{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:JZBEAJYKQSWWBFI6HEV7DCSFO5","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":"50e3f064634212495e5af5b56e8d90fe2fa3db7c2f4e3011d0f457d798ca1177","cross_cats_sorted":["math.DS"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2018-04-22T20:38:02Z","title_canon_sha256":"29c2f0e62c76cea774ecca82972b8b0c528dd348f88e761aab90137beb033da3"},"schema_version":"1.0","source":{"id":"1804.08165","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1804.08165","created_at":"2026-05-18T00:16:55Z"},{"alias_kind":"arxiv_version","alias_value":"1804.08165v2","created_at":"2026-05-18T00:16:55Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1804.08165","created_at":"2026-05-18T00:16:55Z"},{"alias_kind":"pith_short_12","alias_value":"JZBEAJYKQSWW","created_at":"2026-05-18T12:32:33Z"},{"alias_kind":"pith_short_16","alias_value":"JZBEAJYKQSWWBFI6","created_at":"2026-05-18T12:32:33Z"},{"alias_kind":"pith_short_8","alias_value":"JZBEAJYK","created_at":"2026-05-18T12:32:33Z"}],"graph_snapshots":[{"event_id":"sha256:9bf830c510092c32220af53f251583671aaa646992d643bd378195e445004b51","target":"graph","created_at":"2026-05-18T00:16:55Z","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 present a variant of the classical Darboux-Jouanolou Theorem. Our main result provides a characterization of foliations which are pull-backs of foliations on surfaces by rational maps. As an application, we provide a structure theorem for foliations on 3-folds admitting an infinite number of extremal rays.","authors_text":"Calum Spicer, Jorge Vitorio Pereira","cross_cats":["math.DS"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2018-04-22T20:38:02Z","title":"Hypersurfaces quasi-invariant by codimension one foliations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1804.08165","kind":"arxiv","version":2},"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":"sha256:47ebf423750d87d33c8e26edb4c2ba668a6c34dcd9bfc225d7f3dcbb764c1598","target":"record","created_at":"2026-05-18T00:16:55Z","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":"50e3f064634212495e5af5b56e8d90fe2fa3db7c2f4e3011d0f457d798ca1177","cross_cats_sorted":["math.DS"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2018-04-22T20:38:02Z","title_canon_sha256":"29c2f0e62c76cea774ecca82972b8b0c528dd348f88e761aab90137beb033da3"},"schema_version":"1.0","source":{"id":"1804.08165","kind":"arxiv","version":2}},"canonical_sha256":"4e4240270a84ad60951e392bf18a4577537d3b1556cbb6e1ac5f7ea8d4d3d130","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"4e4240270a84ad60951e392bf18a4577537d3b1556cbb6e1ac5f7ea8d4d3d130","first_computed_at":"2026-05-18T00:16:55.375169Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:16:55.375169Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"bwMzHlp+GTBY+xSq9tACqilxB/PTHGFaiU9brEEr5I2TzVHCB62oVrRCRjF43zI5HhWWtkdfMJAA3LKuPeQLAg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:16:55.375783Z","signed_message":"canonical_sha256_bytes"},"source_id":"1804.08165","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:47ebf423750d87d33c8e26edb4c2ba668a6c34dcd9bfc225d7f3dcbb764c1598","sha256:9bf830c510092c32220af53f251583671aaa646992d643bd378195e445004b51"],"state_sha256":"bfc75657d768e7e318c92b1c277f62e93eb6a4c020998acc41ed1efc73ae5c80"}