{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:QYSY3NBR7EMNTFY43WONHO6PU4","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":"6b4ed68695d3b9f88b5f025755d5d5a1e69873d2dffb5101b5e49308bf039c70","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2014-05-02T23:33:19Z","title_canon_sha256":"adbec2d13fedcf77a59b2bac46caf69b29536b4966f4d29c53d96029c7777980"},"schema_version":"1.0","source":{"id":"1405.0539","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1405.0539","created_at":"2026-05-18T01:17:05Z"},{"alias_kind":"arxiv_version","alias_value":"1405.0539v4","created_at":"2026-05-18T01:17:05Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1405.0539","created_at":"2026-05-18T01:17:05Z"},{"alias_kind":"pith_short_12","alias_value":"QYSY3NBR7EMN","created_at":"2026-05-18T12:28:46Z"},{"alias_kind":"pith_short_16","alias_value":"QYSY3NBR7EMNTFY4","created_at":"2026-05-18T12:28:46Z"},{"alias_kind":"pith_short_8","alias_value":"QYSY3NBR","created_at":"2026-05-18T12:28:46Z"}],"graph_snapshots":[{"event_id":"sha256:c7d9efe386e004227149135352ceba31bb968a3e66e6e901eea1fd6aab1a4980","target":"graph","created_at":"2026-05-18T01:17:05Z","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 prove that the characteristic foliation $F$ on a non-singular divisor $D$ in an irreducible projective hyperkaehler manifold $X$ cannot be algebraic, unless the leaves of $F$ are rational curves or $X$ is a surface. More generally, we show that if $X$ is an arbitrary projective manifold carrying a holomorphic symplectic $2$-form, and $D$ and $F$ are as above, then $F$ can be algebraic with non-rational leaves only when, up to a finite \\'etale cover, $X$ is the product of a symplectic projective manifold $Y$ with a symplectic surface and $D$ is the pull-back of a curve on this surface.\n  Whe","authors_text":"Ekaterina Amerik, Fr\\'ed\\'eric Campana","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2014-05-02T23:33:19Z","title":"Characteristic foliation on non-uniruled smooth divisors on hyperkaehler manifolds"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1405.0539","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":"sha256:25dcc3be79450a97da57034b12921e2220e6c90bc38237f03d0087c3d04516dd","target":"record","created_at":"2026-05-18T01:17:05Z","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":"6b4ed68695d3b9f88b5f025755d5d5a1e69873d2dffb5101b5e49308bf039c70","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2014-05-02T23:33:19Z","title_canon_sha256":"adbec2d13fedcf77a59b2bac46caf69b29536b4966f4d29c53d96029c7777980"},"schema_version":"1.0","source":{"id":"1405.0539","kind":"arxiv","version":4}},"canonical_sha256":"86258db431f918d9971cdd9cd3bbcfa7223d86e395f5c391c61c7412c8b8b792","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"86258db431f918d9971cdd9cd3bbcfa7223d86e395f5c391c61c7412c8b8b792","first_computed_at":"2026-05-18T01:17:05.709524Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:17:05.709524Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"LiEo/VPBPookBxEbGFCNLJeX9zfn92K3PEE5Oy4WUfkAqysHr79Yqmce4fotSMPMpO7h7j4lMlJVK5MY5weKCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:17:05.710242Z","signed_message":"canonical_sha256_bytes"},"source_id":"1405.0539","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:25dcc3be79450a97da57034b12921e2220e6c90bc38237f03d0087c3d04516dd","sha256:c7d9efe386e004227149135352ceba31bb968a3e66e6e901eea1fd6aab1a4980"],"state_sha256":"75f169c956c094d5a5537c776d917f8e33c4510c6e684eec9a4d43a79195a7aa"}