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We prove that there exists a holomorphic change of coordinate $\\phi$ such that $\\phi(M)=(\\mathcal{R}e(h)=0)$ where $h(z)$ is a polynomial of degree $\\mu+1$ and $j^{k}_{0}(h)=P$."},"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":"1003.4999","kind":"arxiv","version":4},"metadata":{"license":"http://creativecommons.org/licenses/by/3.0/","primary_cat":"math.CV","submitted_at":"2010-03-25T20:58:19Z","cross_cats_sorted":[],"title_canon_sha256":"b6004955934adf936d75369b0118dd8a07ca1f214be444231bbb0d2b707dddf3","abstract_canon_sha256":"60a02be84a029fe8fa95f5c0a6d9964ee734fe88d54fa2d6583fcc3927359118"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:13:47.239508Z","signature_b64":"WB9CZy0Jc45ZXq0AXk6FgPp+z44vOyxP0wZoc9+tRrNNja0wyUBmElGJBcIRmKvdiLxEBzdIAE3AjI6JeOFaBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d6c0f827ad3f8f2d8fff2314005d2ae4bef99fb8baedd7b991dd2af9edce9eae","last_reissued_at":"2026-05-18T04:13:47.239093Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:13:47.239093Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On Normal Forms of Singular Levi-Flat Real Analytic Hypersurfaces","license":"http://creativecommons.org/licenses/by/3.0/","headline":"","cross_cats":[],"primary_cat":"math.CV","authors_text":"Arturo Fern\\'andez-P\\'erez","submitted_at":"2010-03-25T20:58:19Z","abstract_excerpt":"Let $F(z)=\\mathcal{R}e(P(z)) + h.o.t$ be such that $M=(F=0)$ defines a germ of real analytic Levi-flat at $0\\in\\mathbb{C}^{n}$, $n\\geq{2}$, where $P(z)$ is a homogeneous polynomial of degree $k$ with an isolated singularity at $0\\in\\mathbb{C}^{n}$ and Milnor number $\\mu$. We prove that there exists a holomorphic change of coordinate $\\phi$ such that $\\phi(M)=(\\mathcal{R}e(h)=0)$ where $h(z)$ is a polynomial of degree $\\mu+1$ and $j^{k}_{0}(h)=P$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1003.4999","kind":"arxiv","version":4},"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":"1003.4999","created_at":"2026-05-18T04:13:47.239152+00:00"},{"alias_kind":"arxiv_version","alias_value":"1003.4999v4","created_at":"2026-05-18T04:13:47.239152+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1003.4999","created_at":"2026-05-18T04:13:47.239152+00:00"},{"alias_kind":"pith_short_12","alias_value":"23APQJ5NH6HS","created_at":"2026-05-18T12:26:03.138858+00:00"},{"alias_kind":"pith_short_16","alias_value":"23APQJ5NH6HS3D77","created_at":"2026-05-18T12:26:03.138858+00:00"},{"alias_kind":"pith_short_8","alias_value":"23APQJ5N","created_at":"2026-05-18T12:26:03.138858+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/23APQJ5NH6HS3D77EMKAAXJK4S","json":"https://pith.science/pith/23APQJ5NH6HS3D77EMKAAXJK4S.json","graph_json":"https://pith.science/api/pith-number/23APQJ5NH6HS3D77EMKAAXJK4S/graph.json","events_json":"https://pith.science/api/pith-number/23APQJ5NH6HS3D77EMKAAXJK4S/events.json","paper":"https://pith.science/paper/23APQJ5N"},"agent_actions":{"view_html":"https://pith.science/pith/23APQJ5NH6HS3D77EMKAAXJK4S","download_json":"https://pith.science/pith/23APQJ5NH6HS3D77EMKAAXJK4S.json","view_paper":"https://pith.science/paper/23APQJ5N","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1003.4999&json=true","fetch_graph":"https://pith.science/api/pith-number/23APQJ5NH6HS3D77EMKAAXJK4S/graph.json","fetch_events":"https://pith.science/api/pith-number/23APQJ5NH6HS3D77EMKAAXJK4S/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/23APQJ5NH6HS3D77EMKAAXJK4S/action/timestamp_anchor","attest_storage":"https://pith.science/pith/23APQJ5NH6HS3D77EMKAAXJK4S/action/storage_attestation","attest_author":"https://pith.science/pith/23APQJ5NH6HS3D77EMKAAXJK4S/action/author_attestation","sign_citation":"https://pith.science/pith/23APQJ5NH6HS3D77EMKAAXJK4S/action/citation_signature","submit_replication":"https://pith.science/pith/23APQJ5NH6HS3D77EMKAAXJK4S/action/replication_record"}},"created_at":"2026-05-18T04:13:47.239152+00:00","updated_at":"2026-05-18T04:13:47.239152+00:00"}