{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:SE4XY3JS55GCS7HKYFXBLESTDT","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":"442f1695460ff5e8df30c365d3054ef61da19c6de5cfd4b5ad0359503211aa51","cross_cats_sorted":["math.AG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2013-03-19T19:31:16Z","title_canon_sha256":"efe649ccae5de546d5648733a74dfbad9ca76b1e58282e0240d195d52be85e29"},"schema_version":"1.0","source":{"id":"1303.4712","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1303.4712","created_at":"2026-05-18T00:03:34Z"},{"alias_kind":"arxiv_version","alias_value":"1303.4712v3","created_at":"2026-05-18T00:03:34Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1303.4712","created_at":"2026-05-18T00:03:34Z"},{"alias_kind":"pith_short_12","alias_value":"SE4XY3JS55GC","created_at":"2026-05-18T12:27:59Z"},{"alias_kind":"pith_short_16","alias_value":"SE4XY3JS55GCS7HK","created_at":"2026-05-18T12:27:59Z"},{"alias_kind":"pith_short_8","alias_value":"SE4XY3JS","created_at":"2026-05-18T12:27:59Z"}],"graph_snapshots":[{"event_id":"sha256:620473c29c1e38451bafe318b70e2b4755a098be64ff400f3a58ed7dcd51e060","target":"graph","created_at":"2026-05-18T00:03:34Z","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 prove a singular version of the Engel theorem. We prove a normal form theorem for germs of holomorphic singular Engel systems with good conditions on its singular set. As an application, we prove that there exists an integral analytic curve passing through the singular points of the system. Also, we prove that a globally decomposable Engel system on a four dimensional projective space has singular set with atypical codimension.","authors_text":"Luis G. Maza, Maur\\'icio Corr\\^ea Jr","cross_cats":["math.AG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2013-03-19T19:31:16Z","title":"Engel theorem through singularities"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1303.4712","kind":"arxiv","version":3},"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":"sha256:1edca3e1a245d61bfb73a9b2d451d0e9c885533392556476ceb2dd702c28ca1c","target":"record","created_at":"2026-05-18T00:03:34Z","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":"442f1695460ff5e8df30c365d3054ef61da19c6de5cfd4b5ad0359503211aa51","cross_cats_sorted":["math.AG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2013-03-19T19:31:16Z","title_canon_sha256":"efe649ccae5de546d5648733a74dfbad9ca76b1e58282e0240d195d52be85e29"},"schema_version":"1.0","source":{"id":"1303.4712","kind":"arxiv","version":3}},"canonical_sha256":"91397c6d32ef4c297ceac16e1592531cd07532ee4fd4945cbf64e6735b24c6a9","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"91397c6d32ef4c297ceac16e1592531cd07532ee4fd4945cbf64e6735b24c6a9","first_computed_at":"2026-05-18T00:03:34.711518Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:03:34.711518Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"mALyVwq6HHRMPX4aIvaiadWrR6BvsLbcNWXLWsjOfoxnim+kIiTrw6WcZi48AoxEzqBt16ZdfqZVlcfSWYYxBg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:03:34.712250Z","signed_message":"canonical_sha256_bytes"},"source_id":"1303.4712","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1edca3e1a245d61bfb73a9b2d451d0e9c885533392556476ceb2dd702c28ca1c","sha256:620473c29c1e38451bafe318b70e2b4755a098be64ff400f3a58ed7dcd51e060"],"state_sha256":"7a4fa24c7cb62c0ccb580afbea14fc1dd7719146dcd5ef30ed652ca98c1f24dd"}