{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2017:FGTWL2CX6TLJ3VCVH2PVCTWDEK","short_pith_number":"pith:FGTWL2CX","schema_version":"1.0","canonical_sha256":"29a765e857f4d69dd4553e9f514ec322835bf087275be0bdb9662ae9983f8101","source":{"kind":"arxiv","id":"1710.02893","version":2},"attestation_state":"computed","paper":{"title":"Local normal forms of singular Levi-flat hypersurfaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CV","authors_text":"Arturo Fern\\'andez-P\\'erez, Gustavo Marra","submitted_at":"2017-10-08T22:17:27Z","abstract_excerpt":"We study normal forms of germs of singular real-analytic Levi-flat hypersurfaces. We prove the existence of rigid normal forms for singular Levi-flat hypersurfaces which are defined by the vanishing of the real part of complex quasi-homogeneous polynomials with isolated singularity. This result generalizes previous results of Burns-Gong and Fern\\'andez-P\\'erez. Furthermore, we prove the existence of two new rigid normal forms for singular real-analytic Levi-flat hypersurfaces which are preserved by a change of isochore coordinates, that is, a change of coordinates that preserves volume."},"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":"1710.02893","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2017-10-08T22:17:27Z","cross_cats_sorted":[],"title_canon_sha256":"7d9caf9eae42618835dd0e075565bd8f34a8b4eac02becf876f00af1c8428fee","abstract_canon_sha256":"2ba8a5852b3b655ffc60a821f2606a5fb48797c2e52811a28e54055eac4ebac3"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:03:24.933508Z","signature_b64":"ANnty1LWI6BERs5QHca9uN5FkuKyEyr14nlM1f8wRl19BPheE+aAnDMuTyx7wpwDcN/nZmx5cQP4aDi4jfQ0DA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"29a765e857f4d69dd4553e9f514ec322835bf087275be0bdb9662ae9983f8101","last_reissued_at":"2026-05-18T00:03:24.933052Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:03:24.933052Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Local normal forms of singular Levi-flat hypersurfaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CV","authors_text":"Arturo Fern\\'andez-P\\'erez, Gustavo Marra","submitted_at":"2017-10-08T22:17:27Z","abstract_excerpt":"We study normal forms of germs of singular real-analytic Levi-flat hypersurfaces. We prove the existence of rigid normal forms for singular Levi-flat hypersurfaces which are defined by the vanishing of the real part of complex quasi-homogeneous polynomials with isolated singularity. This result generalizes previous results of Burns-Gong and Fern\\'andez-P\\'erez. Furthermore, we prove the existence of two new rigid normal forms for singular real-analytic Levi-flat hypersurfaces which are preserved by a change of isochore coordinates, that is, a change of coordinates that preserves volume."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1710.02893","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":"1710.02893","created_at":"2026-05-18T00:03:24.933123+00:00"},{"alias_kind":"arxiv_version","alias_value":"1710.02893v2","created_at":"2026-05-18T00:03:24.933123+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1710.02893","created_at":"2026-05-18T00:03:24.933123+00:00"},{"alias_kind":"pith_short_12","alias_value":"FGTWL2CX6TLJ","created_at":"2026-05-18T12:31:15.632608+00:00"},{"alias_kind":"pith_short_16","alias_value":"FGTWL2CX6TLJ3VCV","created_at":"2026-05-18T12:31:15.632608+00:00"},{"alias_kind":"pith_short_8","alias_value":"FGTWL2CX","created_at":"2026-05-18T12:31:15.632608+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/FGTWL2CX6TLJ3VCVH2PVCTWDEK","json":"https://pith.science/pith/FGTWL2CX6TLJ3VCVH2PVCTWDEK.json","graph_json":"https://pith.science/api/pith-number/FGTWL2CX6TLJ3VCVH2PVCTWDEK/graph.json","events_json":"https://pith.science/api/pith-number/FGTWL2CX6TLJ3VCVH2PVCTWDEK/events.json","paper":"https://pith.science/paper/FGTWL2CX"},"agent_actions":{"view_html":"https://pith.science/pith/FGTWL2CX6TLJ3VCVH2PVCTWDEK","download_json":"https://pith.science/pith/FGTWL2CX6TLJ3VCVH2PVCTWDEK.json","view_paper":"https://pith.science/paper/FGTWL2CX","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1710.02893&json=true","fetch_graph":"https://pith.science/api/pith-number/FGTWL2CX6TLJ3VCVH2PVCTWDEK/graph.json","fetch_events":"https://pith.science/api/pith-number/FGTWL2CX6TLJ3VCVH2PVCTWDEK/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/FGTWL2CX6TLJ3VCVH2PVCTWDEK/action/timestamp_anchor","attest_storage":"https://pith.science/pith/FGTWL2CX6TLJ3VCVH2PVCTWDEK/action/storage_attestation","attest_author":"https://pith.science/pith/FGTWL2CX6TLJ3VCVH2PVCTWDEK/action/author_attestation","sign_citation":"https://pith.science/pith/FGTWL2CX6TLJ3VCVH2PVCTWDEK/action/citation_signature","submit_replication":"https://pith.science/pith/FGTWL2CX6TLJ3VCVH2PVCTWDEK/action/replication_record"}},"created_at":"2026-05-18T00:03:24.933123+00:00","updated_at":"2026-05-18T00:03:24.933123+00:00"}