{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:JKH7RU3PJECGZCLXY6UZBFVT4U","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":"0d00b2cffe7907afadd947737cd1deff930196330159f559957ac0895d2e48fa","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2013-11-21T16:49:55Z","title_canon_sha256":"0d792ff0915a5b78814d21a45caf25330d5c4a0af13f48bb1405dd95e75c0be8"},"schema_version":"1.0","source":{"id":"1311.5475","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1311.5475","created_at":"2026-05-18T03:06:33Z"},{"alias_kind":"arxiv_version","alias_value":"1311.5475v1","created_at":"2026-05-18T03:06:33Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1311.5475","created_at":"2026-05-18T03:06:33Z"},{"alias_kind":"pith_short_12","alias_value":"JKH7RU3PJECG","created_at":"2026-05-18T12:27:49Z"},{"alias_kind":"pith_short_16","alias_value":"JKH7RU3PJECGZCLX","created_at":"2026-05-18T12:27:49Z"},{"alias_kind":"pith_short_8","alias_value":"JKH7RU3P","created_at":"2026-05-18T12:27:49Z"}],"graph_snapshots":[{"event_id":"sha256:76e54f2e6a61e63ed84df9317d65abe796b9a93e87362654cda79b6bcf478e62","target":"graph","created_at":"2026-05-18T03:06:33Z","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":"The descriptions (up to isomorphism) of naturally graded $p$-filiform Leibniz algebras and $p$-filiform ($p\\leq 3$) Leibniz algebras of maximum length are known. In this paper we study the gradation of maximum length for $p$-filiform Leibniz algebras. The present work aims at the classification of complex $p$-filiform ($p \\geq 4$) Leibniz algebras of maximum length.","authors_text":"B.A. Omirov, E.M. Canete, J.R. Gomez, L.M. Camacho","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2013-11-21T16:49:55Z","title":"p-filiform Leibniz algebras of maximum length"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1311.5475","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":"sha256:4777200f67bb9f1af4dde0519a19d4219363cf3dcdc014be4066c74df31c1d33","target":"record","created_at":"2026-05-18T03:06:33Z","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":"0d00b2cffe7907afadd947737cd1deff930196330159f559957ac0895d2e48fa","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2013-11-21T16:49:55Z","title_canon_sha256":"0d792ff0915a5b78814d21a45caf25330d5c4a0af13f48bb1405dd95e75c0be8"},"schema_version":"1.0","source":{"id":"1311.5475","kind":"arxiv","version":1}},"canonical_sha256":"4a8ff8d36f49046c8977c7a99096b3e53d2326b10adda30e4f0fc1f9967aa7d2","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"4a8ff8d36f49046c8977c7a99096b3e53d2326b10adda30e4f0fc1f9967aa7d2","first_computed_at":"2026-05-18T03:06:33.272989Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:06:33.272989Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"xFk4dA9gwaAqgwzjSdDzsSOmloC7McjOcGlefEDYSftE++A5pd/Cb99QXdi3N+wtoNAmbCDMN0C/2S/oWHOnBg==","signature_status":"signed_v1","signed_at":"2026-05-18T03:06:33.273450Z","signed_message":"canonical_sha256_bytes"},"source_id":"1311.5475","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:4777200f67bb9f1af4dde0519a19d4219363cf3dcdc014be4066c74df31c1d33","sha256:76e54f2e6a61e63ed84df9317d65abe796b9a93e87362654cda79b6bcf478e62"],"state_sha256":"3a66d793204638d8a84f01d1c3d2a2a1dd7c781d79e11871b512239029b87074"}