{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:2YBIHAVXPRSHL4LNIXHLWKILEG","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":"2daf0b8365b379851c2a815ee11306fe43d7c7e69958731ef465d91a6813cf1a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2010-08-04T14:58:13Z","title_canon_sha256":"5221bf67570b84fd8fdcd58267ebf53fe38b1b4edb7d29c205823613a14202d0"},"schema_version":"1.0","source":{"id":"1008.0797","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1008.0797","created_at":"2026-05-18T04:15:48Z"},{"alias_kind":"arxiv_version","alias_value":"1008.0797v2","created_at":"2026-05-18T04:15:48Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1008.0797","created_at":"2026-05-18T04:15:48Z"},{"alias_kind":"pith_short_12","alias_value":"2YBIHAVXPRSH","created_at":"2026-05-18T12:26:03Z"},{"alias_kind":"pith_short_16","alias_value":"2YBIHAVXPRSHL4LN","created_at":"2026-05-18T12:26:03Z"},{"alias_kind":"pith_short_8","alias_value":"2YBIHAVX","created_at":"2026-05-18T12:26:03Z"}],"graph_snapshots":[{"event_id":"sha256:7054b8faa58d3c772e395ba8faf72b00a9393861d3c4226a5df3a2c52f0f0508","target":"graph","created_at":"2026-05-18T04:15:48Z","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 introduce obstructions to the existence of a calibrated G_2-structure on a Lie algebra g of dimension seven, not necessarily nilpotent. In particular, we prove that if there is a Lie algebra epimorphism from g to a six-dimensional Lie algebra h with kernel contained in the center of g, then h has a symplectic form. As a consequence, we obtain a classification of the nilpotent Lie algebras that admit a calibrated G_2-structure.","authors_text":"Diego Conti, Marisa Fern\\'andez","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2010-08-04T14:58:13Z","title":"Nilmanifolds with a calibrated G_2-structure"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1008.0797","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":"sha256:29973c680d61f78aa58d0a7ddcc64db1564933c114eb8423d2379ec12dfe9612","target":"record","created_at":"2026-05-18T04:15:48Z","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":"2daf0b8365b379851c2a815ee11306fe43d7c7e69958731ef465d91a6813cf1a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2010-08-04T14:58:13Z","title_canon_sha256":"5221bf67570b84fd8fdcd58267ebf53fe38b1b4edb7d29c205823613a14202d0"},"schema_version":"1.0","source":{"id":"1008.0797","kind":"arxiv","version":2}},"canonical_sha256":"d6028382b77c6475f16d45cebb290b21bb52d0306c266f42d70c37091164b1e5","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d6028382b77c6475f16d45cebb290b21bb52d0306c266f42d70c37091164b1e5","first_computed_at":"2026-05-18T04:15:48.159719Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:15:48.159719Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"nsmi/mRcZv5Bff+slC8PbgFaAAW7dI/TbtNdY0aks9sDzMDssX5JoICHuCratSradxZ3uGJv4VyhQZCpSuy9Dw==","signature_status":"signed_v1","signed_at":"2026-05-18T04:15:48.160252Z","signed_message":"canonical_sha256_bytes"},"source_id":"1008.0797","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:29973c680d61f78aa58d0a7ddcc64db1564933c114eb8423d2379ec12dfe9612","sha256:7054b8faa58d3c772e395ba8faf72b00a9393861d3c4226a5df3a2c52f0f0508"],"state_sha256":"9887db1e221277c229b30173a9847cf6bfea699d70d23abbbfad91ac0439d198"}