{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:GXGW7LWVVPOXWLWLJY3UGZXQIB","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"95b10ecde770a76a73327b0233c2e1c829a78eeaf8d26fb0c36d93addc9683d2","cross_cats_sorted":["math.DS"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2010-12-29T18:01:17Z","title_canon_sha256":"0ae4024e1d35aef130efcdcd3cbc4c9d89ec362603656b59b6a8cdcbeaae13f9"},"schema_version":"1.0","source":{"id":"1012.5993","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1012.5993","created_at":"2026-05-18T03:05:35Z"},{"alias_kind":"arxiv_version","alias_value":"1012.5993v3","created_at":"2026-05-18T03:05:35Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1012.5993","created_at":"2026-05-18T03:05:35Z"},{"alias_kind":"pith_short_12","alias_value":"GXGW7LWVVPOX","created_at":"2026-05-18T12:26:07Z"},{"alias_kind":"pith_short_16","alias_value":"GXGW7LWVVPOXWLWL","created_at":"2026-05-18T12:26:07Z"},{"alias_kind":"pith_short_8","alias_value":"GXGW7LWV","created_at":"2026-05-18T12:26:07Z"}],"graph_snapshots":[{"event_id":"sha256:bd2521a764fd52a461f48d1af567c4802682f29a48ac000732a975e89cae2694","target":"graph","created_at":"2026-05-18T03:05:35Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"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.","authors_text":"Jiri Lebl","cross_cats":["math.DS"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2010-12-29T18:01:17Z","title":"Singular set of a Levi-flat hypersurface is Levi-flat"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1012.5993","kind":"arxiv","version":3},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:6b4f421d2f3f8b0bead71c434ac47b5652a3d0d1d95077aeb155ba3ebd5fce54","target":"record","created_at":"2026-05-18T03:05:35Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"95b10ecde770a76a73327b0233c2e1c829a78eeaf8d26fb0c36d93addc9683d2","cross_cats_sorted":["math.DS"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2010-12-29T18:01:17Z","title_canon_sha256":"0ae4024e1d35aef130efcdcd3cbc4c9d89ec362603656b59b6a8cdcbeaae13f9"},"schema_version":"1.0","source":{"id":"1012.5993","kind":"arxiv","version":3}},"canonical_sha256":"35cd6faed5abdd7b2ecb4e374366f04070b229c570f92f33aaf5e4fd4e3fb53c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"35cd6faed5abdd7b2ecb4e374366f04070b229c570f92f33aaf5e4fd4e3fb53c","first_computed_at":"2026-05-18T03:05:35.926026Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:05:35.926026Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"9XVYhYC3V0kM5S42JBU7n07OyiiVxfa3vfqRrMpwICa3XDTESNm28O8l6eJqOH9etEdJbtdSSoC6ap4yyhrLDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T03:05:35.926622Z","signed_message":"canonical_sha256_bytes"},"source_id":"1012.5993","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:6b4f421d2f3f8b0bead71c434ac47b5652a3d0d1d95077aeb155ba3ebd5fce54","sha256:bd2521a764fd52a461f48d1af567c4802682f29a48ac000732a975e89cae2694"],"state_sha256":"ccc81960ba430b44b5ca47f356c979feca088feb1ff25ad86402fe7038c69755"}