{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2005:3CXL7E7ICSKJAK4E7RZ6AXZKBG","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":"37f6bde2d8f51c98cda6e962ff74e86f75b3a81a879a2264a40ba19306cef8b8","cross_cats_sorted":["math.QA"],"license":"","primary_cat":"math.AG","submitted_at":"2005-07-14T10:00:33Z","title_canon_sha256":"67f3f919bfeae44d8f7ed0cc49bfad075260e93f6f3e5a424984ece57d218f58"},"schema_version":"1.0","source":{"id":"math/0507287","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0507287","created_at":"2026-05-18T03:45:40Z"},{"alias_kind":"arxiv_version","alias_value":"math/0507287v2","created_at":"2026-05-18T03:45:40Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0507287","created_at":"2026-05-18T03:45:40Z"},{"alias_kind":"pith_short_12","alias_value":"3CXL7E7ICSKJ","created_at":"2026-05-18T12:25:52Z"},{"alias_kind":"pith_short_16","alias_value":"3CXL7E7ICSKJAK4E","created_at":"2026-05-18T12:25:52Z"},{"alias_kind":"pith_short_8","alias_value":"3CXL7E7I","created_at":"2026-05-18T12:25:52Z"}],"graph_snapshots":[{"event_id":"sha256:bdaff65cb3f6562569bdeb8bfe4670b2dd9169ce2c0e9c2a82e3af2a478c307a","target":"graph","created_at":"2026-05-18T03:45:40Z","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":"To every morphism $\\chi\\colon L\\to M$ of differential graded Lie algebras we associate a functors of artin rings $\\Def_\\chi$ whose tangent and obstruction spaces are respectively the first and second cohomology group of the cylinder of $\\chi$. Such construction applies to Hilbert and Brill-Noether functors and allow to prove with ease that every higher obstruction to deforming a smooth submanifold of a Kaehler manifold is annihilated by the semiregularity map.","authors_text":"Marco Manetti","cross_cats":["math.QA"],"headline":"","license":"","primary_cat":"math.AG","submitted_at":"2005-07-14T10:00:33Z","title":"Lie description of higher obstructions to deforming submanifolds"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0507287","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":"sha256:598a3eb697c60b9c38a711efb6da904818df47b1f1823fdfd9e4cfd89037a98e","target":"record","created_at":"2026-05-18T03:45:40Z","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":"37f6bde2d8f51c98cda6e962ff74e86f75b3a81a879a2264a40ba19306cef8b8","cross_cats_sorted":["math.QA"],"license":"","primary_cat":"math.AG","submitted_at":"2005-07-14T10:00:33Z","title_canon_sha256":"67f3f919bfeae44d8f7ed0cc49bfad075260e93f6f3e5a424984ece57d218f58"},"schema_version":"1.0","source":{"id":"math/0507287","kind":"arxiv","version":2}},"canonical_sha256":"d8aebf93e81494902b84fc73e05f2a098e4ae8f515b63906db01c29b6766edab","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d8aebf93e81494902b84fc73e05f2a098e4ae8f515b63906db01c29b6766edab","first_computed_at":"2026-05-18T03:45:40.387274Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:45:40.387274Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"3lzwI4fTrhGifrh5AR7zObPK43M7c9NQPhI9prOU/kOW+Clp+jU4WEfaQ5xitsE5s8DBw+rwknHis0KU+0VHBg==","signature_status":"signed_v1","signed_at":"2026-05-18T03:45:40.387692Z","signed_message":"canonical_sha256_bytes"},"source_id":"math/0507287","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:598a3eb697c60b9c38a711efb6da904818df47b1f1823fdfd9e4cfd89037a98e","sha256:bdaff65cb3f6562569bdeb8bfe4670b2dd9169ce2c0e9c2a82e3af2a478c307a"],"state_sha256":"9db28fed1898277ce5c13825b9b9728597090d239135666ffbd26183195f5c07"}