{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2006:F667MAVE5AE6SQAOWSLODKFEGB","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":"b117b817c04515c34a77a4aa1006eac1bd571f827687a9b113c138f1ef6577cb","cross_cats_sorted":["math.CT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2006-12-23T03:44:16Z","title_canon_sha256":"3827a22c1f503d136bdeb639ae2a1d4b1ff393407cfb5d5b9e7e2a40cbee87cc"},"schema_version":"1.0","source":{"id":"math/0612735","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0612735","created_at":"2026-05-18T03:51:13Z"},{"alias_kind":"arxiv_version","alias_value":"math/0612735v2","created_at":"2026-05-18T03:51:13Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0612735","created_at":"2026-05-18T03:51:13Z"},{"alias_kind":"pith_short_12","alias_value":"F667MAVE5AE6","created_at":"2026-05-18T12:25:53Z"},{"alias_kind":"pith_short_16","alias_value":"F667MAVE5AE6SQAO","created_at":"2026-05-18T12:25:53Z"},{"alias_kind":"pith_short_8","alias_value":"F667MAVE","created_at":"2026-05-18T12:25:53Z"}],"graph_snapshots":[{"event_id":"sha256:f06eff15a4b14e3922c7515096b96eec2bc4a50e84cd4bd89c451c9ec90f674e","target":"graph","created_at":"2026-05-18T03:51:13Z","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 this paper we prove that in classifying of complex filiform Leibniz algebras, for which its naturally graded algebra is non-Lie algebra, it suffices to consider some special basis transformations. Moreover, we establish a criterion whether given two such Leibniz algebras are isomorphic in terms of such transformations. The classification problem of filiform Leibniz algebras, for which its naturally graded algebras are non-Lie in an arbitrary dimension, is reduced to the investigation of the obtained conditions.","authors_text":"B. A. Omirov, J. R. G\\'omez","cross_cats":["math.CT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2006-12-23T03:44:16Z","title":"On classification of complex filiform Leibniz algebras"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0612735","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":"sha256:4eb04e08475808ffde33029f48f771698f5ca72d8e4de7b0a5e496999a62eea4","target":"record","created_at":"2026-05-18T03:51:13Z","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":"b117b817c04515c34a77a4aa1006eac1bd571f827687a9b113c138f1ef6577cb","cross_cats_sorted":["math.CT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2006-12-23T03:44:16Z","title_canon_sha256":"3827a22c1f503d136bdeb639ae2a1d4b1ff393407cfb5d5b9e7e2a40cbee87cc"},"schema_version":"1.0","source":{"id":"math/0612735","kind":"arxiv","version":2}},"canonical_sha256":"2fbdf602a4e809e9400eb496e1a8a43073b2d29a4350f04bd53f343df389a71c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"2fbdf602a4e809e9400eb496e1a8a43073b2d29a4350f04bd53f343df389a71c","first_computed_at":"2026-05-18T03:51:13.180894Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:51:13.180894Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"KbfRZzmJt7R6hc9FB6tvEvowVZMG5+gOeqyjeLUdLi0hQyvmn7srK2nQsZfvdMzv85OytcH4xI0+CSwmbPkCAg==","signature_status":"signed_v1","signed_at":"2026-05-18T03:51:13.181593Z","signed_message":"canonical_sha256_bytes"},"source_id":"math/0612735","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:4eb04e08475808ffde33029f48f771698f5ca72d8e4de7b0a5e496999a62eea4","sha256:f06eff15a4b14e3922c7515096b96eec2bc4a50e84cd4bd89c451c9ec90f674e"],"state_sha256":"42a59b4ec502d8544240c0404710ce93fb1daf5d768cc1e9dd1d7b6eb0e7946f"}