{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:QEDT2FLINFGKVLALUMIQYTQ2VV","short_pith_number":"pith:QEDT2FLI","canonical_record":{"source":{"id":"1701.00790","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2017-01-03T19:17:15Z","cross_cats_sorted":["math.AC","math.CV"],"title_canon_sha256":"2b8a8f08a4fc4abf80028b9eb0c04d9f13c54c8e83c7a1e316ba13abe321d3b2","abstract_canon_sha256":"b2093d36ff0cf2efcd98940241b1e1d62aa894ac5a452983e677d41c5aaaa842"},"schema_version":"1.0"},"canonical_sha256":"81073d1568694caaac0ba3110c4e1aad74cbc4c27a6978873630c9fad0a079a4","source":{"kind":"arxiv","id":"1701.00790","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1701.00790","created_at":"2026-05-17T23:58:19Z"},{"alias_kind":"arxiv_version","alias_value":"1701.00790v3","created_at":"2026-05-17T23:58:19Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1701.00790","created_at":"2026-05-17T23:58:19Z"},{"alias_kind":"pith_short_12","alias_value":"QEDT2FLINFGK","created_at":"2026-05-18T12:31:37Z"},{"alias_kind":"pith_short_16","alias_value":"QEDT2FLINFGKVLAL","created_at":"2026-05-18T12:31:37Z"},{"alias_kind":"pith_short_8","alias_value":"QEDT2FLI","created_at":"2026-05-18T12:31:37Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:QEDT2FLINFGKVLALUMIQYTQ2VV","target":"record","payload":{"canonical_record":{"source":{"id":"1701.00790","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2017-01-03T19:17:15Z","cross_cats_sorted":["math.AC","math.CV"],"title_canon_sha256":"2b8a8f08a4fc4abf80028b9eb0c04d9f13c54c8e83c7a1e316ba13abe321d3b2","abstract_canon_sha256":"b2093d36ff0cf2efcd98940241b1e1d62aa894ac5a452983e677d41c5aaaa842"},"schema_version":"1.0"},"canonical_sha256":"81073d1568694caaac0ba3110c4e1aad74cbc4c27a6978873630c9fad0a079a4","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:58:19.754659Z","signature_b64":"kokUw2hatqAI+TzgHL71UF5PKKpVFxfazoiDiEPy7ZRtT117HMWEnIZiHyJ//oiaxtcNrOe8c6PGPMzpeRTQBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"81073d1568694caaac0ba3110c4e1aad74cbc4c27a6978873630c9fad0a079a4","last_reissued_at":"2026-05-17T23:58:19.754165Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:58:19.754165Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1701.00790","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-17T23:58:19Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"gUXYr51jFYPApGeiMvKtPfvI86UayNPkjKAahYweyXSpOXETMf/+b4NuWeHpgt9/4GCBfgMmXTpxSTt90uEnAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-27T10:35:17.903347Z"},"content_sha256":"2ab9034551e41206379639a8994d94847691914c0cbbbc5b71346e6b433eb700","schema_version":"1.0","event_id":"sha256:2ab9034551e41206379639a8994d94847691914c0cbbbc5b71346e6b433eb700"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:QEDT2FLINFGKVLALUMIQYTQ2VV","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Birational geometry of foliations associated to simple derivations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AC","math.CV"],"primary_cat":"math.AG","authors_text":"Gael Cousin, Ivan Pan, Luis Gustavo Mendes","submitted_at":"2017-01-03T19:17:15Z","abstract_excerpt":"We propose a study of the foliations of the projective plane induced by simple derivations of the polynomial ring in two indeterminates over the complex field. These correspond to foliations which have no invariant algebraic curve nor singularities in the complement of a line. We establish the position of these foliations in the birational classification of foliations and prove the finiteness of their birational symmetries. Most of the results apply to wider classes of foliations."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1701.00790","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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-17T23:58:19Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"tEdleyK5PdbuLu5xksTAKQslJkk/vmOV+H27wL1xmguUgD9i8y/v7Hokpu5gRNAXxplWfDKq5bUDGGmiY54cBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-27T10:35:17.903897Z"},"content_sha256":"6f9f7d69f2822385b066439e6ce2f189c45d73578845c2883e19ada693e63c53","schema_version":"1.0","event_id":"sha256:6f9f7d69f2822385b066439e6ce2f189c45d73578845c2883e19ada693e63c53"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/QEDT2FLINFGKVLALUMIQYTQ2VV/bundle.json","state_url":"https://pith.science/pith/QEDT2FLINFGKVLALUMIQYTQ2VV/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/QEDT2FLINFGKVLALUMIQYTQ2VV/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-06-27T10:35:17Z","links":{"resolver":"https://pith.science/pith/QEDT2FLINFGKVLALUMIQYTQ2VV","bundle":"https://pith.science/pith/QEDT2FLINFGKVLALUMIQYTQ2VV/bundle.json","state":"https://pith.science/pith/QEDT2FLINFGKVLALUMIQYTQ2VV/state.json","well_known_bundle":"https://pith.science/.well-known/pith/QEDT2FLINFGKVLALUMIQYTQ2VV/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:QEDT2FLINFGKVLALUMIQYTQ2VV","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":"b2093d36ff0cf2efcd98940241b1e1d62aa894ac5a452983e677d41c5aaaa842","cross_cats_sorted":["math.AC","math.CV"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2017-01-03T19:17:15Z","title_canon_sha256":"2b8a8f08a4fc4abf80028b9eb0c04d9f13c54c8e83c7a1e316ba13abe321d3b2"},"schema_version":"1.0","source":{"id":"1701.00790","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1701.00790","created_at":"2026-05-17T23:58:19Z"},{"alias_kind":"arxiv_version","alias_value":"1701.00790v3","created_at":"2026-05-17T23:58:19Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1701.00790","created_at":"2026-05-17T23:58:19Z"},{"alias_kind":"pith_short_12","alias_value":"QEDT2FLINFGK","created_at":"2026-05-18T12:31:37Z"},{"alias_kind":"pith_short_16","alias_value":"QEDT2FLINFGKVLAL","created_at":"2026-05-18T12:31:37Z"},{"alias_kind":"pith_short_8","alias_value":"QEDT2FLI","created_at":"2026-05-18T12:31:37Z"}],"graph_snapshots":[{"event_id":"sha256:6f9f7d69f2822385b066439e6ce2f189c45d73578845c2883e19ada693e63c53","target":"graph","created_at":"2026-05-17T23:58:19Z","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 propose a study of the foliations of the projective plane induced by simple derivations of the polynomial ring in two indeterminates over the complex field. These correspond to foliations which have no invariant algebraic curve nor singularities in the complement of a line. We establish the position of these foliations in the birational classification of foliations and prove the finiteness of their birational symmetries. Most of the results apply to wider classes of foliations.","authors_text":"Gael Cousin, Ivan Pan, Luis Gustavo Mendes","cross_cats":["math.AC","math.CV"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2017-01-03T19:17:15Z","title":"Birational geometry of foliations associated to simple derivations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1701.00790","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":"sha256:2ab9034551e41206379639a8994d94847691914c0cbbbc5b71346e6b433eb700","target":"record","created_at":"2026-05-17T23:58:19Z","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":"b2093d36ff0cf2efcd98940241b1e1d62aa894ac5a452983e677d41c5aaaa842","cross_cats_sorted":["math.AC","math.CV"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2017-01-03T19:17:15Z","title_canon_sha256":"2b8a8f08a4fc4abf80028b9eb0c04d9f13c54c8e83c7a1e316ba13abe321d3b2"},"schema_version":"1.0","source":{"id":"1701.00790","kind":"arxiv","version":3}},"canonical_sha256":"81073d1568694caaac0ba3110c4e1aad74cbc4c27a6978873630c9fad0a079a4","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"81073d1568694caaac0ba3110c4e1aad74cbc4c27a6978873630c9fad0a079a4","first_computed_at":"2026-05-17T23:58:19.754165Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:58:19.754165Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"kokUw2hatqAI+TzgHL71UF5PKKpVFxfazoiDiEPy7ZRtT117HMWEnIZiHyJ//oiaxtcNrOe8c6PGPMzpeRTQBg==","signature_status":"signed_v1","signed_at":"2026-05-17T23:58:19.754659Z","signed_message":"canonical_sha256_bytes"},"source_id":"1701.00790","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2ab9034551e41206379639a8994d94847691914c0cbbbc5b71346e6b433eb700","sha256:6f9f7d69f2822385b066439e6ce2f189c45d73578845c2883e19ada693e63c53"],"state_sha256":"638ed76eb113fae2c125927cf951f54ed07f48f733980ce3d63c204bd6d30eea"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"V4dGlVLsR3ZYpb91sZUQ9roOh3dmXLLX3SiSE17L7INkgjPA9gpNcWs8VsgEwZ34Y5u0bi1Zymj0LmCrapffBg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-27T10:35:17.906254Z","bundle_sha256":"710bdc3d4f7c220d4aa57873b2884dc03aa9db3267cbfdd870baaf5c1efa1ee1"}}