{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:JLOYXKOUI3HNG7GX6ZRBJ2HLE7","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":"3929188facf441ff2f9f326764b2a20b94e516cea70ec633c978757cc11946cb","cross_cats_sorted":["math.CA","math.CV"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2018-12-06T12:27:57Z","title_canon_sha256":"bac0209fb95a1cb0635a13e61bc02d6769c0e7b8c8e719085a7ce25202a882d1"},"schema_version":"1.0","source":{"id":"1812.02491","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1812.02491","created_at":"2026-05-17T23:58:55Z"},{"alias_kind":"arxiv_version","alias_value":"1812.02491v1","created_at":"2026-05-17T23:58:55Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1812.02491","created_at":"2026-05-17T23:58:55Z"},{"alias_kind":"pith_short_12","alias_value":"JLOYXKOUI3HN","created_at":"2026-05-18T12:32:31Z"},{"alias_kind":"pith_short_16","alias_value":"JLOYXKOUI3HNG7GX","created_at":"2026-05-18T12:32:31Z"},{"alias_kind":"pith_short_8","alias_value":"JLOYXKOU","created_at":"2026-05-18T12:32:31Z"}],"graph_snapshots":[{"event_id":"sha256:2cd619f326eb9d036cbed07fbb7b604d322f5cc0f34d30a30fbe72d9b70d1595","target":"graph","created_at":"2026-05-17T23:58:55Z","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 studies germs of holomorphic vector fields at the origin of C3 that are tangent to holomorphic foliations of codimension one. Two situations are considered. First, we assume hypotheses on the reduction of singularities of the vector field - for instance, that the final models belong to a family of vector fields whose linear parts have eigenvalues satisfying a condition of non-resonance - in order to conclude that the foliation is of complex hyperbolic type, that is, without saddle-nodes in its reduction of singularities. In the second part, we prove that a vector field that is tan","authors_text":"Dan\\'ubia Junca, Rog\\'erio Mol","cross_cats":["math.CA","math.CV"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2018-12-06T12:27:57Z","title":"Holomorphic vector fields tangent to foliations in dimension three"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1812.02491","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:b4ef885a49bf054e4cfc69468c7c7bbd2cbfccb3ead4230d88a3c2655b4edc3c","target":"record","created_at":"2026-05-17T23:58:55Z","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":"3929188facf441ff2f9f326764b2a20b94e516cea70ec633c978757cc11946cb","cross_cats_sorted":["math.CA","math.CV"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2018-12-06T12:27:57Z","title_canon_sha256":"bac0209fb95a1cb0635a13e61bc02d6769c0e7b8c8e719085a7ce25202a882d1"},"schema_version":"1.0","source":{"id":"1812.02491","kind":"arxiv","version":1}},"canonical_sha256":"4add8ba9d446ced37cd7f66214e8eb27ed30d37e93fc8245d7df4a13e3b5cff7","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"4add8ba9d446ced37cd7f66214e8eb27ed30d37e93fc8245d7df4a13e3b5cff7","first_computed_at":"2026-05-17T23:58:55.555229Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:58:55.555229Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"3FhLdc4TLc72fQ5Ee1Mc6N+AMbYoEmB0go9AowLMmjb5fhf52PZgwPutXeMeC+K2HKeH8YKhv9I9XkZ6WTpcAg==","signature_status":"signed_v1","signed_at":"2026-05-17T23:58:55.555673Z","signed_message":"canonical_sha256_bytes"},"source_id":"1812.02491","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b4ef885a49bf054e4cfc69468c7c7bbd2cbfccb3ead4230d88a3c2655b4edc3c","sha256:2cd619f326eb9d036cbed07fbb7b604d322f5cc0f34d30a30fbe72d9b70d1595"],"state_sha256":"18dbc6d5dcde49e572d73607bc2f6d90e5265d5be5827e3740cd74f8ba52d882"}