{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:GQVU2CYGSO4LVAUIEV3NPN7CXU","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":"ff653e1557828f2d3c40a8b37bb1e6920044e295d1fad8f5ab550ad0a4aa6804","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2014-07-30T06:45:33Z","title_canon_sha256":"58168815d8cc8fb260d4f3d0d81a7f8f782862fe71069b2fd5766e3ef44f3bf1"},"schema_version":"1.0","source":{"id":"1407.7956","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1407.7956","created_at":"2026-05-18T02:46:13Z"},{"alias_kind":"arxiv_version","alias_value":"1407.7956v1","created_at":"2026-05-18T02:46:13Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1407.7956","created_at":"2026-05-18T02:46:13Z"},{"alias_kind":"pith_short_12","alias_value":"GQVU2CYGSO4L","created_at":"2026-05-18T12:28:30Z"},{"alias_kind":"pith_short_16","alias_value":"GQVU2CYGSO4LVAUI","created_at":"2026-05-18T12:28:30Z"},{"alias_kind":"pith_short_8","alias_value":"GQVU2CYG","created_at":"2026-05-18T12:28:30Z"}],"graph_snapshots":[{"event_id":"sha256:0e4df9e898884bf40710c796cfc1bd94b149617978065834a1063dd50b41206d","target":"graph","created_at":"2026-05-18T02:46:13Z","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 the description of solvable Lie algebras with triangular nilradicals is extended to Leibniz algebras. It is proven that the matrices of the left and right operators on elements of Leibniz algebra have upper triangular forms. We establish that solvable Leibniz algebra of a maximal possible dimension with a given triangular nilradical is a Lie algebra. Furthermore, solvable Leibniz algebras with triangular nilradicals of low dimensions are classified.","authors_text":"A.Kh. Khudoyberdiyev, B. A. Omirov, I.A. Karimjanov","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2014-07-30T06:45:33Z","title":"Solvable Leibniz algebras with triangular nilradicals"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1407.7956","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:ca154238efbf74c62be0721ec12fdc8ec65d8bc1949886e68937ae8c910b0875","target":"record","created_at":"2026-05-18T02:46:13Z","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":"ff653e1557828f2d3c40a8b37bb1e6920044e295d1fad8f5ab550ad0a4aa6804","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2014-07-30T06:45:33Z","title_canon_sha256":"58168815d8cc8fb260d4f3d0d81a7f8f782862fe71069b2fd5766e3ef44f3bf1"},"schema_version":"1.0","source":{"id":"1407.7956","kind":"arxiv","version":1}},"canonical_sha256":"342b4d0b0693b8ba82882576d7b7e2bd01b70cb130970a95707af0a0d0d20b21","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"342b4d0b0693b8ba82882576d7b7e2bd01b70cb130970a95707af0a0d0d20b21","first_computed_at":"2026-05-18T02:46:13.966521Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:46:13.966521Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"doRjc5C3NTtC9+mTFQ/5Bv2x3lt06oPDhMkorvLNGlKmXYQlAgl0ddRdcTjWurZsNZAl1ayrNiLnxaciQniKCw==","signature_status":"signed_v1","signed_at":"2026-05-18T02:46:13.967281Z","signed_message":"canonical_sha256_bytes"},"source_id":"1407.7956","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ca154238efbf74c62be0721ec12fdc8ec65d8bc1949886e68937ae8c910b0875","sha256:0e4df9e898884bf40710c796cfc1bd94b149617978065834a1063dd50b41206d"],"state_sha256":"cb709d0e376a2036c0cecc0305ae29552328e9a46d7ef76b03aa81e530367439"}