{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:IYJX676XMKZQFUV2TG4UKL5KXT","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":"7e4f318b3342658933426d1894dfe2c215d410c663c1a4d092a33991b849155f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2017-03-31T03:54:34Z","title_canon_sha256":"d23e0a06955a88c00c4f1907f14f99b2356b9b531d1ba920b1a5893933b889b4"},"schema_version":"1.0","source":{"id":"1703.10749","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1703.10749","created_at":"2026-05-18T00:46:51Z"},{"alias_kind":"arxiv_version","alias_value":"1703.10749v2","created_at":"2026-05-18T00:46:51Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1703.10749","created_at":"2026-05-18T00:46:51Z"},{"alias_kind":"pith_short_12","alias_value":"IYJX676XMKZQ","created_at":"2026-05-18T12:31:21Z"},{"alias_kind":"pith_short_16","alias_value":"IYJX676XMKZQFUV2","created_at":"2026-05-18T12:31:21Z"},{"alias_kind":"pith_short_8","alias_value":"IYJX676X","created_at":"2026-05-18T12:31:21Z"}],"graph_snapshots":[{"event_id":"sha256:c3386e253c1b45d12c2f76646dedc8857defe25300928be8bc5a57f5acf5d54e","target":"graph","created_at":"2026-05-18T00:46:51Z","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 study in this paper several properties concerning singularities of foliations in $(\\mathbb{C}^3,\\mathbf{0})$ that are pull-back of dicritical foliations in $(\\mathbb{C}^2,\\mathbf{0})$. Particularly, we will investigate the existence of first integrals (holomorphic and meromorphic) and the dicriticalness of such a foliation. In the study of meromorphic first integrals we follow the same method used by R. Meziani and P. Sad in dimension two. While the foliations we study are pull-back of foliations in $(\\mathbb{C}^2,\\mathbf{0})$, the adaptations are not straightforward.","authors_text":"Hern\\'an Neciosup, Jorge Mozo Fern\\'andez, Percy Fern\\'andez S\\'anchez","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2017-03-31T03:54:34Z","title":"Dicritical nilpotent holomorphic foliations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1703.10749","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":"sha256:4e0f792e229ccc536aafa934035710c34124055b607550ce31343a3bcb12e65f","target":"record","created_at":"2026-05-18T00:46:51Z","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":"7e4f318b3342658933426d1894dfe2c215d410c663c1a4d092a33991b849155f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2017-03-31T03:54:34Z","title_canon_sha256":"d23e0a06955a88c00c4f1907f14f99b2356b9b531d1ba920b1a5893933b889b4"},"schema_version":"1.0","source":{"id":"1703.10749","kind":"arxiv","version":2}},"canonical_sha256":"46137f7fd762b302d2ba99b9452faabcd7ff9af6dc912587f109d3cee584c636","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"46137f7fd762b302d2ba99b9452faabcd7ff9af6dc912587f109d3cee584c636","first_computed_at":"2026-05-18T00:46:51.186856Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:46:51.186856Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"WWsZxu1b+29q53eVIvaM6DNHnpKH0zHNQRYK7R5NIwVjFINQEqTIf2oL/CEgaaAQkdWhjET2knBmwAF7yzPUBA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:46:51.187599Z","signed_message":"canonical_sha256_bytes"},"source_id":"1703.10749","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:4e0f792e229ccc536aafa934035710c34124055b607550ce31343a3bcb12e65f","sha256:c3386e253c1b45d12c2f76646dedc8857defe25300928be8bc5a57f5acf5d54e"],"state_sha256":"82efd779a417fc952ecfa6985a5d249531c7bc1931dbda7b8c4a9d15b5a9faaf"}