{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2008:YSCKKIWYWP63F5FYZ2HW5IDOX5","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":"b3b8775c1eb5946df6d160c188090ff092fba62a52f30c529c46dfbff702cd3b","cross_cats_sorted":["math.AG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2008-05-13T00:03:51Z","title_canon_sha256":"61edec8882fdf3af9680c17a18c8a8e8e747306d3383a514bcd59870939278b5"},"schema_version":"1.0","source":{"id":"0805.1763","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0805.1763","created_at":"2026-05-18T04:01:23Z"},{"alias_kind":"arxiv_version","alias_value":"0805.1763v4","created_at":"2026-05-18T04:01:23Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0805.1763","created_at":"2026-05-18T04:01:23Z"},{"alias_kind":"pith_short_12","alias_value":"YSCKKIWYWP63","created_at":"2026-05-18T12:25:58Z"},{"alias_kind":"pith_short_16","alias_value":"YSCKKIWYWP63F5FY","created_at":"2026-05-18T12:25:58Z"},{"alias_kind":"pith_short_8","alias_value":"YSCKKIWY","created_at":"2026-05-18T12:25:58Z"}],"graph_snapshots":[{"event_id":"sha256:39f91ea4b054e7905e7923212c6c87190a6e4a045a540f18e2b612814eda14c1","target":"graph","created_at":"2026-05-18T04:01:23Z","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 singular real-analytic Levi-flat hypersurfaces in complex projective space. We define the rank of an algebraic Levi-flat hypersurface and study the connections between rank, degree, and the type and size of the singularity. In particular, we study degenerate singularities of algebraic Levi-flat hypersurfaces. We then give necessary and sufficient conditions for a Levi-flat hypersurface to be a pullback of a real-analytic curve in $\\mathbb{C}$ via a meromorphic function. Among other examples, we construct a nonalgebraic semianalytic Levi-flat hypersurface with compact leaves that is a ","authors_text":"Jiri Lebl","cross_cats":["math.AG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2008-05-13T00:03:51Z","title":"Algebraic Levi-flat hypervarieties in complex projective space"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0805.1763","kind":"arxiv","version":4},"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":"sha256:96b84707da0858b0af6288df7ab349e6eacebd66a76cbe64ccb0b526f22bf7d5","target":"record","created_at":"2026-05-18T04:01:23Z","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":"b3b8775c1eb5946df6d160c188090ff092fba62a52f30c529c46dfbff702cd3b","cross_cats_sorted":["math.AG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2008-05-13T00:03:51Z","title_canon_sha256":"61edec8882fdf3af9680c17a18c8a8e8e747306d3383a514bcd59870939278b5"},"schema_version":"1.0","source":{"id":"0805.1763","kind":"arxiv","version":4}},"canonical_sha256":"c484a522d8b3fdb2f4b8ce8f6ea06ebf741a9fc171113e201f476104773db2cf","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c484a522d8b3fdb2f4b8ce8f6ea06ebf741a9fc171113e201f476104773db2cf","first_computed_at":"2026-05-18T04:01:23.903686Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:01:23.903686Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"S9N/55HYiIv5GODk1vVbfH6F8TB80Y74iMeHR+bCSgVG62urtqX49I4a53w9QDs/uyD6CS+OCYaK8gHTa6SgBg==","signature_status":"signed_v1","signed_at":"2026-05-18T04:01:23.904447Z","signed_message":"canonical_sha256_bytes"},"source_id":"0805.1763","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:96b84707da0858b0af6288df7ab349e6eacebd66a76cbe64ccb0b526f22bf7d5","sha256:39f91ea4b054e7905e7923212c6c87190a6e4a045a540f18e2b612814eda14c1"],"state_sha256":"6d01eed779992ba6a8f6e476cc7246f5d7d3ecd5f7c49e0e899cf977ea38ad49"}