{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:N6VQK6CTIGEB6FOBGTCHM54ST5","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":"a1da23799c912a1dd730d691fd27f91194b5f39e16f6d4dac72dfa6a26a01b03","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2018-10-29T20:09:34Z","title_canon_sha256":"eef8778eb6700cdbab8f773ab2ac122e79301f777514e22ed7bd226c0ef82025"},"schema_version":"1.0","source":{"id":"1810.12386","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1810.12386","created_at":"2026-05-17T23:43:50Z"},{"alias_kind":"arxiv_version","alias_value":"1810.12386v2","created_at":"2026-05-17T23:43:50Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1810.12386","created_at":"2026-05-17T23:43:50Z"},{"alias_kind":"pith_short_12","alias_value":"N6VQK6CTIGEB","created_at":"2026-05-18T12:32:40Z"},{"alias_kind":"pith_short_16","alias_value":"N6VQK6CTIGEB6FOB","created_at":"2026-05-18T12:32:40Z"},{"alias_kind":"pith_short_8","alias_value":"N6VQK6CT","created_at":"2026-05-18T12:32:40Z"}],"graph_snapshots":[{"event_id":"sha256:6ba5b6c13c55086bcc5b8454c6a2bb05493611f9bf40a9bae9f04686b3c3cf48","target":"graph","created_at":"2026-05-17T23:43:50Z","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 study solvable Lie algebras in prime characteristic $p$ that admit non-singular derivations. We show that Jacobson's Theorem remains true if the quotients of the derived series have dimension less than~$p$. We also study the structure of Lie algebras with non-singular derivations in which the derived subalgebra is abelian and has codimension~one. The paper presents some new examples of solvable, but not nilpotent, Lie algebras of derived length~3 with non-singular derivations.","authors_text":"Csaba Schneider, Marcos Goulart Lima","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2018-10-29T20:09:34Z","title":"Non-singular derivations of solvable Lie algebras in prime characteristic"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1810.12386","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":"sha256:6548d6bee841f37b24c91865e8bef35ace9d16fe0bf9b76f40f3efa892eaaf58","target":"record","created_at":"2026-05-17T23:43:50Z","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":"a1da23799c912a1dd730d691fd27f91194b5f39e16f6d4dac72dfa6a26a01b03","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2018-10-29T20:09:34Z","title_canon_sha256":"eef8778eb6700cdbab8f773ab2ac122e79301f777514e22ed7bd226c0ef82025"},"schema_version":"1.0","source":{"id":"1810.12386","kind":"arxiv","version":2}},"canonical_sha256":"6fab05785341881f15c134c47677929f4af3bf47f3d492e5df50b94f8d9eca38","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6fab05785341881f15c134c47677929f4af3bf47f3d492e5df50b94f8d9eca38","first_computed_at":"2026-05-17T23:43:50.584210Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:43:50.584210Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"XNfU3Hdu/pgGG0fYk/Ins+RCuqYU7bxkG72t7UzabJUcN/Wzm35ulAIdy4UGLeAMOeOjMunRc/3f9HG9RvDfAg==","signature_status":"signed_v1","signed_at":"2026-05-17T23:43:50.584989Z","signed_message":"canonical_sha256_bytes"},"source_id":"1810.12386","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:6548d6bee841f37b24c91865e8bef35ace9d16fe0bf9b76f40f3efa892eaaf58","sha256:6ba5b6c13c55086bcc5b8454c6a2bb05493611f9bf40a9bae9f04686b3c3cf48"],"state_sha256":"a86ad8a253ce1b4ecc8de724b973f2b847802631dfd4c670e230e97f6107eb19"}