{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:RUB5RGQUNZEL6A2E5U2LOYHO5K","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":"e386ec5c52315b175133d20cd7825e991394c11456235daf08bb097acd8c3760","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2018-03-23T16:52:49Z","title_canon_sha256":"d46d21f26023933acbbaf99c302e2f948639c5eb95397f676a5c9599de9949a6"},"schema_version":"1.0","source":{"id":"1803.08878","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1803.08878","created_at":"2026-05-18T00:09:15Z"},{"alias_kind":"arxiv_version","alias_value":"1803.08878v1","created_at":"2026-05-18T00:09:15Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1803.08878","created_at":"2026-05-18T00:09:15Z"},{"alias_kind":"pith_short_12","alias_value":"RUB5RGQUNZEL","created_at":"2026-05-18T12:32:50Z"},{"alias_kind":"pith_short_16","alias_value":"RUB5RGQUNZEL6A2E","created_at":"2026-05-18T12:32:50Z"},{"alias_kind":"pith_short_8","alias_value":"RUB5RGQU","created_at":"2026-05-18T12:32:50Z"}],"graph_snapshots":[{"event_id":"sha256:50a21f0493ed7bbc4313dd31ac27beed2cc5ecaa4065afdbaebac64160b23c6f","target":"graph","created_at":"2026-05-18T00:09:15Z","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":"Starting with Lie's classification of finite-dimensional transitive Lie algebras of vector fields on $\\mathbb C^2$ we construct Lie algebras of vector fields on the bundle $\\mathbb C^2 \\times \\mathbb C$ by lifting the Lie algebras from the base. There are essentially three types of transitive lifts and we compute all of them for the Lie algebras from Lie's classification. The simplest type of lift is encoded by Lie algebra cohomology.","authors_text":"Eivind Schneider","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2018-03-23T16:52:49Z","title":"Projectable Lie algebras of vector fields in 3D"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1803.08878","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:e47adf76d9df8dec3bda9a0d8c7478506549c087818ef0d6ff16607e6eb35b50","target":"record","created_at":"2026-05-18T00:09:15Z","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":"e386ec5c52315b175133d20cd7825e991394c11456235daf08bb097acd8c3760","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2018-03-23T16:52:49Z","title_canon_sha256":"d46d21f26023933acbbaf99c302e2f948639c5eb95397f676a5c9599de9949a6"},"schema_version":"1.0","source":{"id":"1803.08878","kind":"arxiv","version":1}},"canonical_sha256":"8d03d89a146e48bf0344ed34b760eeeaa875fa855ce4291ec6e5caf456ae6448","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"8d03d89a146e48bf0344ed34b760eeeaa875fa855ce4291ec6e5caf456ae6448","first_computed_at":"2026-05-18T00:09:15.367097Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:09:15.367097Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"GFOV23f3AbR2BF5Jr2qGGGY2GcI8veb6MLl87mm/pVvjCXj6QdMQyLFLTPvtZg3bMmf3ZG8DMWjs5DvQehCGCA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:09:15.367760Z","signed_message":"canonical_sha256_bytes"},"source_id":"1803.08878","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e47adf76d9df8dec3bda9a0d8c7478506549c087818ef0d6ff16607e6eb35b50","sha256:50a21f0493ed7bbc4313dd31ac27beed2cc5ecaa4065afdbaebac64160b23c6f"],"state_sha256":"af1a8eb16fbbcd80db45cf66b9c39c3769479e9c3c4a01e61639be59ffa7bbec"}