{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:JSM4RVKJPPKSWSESORTKNPDYP2","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":"ba20575cb016b98e826932e267210211be13fe65b15d9db93229d2441eb37028","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2019-06-20T13:44:53Z","title_canon_sha256":"6d7a80528049fad5e8b8ccc4d54ece91513073e2577f20c26c8afb53776980cf"},"schema_version":"1.0","source":{"id":"1906.08614","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1906.08614","created_at":"2026-05-17T23:42:51Z"},{"alias_kind":"arxiv_version","alias_value":"1906.08614v1","created_at":"2026-05-17T23:42:51Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1906.08614","created_at":"2026-05-17T23:42:51Z"},{"alias_kind":"pith_short_12","alias_value":"JSM4RVKJPPKS","created_at":"2026-05-18T12:33:21Z"},{"alias_kind":"pith_short_16","alias_value":"JSM4RVKJPPKSWSES","created_at":"2026-05-18T12:33:21Z"},{"alias_kind":"pith_short_8","alias_value":"JSM4RVKJ","created_at":"2026-05-18T12:33:21Z"}],"graph_snapshots":[{"event_id":"sha256:668c2ce5bcc112e0f24aac58dd4b0389c4107d049afaa342513a28bb7c48c3a7","target":"graph","created_at":"2026-05-17T23:42:51Z","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":"This article is a survey of two subjects: the first part is devoted to field generators in two variables, and the second to birational endomorphisms of the affine plane. Each one of these subjects originated in Abhyankar's seminar in Purdue University in the 1970s. Note that the part on field generators is more than a survey, since it contains a considerable amount of new material.","authors_text":"Daniel Daigle, Pierrette Cassou-Nogu\\`es","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2019-06-20T13:44:53Z","title":"Field generators in two variables and birational endomorphisms of $\\mathbb{A}^2$"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1906.08614","kind":"arxiv","version":1},"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":"sha256:8b761cd3a74ade8bebbc78716d6c7c3d293214048e6cabbad74ebbe958011dd1","target":"record","created_at":"2026-05-17T23:42:51Z","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":"ba20575cb016b98e826932e267210211be13fe65b15d9db93229d2441eb37028","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2019-06-20T13:44:53Z","title_canon_sha256":"6d7a80528049fad5e8b8ccc4d54ece91513073e2577f20c26c8afb53776980cf"},"schema_version":"1.0","source":{"id":"1906.08614","kind":"arxiv","version":1}},"canonical_sha256":"4c99c8d5497bd52b48927466a6bc787eba7d56373a27f8155465ddcc44948271","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"4c99c8d5497bd52b48927466a6bc787eba7d56373a27f8155465ddcc44948271","first_computed_at":"2026-05-17T23:42:51.933041Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:42:51.933041Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Hrk4wziNspo048TINKqy704tmWBS7qXWZoDPMfNlPeOAmatawuZaQ57RR4Bygyp/vq3OutZBNapJEnr0dMUJBQ==","signature_status":"signed_v1","signed_at":"2026-05-17T23:42:51.933550Z","signed_message":"canonical_sha256_bytes"},"source_id":"1906.08614","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8b761cd3a74ade8bebbc78716d6c7c3d293214048e6cabbad74ebbe958011dd1","sha256:668c2ce5bcc112e0f24aac58dd4b0389c4107d049afaa342513a28bb7c48c3a7"],"state_sha256":"e15f460cab2c9ee018cb9d269b6daff62b15e0239f04a40be1a3b290748b927a"}