{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:URRCDXJU6IBO4CZZPI25O6JYBO","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":"cf8feca61c55a172a68ce8b7d57f7939dfae3360e6fa5e5c41853d2eef2c2660","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2019-07-21T15:32:57Z","title_canon_sha256":"1c725976dc02d17e841119674ed0305495b9db79fd4c025e887b4e9daf59ba4e"},"schema_version":"1.0","source":{"id":"1907.08989","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1907.08989","created_at":"2026-05-17T23:40:02Z"},{"alias_kind":"arxiv_version","alias_value":"1907.08989v1","created_at":"2026-05-17T23:40:02Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1907.08989","created_at":"2026-05-17T23:40:02Z"},{"alias_kind":"pith_short_12","alias_value":"URRCDXJU6IBO","created_at":"2026-05-18T12:33:30Z"},{"alias_kind":"pith_short_16","alias_value":"URRCDXJU6IBO4CZZ","created_at":"2026-05-18T12:33:30Z"},{"alias_kind":"pith_short_8","alias_value":"URRCDXJU","created_at":"2026-05-18T12:33:30Z"}],"graph_snapshots":[{"event_id":"sha256:e8db4852423abd33f7bb84d60b26ded371980c8eede2191bd57c1e844bbf7ec5","target":"graph","created_at":"2026-05-17T23:40:02Z","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":"Let $ W(n) $ be Jacobson-Witt algebra over algebraic closed field $ \\mathbb{K} $ with positive characteristic $ p>2. $ It is difficult to classify all Borel subalgebras of $ W(n) $ or non-classical restricted simple Lie algebras. The present paper and \\cite{S7} study two kinds of subalgebras which are easily to understand and highly related to Borel subalgebras.\n  In \\cite{S7}, the last author investigates a class of special Borel subalgebras of $W(n)$ which is called homogeneous Borel subalgebras. The present paper focuses on subalgebras of $ W(n) $ which are related to Borel subalgebras such","authors_text":"Bin Shu, Ke Ou","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2019-07-21T15:32:57Z","title":"Borel subalgebras of Cartan Type Lie Algebras"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1907.08989","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:bf095e0e5550e2a29c30f4ea8307cec7343a705cc616dcd65763873fc45d8b91","target":"record","created_at":"2026-05-17T23:40:02Z","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":"cf8feca61c55a172a68ce8b7d57f7939dfae3360e6fa5e5c41853d2eef2c2660","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2019-07-21T15:32:57Z","title_canon_sha256":"1c725976dc02d17e841119674ed0305495b9db79fd4c025e887b4e9daf59ba4e"},"schema_version":"1.0","source":{"id":"1907.08989","kind":"arxiv","version":1}},"canonical_sha256":"a46221dd34f202ee0b397a35d779380b9ec77ac4ad0603a4e5e69bd3cb5fa971","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a46221dd34f202ee0b397a35d779380b9ec77ac4ad0603a4e5e69bd3cb5fa971","first_computed_at":"2026-05-17T23:40:02.488332Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:40:02.488332Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"oydIT0aek5GHMQu4+fT3c7g0aMFJoMqFLFdXV6yUY3jg/mLaeKtrIV0k+ysmhaTEQVTHpzh0f3p5+mJaXaX/BA==","signature_status":"signed_v1","signed_at":"2026-05-17T23:40:02.488851Z","signed_message":"canonical_sha256_bytes"},"source_id":"1907.08989","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:bf095e0e5550e2a29c30f4ea8307cec7343a705cc616dcd65763873fc45d8b91","sha256:e8db4852423abd33f7bb84d60b26ded371980c8eede2191bd57c1e844bbf7ec5"],"state_sha256":"ea3039b5b8480377c61384acc65a3a6fc415a1b8dfdc9e7697b09d71fdc8d851"}