{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2017:IYJX676XMKZQFUV2TG4UKL5KXT","short_pith_number":"pith:IYJX676X","schema_version":"1.0","canonical_sha256":"46137f7fd762b302d2ba99b9452faabcd7ff9af6dc912587f109d3cee584c636","source":{"kind":"arxiv","id":"1703.10749","version":2},"attestation_state":"computed","paper":{"title":"Dicritical nilpotent holomorphic foliations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Hern\\'an Neciosup, Jorge Mozo Fern\\'andez, Percy Fern\\'andez S\\'anchez","submitted_at":"2017-03-31T03:54:34Z","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."},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1703.10749","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2017-03-31T03:54:34Z","cross_cats_sorted":[],"title_canon_sha256":"d23e0a06955a88c00c4f1907f14f99b2356b9b531d1ba920b1a5893933b889b4","abstract_canon_sha256":"7e4f318b3342658933426d1894dfe2c215d410c663c1a4d092a33991b849155f"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:46:51.187599Z","signature_b64":"WWsZxu1b+29q53eVIvaM6DNHnpKH0zHNQRYK7R5NIwVjFINQEqTIf2oL/CEgaaAQkdWhjET2knBmwAF7yzPUBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"46137f7fd762b302d2ba99b9452faabcd7ff9af6dc912587f109d3cee584c636","last_reissued_at":"2026-05-18T00:46:51.186856Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:46:51.186856Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Dicritical nilpotent holomorphic foliations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Hern\\'an Neciosup, Jorge Mozo Fern\\'andez, Percy Fern\\'andez S\\'anchez","submitted_at":"2017-03-31T03:54:34Z","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."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1703.10749","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"aliases":[{"alias_kind":"arxiv","alias_value":"1703.10749","created_at":"2026-05-18T00:46:51.186987+00:00"},{"alias_kind":"arxiv_version","alias_value":"1703.10749v2","created_at":"2026-05-18T00:46:51.186987+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1703.10749","created_at":"2026-05-18T00:46:51.186987+00:00"},{"alias_kind":"pith_short_12","alias_value":"IYJX676XMKZQ","created_at":"2026-05-18T12:31:21.493067+00:00"},{"alias_kind":"pith_short_16","alias_value":"IYJX676XMKZQFUV2","created_at":"2026-05-18T12:31:21.493067+00:00"},{"alias_kind":"pith_short_8","alias_value":"IYJX676X","created_at":"2026-05-18T12:31:21.493067+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/IYJX676XMKZQFUV2TG4UKL5KXT","json":"https://pith.science/pith/IYJX676XMKZQFUV2TG4UKL5KXT.json","graph_json":"https://pith.science/api/pith-number/IYJX676XMKZQFUV2TG4UKL5KXT/graph.json","events_json":"https://pith.science/api/pith-number/IYJX676XMKZQFUV2TG4UKL5KXT/events.json","paper":"https://pith.science/paper/IYJX676X"},"agent_actions":{"view_html":"https://pith.science/pith/IYJX676XMKZQFUV2TG4UKL5KXT","download_json":"https://pith.science/pith/IYJX676XMKZQFUV2TG4UKL5KXT.json","view_paper":"https://pith.science/paper/IYJX676X","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1703.10749&json=true","fetch_graph":"https://pith.science/api/pith-number/IYJX676XMKZQFUV2TG4UKL5KXT/graph.json","fetch_events":"https://pith.science/api/pith-number/IYJX676XMKZQFUV2TG4UKL5KXT/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/IYJX676XMKZQFUV2TG4UKL5KXT/action/timestamp_anchor","attest_storage":"https://pith.science/pith/IYJX676XMKZQFUV2TG4UKL5KXT/action/storage_attestation","attest_author":"https://pith.science/pith/IYJX676XMKZQFUV2TG4UKL5KXT/action/author_attestation","sign_citation":"https://pith.science/pith/IYJX676XMKZQFUV2TG4UKL5KXT/action/citation_signature","submit_replication":"https://pith.science/pith/IYJX676XMKZQFUV2TG4UKL5KXT/action/replication_record"}},"created_at":"2026-05-18T00:46:51.186987+00:00","updated_at":"2026-05-18T00:46:51.186987+00:00"}