{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2016:UUC7WFHNFEW46Z3DNLGCR2O64A","short_pith_number":"pith:UUC7WFHN","schema_version":"1.0","canonical_sha256":"a505fb14ed292dcf67636acc28e9dee03f72dc1bcca420bfa3c75e89265fb675","source":{"kind":"arxiv","id":"1606.07242","version":1},"attestation_state":"computed","paper":{"title":"Holomorphic normal form of nonlinear perturbations of nilpotent vector fields","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CV"],"primary_cat":"math.DS","authors_text":"Freek Verstringe, Laurent Stolovitch (JAD)","submitted_at":"2016-06-23T09:30:52Z","abstract_excerpt":"We consider germs of holomorphic vector fields at a fixed point having a nilpotent linear part at that point, in dimension $n \\geq 3$. Based on Belitskii's work, we know that such a vector field is formally conjugate to a (formal) normal form. We give a condition on that normal form which ensure that the normalizing transformation is holomorphic at the fixed point. We shall show that this sufficient condition is a nilpotent version of Bruno's condition (A). In dimension 2, no condition is required since, according to Str{\\'o}zyna- Zoladek, each such germ is holomorphically conjugate to a Taken"},"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":"1606.07242","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2016-06-23T09:30:52Z","cross_cats_sorted":["math.CV"],"title_canon_sha256":"ce7b9af414296a6e8afaafa2b1f21324fcdfdaa204519f74497f5ab9b2aa854c","abstract_canon_sha256":"0196578f09ca5538c8eeb8938d4956404f48821f084235f450c775cd826b8c00"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:08:08.804446Z","signature_b64":"aDVHf32cSy1f0QQ7FGABytUW2+XMBULPwRR9b3MCZGFIfa/bt7chViAMOqKMF7P4A14RTEylEHiVm2ufP4oqAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a505fb14ed292dcf67636acc28e9dee03f72dc1bcca420bfa3c75e89265fb675","last_reissued_at":"2026-05-18T01:08:08.803967Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:08:08.803967Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Holomorphic normal form of nonlinear perturbations of nilpotent vector fields","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CV"],"primary_cat":"math.DS","authors_text":"Freek Verstringe, Laurent Stolovitch (JAD)","submitted_at":"2016-06-23T09:30:52Z","abstract_excerpt":"We consider germs of holomorphic vector fields at a fixed point having a nilpotent linear part at that point, in dimension $n \\geq 3$. Based on Belitskii's work, we know that such a vector field is formally conjugate to a (formal) normal form. We give a condition on that normal form which ensure that the normalizing transformation is holomorphic at the fixed point. We shall show that this sufficient condition is a nilpotent version of Bruno's condition (A). In dimension 2, no condition is required since, according to Str{\\'o}zyna- Zoladek, each such germ is holomorphically conjugate to a Taken"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1606.07242","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":"1606.07242","created_at":"2026-05-18T01:08:08.804031+00:00"},{"alias_kind":"arxiv_version","alias_value":"1606.07242v1","created_at":"2026-05-18T01:08:08.804031+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1606.07242","created_at":"2026-05-18T01:08:08.804031+00:00"},{"alias_kind":"pith_short_12","alias_value":"UUC7WFHNFEW4","created_at":"2026-05-18T12:30:46.583412+00:00"},{"alias_kind":"pith_short_16","alias_value":"UUC7WFHNFEW46Z3D","created_at":"2026-05-18T12:30:46.583412+00:00"},{"alias_kind":"pith_short_8","alias_value":"UUC7WFHN","created_at":"2026-05-18T12:30:46.583412+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/UUC7WFHNFEW46Z3DNLGCR2O64A","json":"https://pith.science/pith/UUC7WFHNFEW46Z3DNLGCR2O64A.json","graph_json":"https://pith.science/api/pith-number/UUC7WFHNFEW46Z3DNLGCR2O64A/graph.json","events_json":"https://pith.science/api/pith-number/UUC7WFHNFEW46Z3DNLGCR2O64A/events.json","paper":"https://pith.science/paper/UUC7WFHN"},"agent_actions":{"view_html":"https://pith.science/pith/UUC7WFHNFEW46Z3DNLGCR2O64A","download_json":"https://pith.science/pith/UUC7WFHNFEW46Z3DNLGCR2O64A.json","view_paper":"https://pith.science/paper/UUC7WFHN","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1606.07242&json=true","fetch_graph":"https://pith.science/api/pith-number/UUC7WFHNFEW46Z3DNLGCR2O64A/graph.json","fetch_events":"https://pith.science/api/pith-number/UUC7WFHNFEW46Z3DNLGCR2O64A/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/UUC7WFHNFEW46Z3DNLGCR2O64A/action/timestamp_anchor","attest_storage":"https://pith.science/pith/UUC7WFHNFEW46Z3DNLGCR2O64A/action/storage_attestation","attest_author":"https://pith.science/pith/UUC7WFHNFEW46Z3DNLGCR2O64A/action/author_attestation","sign_citation":"https://pith.science/pith/UUC7WFHNFEW46Z3DNLGCR2O64A/action/citation_signature","submit_replication":"https://pith.science/pith/UUC7WFHNFEW46Z3DNLGCR2O64A/action/replication_record"}},"created_at":"2026-05-18T01:08:08.804031+00:00","updated_at":"2026-05-18T01:08:08.804031+00:00"}