{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2014:KRYPNCZMLASCD6MZRZ7FVP7AWC","short_pith_number":"pith:KRYPNCZM","schema_version":"1.0","canonical_sha256":"5470f68b2c582421f9998e7e5abfe0b0965fc41f9c992cf2ef358665cb4cde51","source":{"kind":"arxiv","id":"1410.3527","version":1},"attestation_state":"computed","paper":{"title":"2-dimensional Lie algebras and separatrices for vector fields on (C^3,0)","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CV"],"primary_cat":"math.DS","authors_text":"Helena Reis, Julio C. Rebelo","submitted_at":"2014-10-13T22:24:31Z","abstract_excerpt":"We show that holomorphic vector fields on (C^3,0) have separatrices provided that they are embedded in a rank 2 representation of a two-dimensional Lie algebra. In turn, this result enables us to show that the second jet of a holomorphic vector field defined on a compact complex manifold M of dimension 3 cannot vanish at an isolated singular point provided that M carries more than a single holomorphic vector field."},"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":"1410.3527","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2014-10-13T22:24:31Z","cross_cats_sorted":["math.CV"],"title_canon_sha256":"3d66dac0c3dcc0834875d31e9ccdba3e50f4f2cc98bedfabbc8a57a8dedbcd6a","abstract_canon_sha256":"2a3c4cd2b1db42ab5fb3e742e27e7ccb65c2dd4121a0baa1a1d38bdb31f518a8"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:40:09.594619Z","signature_b64":"ccztoVSMdFoyMwUxE8ufLqGrZfQWyQLkd8RC76xsQv2J0l0EAWHs2QKgKdVQTcsHVy1g4U83SYfYOzRCaM0jCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5470f68b2c582421f9998e7e5abfe0b0965fc41f9c992cf2ef358665cb4cde51","last_reissued_at":"2026-05-18T02:40:09.592597Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:40:09.592597Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"2-dimensional Lie algebras and separatrices for vector fields on (C^3,0)","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CV"],"primary_cat":"math.DS","authors_text":"Helena Reis, Julio C. Rebelo","submitted_at":"2014-10-13T22:24:31Z","abstract_excerpt":"We show that holomorphic vector fields on (C^3,0) have separatrices provided that they are embedded in a rank 2 representation of a two-dimensional Lie algebra. In turn, this result enables us to show that the second jet of a holomorphic vector field defined on a compact complex manifold M of dimension 3 cannot vanish at an isolated singular point provided that M carries more than a single holomorphic vector field."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1410.3527","kind":"arxiv","version":1},"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":"1410.3527","created_at":"2026-05-18T02:40:09.592689+00:00"},{"alias_kind":"arxiv_version","alias_value":"1410.3527v1","created_at":"2026-05-18T02:40:09.592689+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1410.3527","created_at":"2026-05-18T02:40:09.592689+00:00"},{"alias_kind":"pith_short_12","alias_value":"KRYPNCZMLASC","created_at":"2026-05-18T12:28:35.611951+00:00"},{"alias_kind":"pith_short_16","alias_value":"KRYPNCZMLASCD6MZ","created_at":"2026-05-18T12:28:35.611951+00:00"},{"alias_kind":"pith_short_8","alias_value":"KRYPNCZM","created_at":"2026-05-18T12:28:35.611951+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/KRYPNCZMLASCD6MZRZ7FVP7AWC","json":"https://pith.science/pith/KRYPNCZMLASCD6MZRZ7FVP7AWC.json","graph_json":"https://pith.science/api/pith-number/KRYPNCZMLASCD6MZRZ7FVP7AWC/graph.json","events_json":"https://pith.science/api/pith-number/KRYPNCZMLASCD6MZRZ7FVP7AWC/events.json","paper":"https://pith.science/paper/KRYPNCZM"},"agent_actions":{"view_html":"https://pith.science/pith/KRYPNCZMLASCD6MZRZ7FVP7AWC","download_json":"https://pith.science/pith/KRYPNCZMLASCD6MZRZ7FVP7AWC.json","view_paper":"https://pith.science/paper/KRYPNCZM","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1410.3527&json=true","fetch_graph":"https://pith.science/api/pith-number/KRYPNCZMLASCD6MZRZ7FVP7AWC/graph.json","fetch_events":"https://pith.science/api/pith-number/KRYPNCZMLASCD6MZRZ7FVP7AWC/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/KRYPNCZMLASCD6MZRZ7FVP7AWC/action/timestamp_anchor","attest_storage":"https://pith.science/pith/KRYPNCZMLASCD6MZRZ7FVP7AWC/action/storage_attestation","attest_author":"https://pith.science/pith/KRYPNCZMLASCD6MZRZ7FVP7AWC/action/author_attestation","sign_citation":"https://pith.science/pith/KRYPNCZMLASCD6MZRZ7FVP7AWC/action/citation_signature","submit_replication":"https://pith.science/pith/KRYPNCZMLASCD6MZRZ7FVP7AWC/action/replication_record"}},"created_at":"2026-05-18T02:40:09.592689+00:00","updated_at":"2026-05-18T02:40:09.592689+00:00"}