hornfeck","cross_cats":[],"headline":"","license":"","primary_cat":"hep-th","submitted_at":"1993-07-28T10:20:14Z","title":"Classification of Structure Constants for W-algebras from Highest Weights"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"hep-th/9307170","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":"sha256:0bdb189c28edf2d85bee9f766eee90b137f9f00402e1c5d5fc279831a315e5c6","target":"record","created_at":"2026-05-18T01:06:04Z","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":"0bd3a13e9544f64bc13ffedaeaff649c9b5a3b39d94bd40b3646a1ba985ca644","cross_cats_sorted":[],"license":"","primary_cat":"hep-th","submitted_at":"1993-07-28T10:20:14Z","title_canon_sha256":"bcfc48bdf560a5619acb6aec6ee75a0128f17297138a8ac9ee432fc9d11c65e9"},"schema_version":"1.0","source":{"id":"hep-th/9307170","kind":"arxiv","version":1}},"canonical_sha256":"22dc2b82aca4011b4244a987f6aef90ea04e42246f941127944cce4a68d9dd82","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"22dc2b82aca4011b4244a987f6aef90ea04e42246f941127944cce4a68d9dd82","first_computed_at":"2026-05-18T01:06:04.820544Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:06:04.820544Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"sCu+myxr1dH1/IxWwi9PjVf/VB8PxOsUmRkseKnxncostvbfNkSb2/KtPibhciRm45TxG3ZvcNLGF0QfP1qdDg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:06:04.821262Z","signed_message":"canonical_sha256_bytes"},"source_id":"hep-th/9307170","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0bdb189c28edf2d85bee9f766eee90b137f9f00402e1c5d5fc279831a315e5c6","sha256:dbd505a25afadc4c1ea97c1a8ac0ea3a691e317cadfee305f3f5b9edaafa83e8"],"state_sha256":"fc9fc9c05cf0cf6e4be2b86b72665fb81b8f35bc96c93c23648ce108b2e9fbdc"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"y0L78V/lsecl3TxqzynDhEgWzwC7YAWHHpymK7yRPaGwirEcwnEzfCd0R2MCZ0wcRtOPmkFSuJfKTLzwVcgKCg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-02T15:40:07.381557Z","bundle_sha256":"79ebefafab8ef7f902e35ccbd758b380f95e3612b3090ff0418d8947284b7283"}}