{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:QJPYZ2CBFV4O6U7DPTNOCXLH6H","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":"7706226ee144282efd990c8272f1f3f1618ca11cc93e793382534cf2c215283e","cross_cats_sorted":["math.GR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2010-04-28T12:04:21Z","title_canon_sha256":"37aadbdd218e89de9b890a09f18bebeaa257e3ba3aaa6f013426eb5c74eaf22d"},"schema_version":"1.0","source":{"id":"1004.5005","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1004.5005","created_at":"2026-05-18T02:24:15Z"},{"alias_kind":"arxiv_version","alias_value":"1004.5005v1","created_at":"2026-05-18T02:24:15Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1004.5005","created_at":"2026-05-18T02:24:15Z"},{"alias_kind":"pith_short_12","alias_value":"QJPYZ2CBFV4O","created_at":"2026-05-18T12:26:12Z"},{"alias_kind":"pith_short_16","alias_value":"QJPYZ2CBFV4O6U7D","created_at":"2026-05-18T12:26:12Z"},{"alias_kind":"pith_short_8","alias_value":"QJPYZ2CB","created_at":"2026-05-18T12:26:12Z"}],"graph_snapshots":[{"event_id":"sha256:3c551546fb85e67c0b71845b5c292f27cef360af4e5b9054bd906d4081c7c3d8","target":"graph","created_at":"2026-05-18T02:24:15Z","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":"Relationships between certain properties of maximal subalgebras of a Lie algebra $L$ and the structure of $L$ itself have been studied by a number of authors. Amongst the maximal subalgebras, however, some exert a greater influence on particular results than others. Here we study properties of those maximal subalgebras that contain Engel subalgebras, and of those that also have codimension greater than one in $L$.","authors_text":"David A. Towers","cross_cats":["math.GR"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2010-04-28T12:04:21Z","title":"On maximal subalgebras of Lie algebras containing Engel subalgebras"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1004.5005","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":"sha256:7a59e068fddc061f7b19a06b75da7cfb605f782c29d65050f8cb1749e2c0b369","target":"record","created_at":"2026-05-18T02:24:15Z","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":"7706226ee144282efd990c8272f1f3f1618ca11cc93e793382534cf2c215283e","cross_cats_sorted":["math.GR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2010-04-28T12:04:21Z","title_canon_sha256":"37aadbdd218e89de9b890a09f18bebeaa257e3ba3aaa6f013426eb5c74eaf22d"},"schema_version":"1.0","source":{"id":"1004.5005","kind":"arxiv","version":1}},"canonical_sha256":"825f8ce8412d78ef53e37cdae15d67f1ca7aa991d2945751833b006f92c0df51","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"825f8ce8412d78ef53e37cdae15d67f1ca7aa991d2945751833b006f92c0df51","first_computed_at":"2026-05-18T02:24:15.486456Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:24:15.486456Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"o/se355nwf4BGGyQOud8SLFckQY62AFA3S7Un1ZRloBwiFQ9qd0EEaPIOW8Y8yilKjc3XtX/werN2huIWLi0Bw==","signature_status":"signed_v1","signed_at":"2026-05-18T02:24:15.486980Z","signed_message":"canonical_sha256_bytes"},"source_id":"1004.5005","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:7a59e068fddc061f7b19a06b75da7cfb605f782c29d65050f8cb1749e2c0b369","sha256:3c551546fb85e67c0b71845b5c292f27cef360af4e5b9054bd906d4081c7c3d8"],"state_sha256":"a2bcef9b01e0da9cfce8f1fe7f3d22955a7f310cf7a4640d0dac77f5dd50cf5d"}