{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:LXKFQOXIHLLQ6EVP57R5XUXVHG","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":"a3b32d43ab9ed1155ad74338a6adc6eb77ec622bfffff124024c74371bfb1c95","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2011-10-07T12:56:53Z","title_canon_sha256":"cc8ae43518ea71971766f09390be776a6aa4cf27229b31f61ac3f2b011cc7f7b"},"schema_version":"1.0","source":{"id":"1110.1512","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1110.1512","created_at":"2026-05-18T03:34:35Z"},{"alias_kind":"arxiv_version","alias_value":"1110.1512v2","created_at":"2026-05-18T03:34:35Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1110.1512","created_at":"2026-05-18T03:34:35Z"},{"alias_kind":"pith_short_12","alias_value":"LXKFQOXIHLLQ","created_at":"2026-05-18T12:26:34Z"},{"alias_kind":"pith_short_16","alias_value":"LXKFQOXIHLLQ6EVP","created_at":"2026-05-18T12:26:34Z"},{"alias_kind":"pith_short_8","alias_value":"LXKFQOXI","created_at":"2026-05-18T12:26:34Z"}],"graph_snapshots":[{"event_id":"sha256:2a82b4cc77f145916536d9675c120a2159c67774bb963a70d932cd3b03b001a0","target":"graph","created_at":"2026-05-18T03:34:35Z","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":"This article can be viewed as a continuation of the articles arXiv:0912.3486 and arXiv:1012.3714 where the decomposable Lie algebras admitting half-flat SU(3)-structures are classified. The new main result is the classification of the indecomposable six-dimensional Lie algebras with five-dimensional nilradical which admit a half-flat SU(3)-structure. As an important step of the proof, a considerable refinement of the classification of six-dimensional Lie algebras with five-dimensional non-Abelian nilradical is established. Additionally, it is proved that all non-solvable six-dimensional Lie al","authors_text":"Fabian Schulte-Hengesbach, Marco Freibert","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2011-10-07T12:56:53Z","title":"Half-flat structures on indecomposable Lie groups"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1110.1512","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:c2f6fe79c22db9ba4f7805dbb25121074f1da61e5431d1cb537c91334277666b","target":"record","created_at":"2026-05-18T03:34:35Z","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":"a3b32d43ab9ed1155ad74338a6adc6eb77ec622bfffff124024c74371bfb1c95","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2011-10-07T12:56:53Z","title_canon_sha256":"cc8ae43518ea71971766f09390be776a6aa4cf27229b31f61ac3f2b011cc7f7b"},"schema_version":"1.0","source":{"id":"1110.1512","kind":"arxiv","version":2}},"canonical_sha256":"5dd4583ae83ad70f12afefe3dbd2f539acab98cd1b91712b5d795437e9bb0566","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"5dd4583ae83ad70f12afefe3dbd2f539acab98cd1b91712b5d795437e9bb0566","first_computed_at":"2026-05-18T03:34:35.837781Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:34:35.837781Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"omUDvXC3yxiEBAK0qlwNJpflDIzFWKlv3Jyy5qfSs7a3DgiRLH/4JvCsCFzRNVHsN+7MlwEafMmfFTft8MFZAg==","signature_status":"signed_v1","signed_at":"2026-05-18T03:34:35.838547Z","signed_message":"canonical_sha256_bytes"},"source_id":"1110.1512","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c2f6fe79c22db9ba4f7805dbb25121074f1da61e5431d1cb537c91334277666b","sha256:2a82b4cc77f145916536d9675c120a2159c67774bb963a70d932cd3b03b001a0"],"state_sha256":"01dcac5a1cf5e8540986e6061c593f522549166f62636f2be834825f35a7444d"}