{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:XCT224ZB6OIR3QLZHVT2CR3B52","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":"e75bc27fb6cf8cb9077a685b9d1751af985281c8635078d60df7b7e443f9f790","cross_cats_sorted":["math.AG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2016-02-23T15:37:34Z","title_canon_sha256":"d57f843aa4dfab5bddd3ef3d5f7dc9f8e01309d1ba5b648aa375e1ab0466b9e2"},"schema_version":"1.0","source":{"id":"1602.07200","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1602.07200","created_at":"2026-05-18T01:17:07Z"},{"alias_kind":"arxiv_version","alias_value":"1602.07200v2","created_at":"2026-05-18T01:17:07Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1602.07200","created_at":"2026-05-18T01:17:07Z"},{"alias_kind":"pith_short_12","alias_value":"XCT224ZB6OIR","created_at":"2026-05-18T12:30:51Z"},{"alias_kind":"pith_short_16","alias_value":"XCT224ZB6OIR3QLZ","created_at":"2026-05-18T12:30:51Z"},{"alias_kind":"pith_short_8","alias_value":"XCT224ZB","created_at":"2026-05-18T12:30:51Z"}],"graph_snapshots":[{"event_id":"sha256:60ca0d3ab423033faa3928213e3400a4bc27d2a86a2377561ae2d50acfa379cc","target":"graph","created_at":"2026-05-18T01:17:07Z","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 description of complex solvable Leibniz algebras whose nilradical is a naturally graded filiform algebra is already known. Unfortunately, a mistake was made in that description. Namely, in the case where the dimension of the solvable Leibniz algebra with nilradical $F_n^1$ is equal to $n+2$, it was asserted that there is no such algebra. However, it was possible for us to find a unique $(n+2)$-dimensional solvable Leibniz algebra with nilradical $F_n^1$. In addition, we establish the triviality of the second group of cohomology for this algebra with coefficients in itself, which implies it","authors_text":"B.A. Omirov, K.K. Masutova, M. Ladra","cross_cats":["math.AG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2016-02-23T15:37:34Z","title":"Solvable Leibniz algebra with non-Lie and non-split naturally graded filiform nilradical and its rigidity"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1602.07200","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":"sha256:6126880ca3efb4baa4352450c422aa0df49bda52990b5b3822ef738042d089f6","target":"record","created_at":"2026-05-18T01:17:07Z","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":"e75bc27fb6cf8cb9077a685b9d1751af985281c8635078d60df7b7e443f9f790","cross_cats_sorted":["math.AG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2016-02-23T15:37:34Z","title_canon_sha256":"d57f843aa4dfab5bddd3ef3d5f7dc9f8e01309d1ba5b648aa375e1ab0466b9e2"},"schema_version":"1.0","source":{"id":"1602.07200","kind":"arxiv","version":2}},"canonical_sha256":"b8a7ad7321f3911dc1793d67a14761ee94fa47fa1b559d00b24f930b9b9d68c1","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b8a7ad7321f3911dc1793d67a14761ee94fa47fa1b559d00b24f930b9b9d68c1","first_computed_at":"2026-05-18T01:17:07.397567Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:17:07.397567Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"h3QRyNCppxGeBNL4NPqkualrKkSaxnMo4DsUy9xKy7LwBDuLqvC45A4wC5uZtfBCokpOR4NODJpWr5AqsSu0Cg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:17:07.398338Z","signed_message":"canonical_sha256_bytes"},"source_id":"1602.07200","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:6126880ca3efb4baa4352450c422aa0df49bda52990b5b3822ef738042d089f6","sha256:60ca0d3ab423033faa3928213e3400a4bc27d2a86a2377561ae2d50acfa379cc"],"state_sha256":"03cc4b86fb31dbe3d241910e5861748b81a5c0573078df5512f274f1e386f6b0"}