{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2010:GXGW7LWVVPOXWLWLJY3UGZXQIB","short_pith_number":"pith:GXGW7LWV","schema_version":"1.0","canonical_sha256":"35cd6faed5abdd7b2ecb4e374366f04070b229c570f92f33aaf5e4fd4e3fb53c","source":{"kind":"arxiv","id":"1012.5993","version":3},"attestation_state":"computed","paper":{"title":"Singular set of a Levi-flat hypersurface is Levi-flat","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DS"],"primary_cat":"math.CV","authors_text":"Jiri Lebl","submitted_at":"2010-12-29T18:01:17Z","abstract_excerpt":"We study the singular set of a singular Levi-flat real-analytic hypersurface. We prove that the singular set of such a hypersurface is Levi-flat in the appropriate sense. We also show that if the singular set is small enough, then the Levi-foliation extends to a singular codimension one holomorphic foliation of a neighborhood of the hypersurface."},"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":"1012.5993","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2010-12-29T18:01:17Z","cross_cats_sorted":["math.DS"],"title_canon_sha256":"0ae4024e1d35aef130efcdcd3cbc4c9d89ec362603656b59b6a8cdcbeaae13f9","abstract_canon_sha256":"95b10ecde770a76a73327b0233c2e1c829a78eeaf8d26fb0c36d93addc9683d2"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:05:35.926622Z","signature_b64":"9XVYhYC3V0kM5S42JBU7n07OyiiVxfa3vfqRrMpwICa3XDTESNm28O8l6eJqOH9etEdJbtdSSoC6ap4yyhrLDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"35cd6faed5abdd7b2ecb4e374366f04070b229c570f92f33aaf5e4fd4e3fb53c","last_reissued_at":"2026-05-18T03:05:35.926026Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:05:35.926026Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Singular set of a Levi-flat hypersurface is Levi-flat","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DS"],"primary_cat":"math.CV","authors_text":"Jiri Lebl","submitted_at":"2010-12-29T18:01:17Z","abstract_excerpt":"We study the singular set of a singular Levi-flat real-analytic hypersurface. We prove that the singular set of such a hypersurface is Levi-flat in the appropriate sense. We also show that if the singular set is small enough, then the Levi-foliation extends to a singular codimension one holomorphic foliation of a neighborhood of the hypersurface."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1012.5993","kind":"arxiv","version":3},"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":"1012.5993","created_at":"2026-05-18T03:05:35.926099+00:00"},{"alias_kind":"arxiv_version","alias_value":"1012.5993v3","created_at":"2026-05-18T03:05:35.926099+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1012.5993","created_at":"2026-05-18T03:05:35.926099+00:00"},{"alias_kind":"pith_short_12","alias_value":"GXGW7LWVVPOX","created_at":"2026-05-18T12:26:07.630475+00:00"},{"alias_kind":"pith_short_16","alias_value":"GXGW7LWVVPOXWLWL","created_at":"2026-05-18T12:26:07.630475+00:00"},{"alias_kind":"pith_short_8","alias_value":"GXGW7LWV","created_at":"2026-05-18T12:26:07.630475+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/GXGW7LWVVPOXWLWLJY3UGZXQIB","json":"https://pith.science/pith/GXGW7LWVVPOXWLWLJY3UGZXQIB.json","graph_json":"https://pith.science/api/pith-number/GXGW7LWVVPOXWLWLJY3UGZXQIB/graph.json","events_json":"https://pith.science/api/pith-number/GXGW7LWVVPOXWLWLJY3UGZXQIB/events.json","paper":"https://pith.science/paper/GXGW7LWV"},"agent_actions":{"view_html":"https://pith.science/pith/GXGW7LWVVPOXWLWLJY3UGZXQIB","download_json":"https://pith.science/pith/GXGW7LWVVPOXWLWLJY3UGZXQIB.json","view_paper":"https://pith.science/paper/GXGW7LWV","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1012.5993&json=true","fetch_graph":"https://pith.science/api/pith-number/GXGW7LWVVPOXWLWLJY3UGZXQIB/graph.json","fetch_events":"https://pith.science/api/pith-number/GXGW7LWVVPOXWLWLJY3UGZXQIB/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/GXGW7LWVVPOXWLWLJY3UGZXQIB/action/timestamp_anchor","attest_storage":"https://pith.science/pith/GXGW7LWVVPOXWLWLJY3UGZXQIB/action/storage_attestation","attest_author":"https://pith.science/pith/GXGW7LWVVPOXWLWLJY3UGZXQIB/action/author_attestation","sign_citation":"https://pith.science/pith/GXGW7LWVVPOXWLWLJY3UGZXQIB/action/citation_signature","submit_replication":"https://pith.science/pith/GXGW7LWVVPOXWLWLJY3UGZXQIB/action/replication_record"}},"created_at":"2026-05-18T03:05:35.926099+00:00","updated_at":"2026-05-18T03:05:35.926099+00:00"}