{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2009:YBK6FZINHDCRCWRNNLHGCT5NHP","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":"adf93b55a74ebb1c59a790de3c1ddc0fceef573111340f386f6028ecd18d1bb4","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2009-09-17T17:53:17Z","title_canon_sha256":"1029bc59febdc1c452a628c486f1f9e0ea6c3bc706e364c6a81f0f3ae6a97787"},"schema_version":"1.0","source":{"id":"0909.3284","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0909.3284","created_at":"2026-05-18T03:01:36Z"},{"alias_kind":"arxiv_version","alias_value":"0909.3284v2","created_at":"2026-05-18T03:01:36Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0909.3284","created_at":"2026-05-18T03:01:36Z"},{"alias_kind":"pith_short_12","alias_value":"YBK6FZINHDCR","created_at":"2026-05-18T12:26:02Z"},{"alias_kind":"pith_short_16","alias_value":"YBK6FZINHDCRCWRN","created_at":"2026-05-18T12:26:02Z"},{"alias_kind":"pith_short_8","alias_value":"YBK6FZIN","created_at":"2026-05-18T12:26:02Z"}],"graph_snapshots":[{"event_id":"sha256:94aaebfe45404683b1e4374cc8f9c4e6b101e95c02ec744671ea56181df64ea0","target":"graph","created_at":"2026-05-18T03:01:36Z","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 classify simple linearly compact n-Lie superalgebras with n>2 over a field F of characteristic 0. The classification is based on a bijective correspondence between non-abelian n-Lie superalgebras and transitive Z-graded Lie superalgebras of the form L=\\oplus_{j=-1}^{n-1} L_j, such that L_{-1}=g, where dim L_{n-1}=1, L_{-1} and L_{n-1} generate L, and [L_j, L_{n-j-1}] =0 for all j, thereby reducing it to the known classification of simple linearly compact Lie superalgebras and their Z-gradings. The list consists of four examples, one of them being the n+1-dimensional vector product n-Lie alg","authors_text":"Nicoletta Cantarini, Victor G. Kac","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2009-09-17T17:53:17Z","title":"Classification of simple linearly compact n-Lie superalgebras"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0909.3284","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:d6491311e9f8d66405a4e686f9c19cc4f964a5e59d063f978288e1540457feb3","target":"record","created_at":"2026-05-18T03:01:36Z","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":"adf93b55a74ebb1c59a790de3c1ddc0fceef573111340f386f6028ecd18d1bb4","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2009-09-17T17:53:17Z","title_canon_sha256":"1029bc59febdc1c452a628c486f1f9e0ea6c3bc706e364c6a81f0f3ae6a97787"},"schema_version":"1.0","source":{"id":"0909.3284","kind":"arxiv","version":2}},"canonical_sha256":"c055e2e50d38c5115a2d6ace614fad3bddd7e7c32dea9cea6a4af15c1ca5773a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c055e2e50d38c5115a2d6ace614fad3bddd7e7c32dea9cea6a4af15c1ca5773a","first_computed_at":"2026-05-18T03:01:36.259515Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:01:36.259515Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"70McRo4Eh2yM4rGM21zdv2iun2F6jb9fU+H9Jv37bRPZLKOA+a0/QEHAUuOar569RX/KnLlDyzMTZoqKP+lwAA==","signature_status":"signed_v1","signed_at":"2026-05-18T03:01:36.260306Z","signed_message":"canonical_sha256_bytes"},"source_id":"0909.3284","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d6491311e9f8d66405a4e686f9c19cc4f964a5e59d063f978288e1540457feb3","sha256:94aaebfe45404683b1e4374cc8f9c4e6b101e95c02ec744671ea56181df64ea0"],"state_sha256":"b436e1b76860cdfc0d29a273b8bafcb261ea493478c1089f04c4f8d8ba901cbc"}