{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2009:5YNC443KKCKEYIEXIQ5SYKW4PB","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":"2fa6afd81e935718810baa680d7eac16c639cb2a1fa4633691cef66b7c7ddf7d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2009-03-19T16:26:52Z","title_canon_sha256":"a1d66511a5df9d5a4fb5894e13e0f75ae24f94e223eaa2c8a274238f3acc86b0"},"schema_version":"1.0","source":{"id":"0903.3359","kind":"arxiv","version":7}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0903.3359","created_at":"2026-05-18T04:42:44Z"},{"alias_kind":"arxiv_version","alias_value":"0903.3359v7","created_at":"2026-05-18T04:42:44Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0903.3359","created_at":"2026-05-18T04:42:44Z"},{"alias_kind":"pith_short_12","alias_value":"5YNC443KKCKE","created_at":"2026-05-18T12:25:58Z"},{"alias_kind":"pith_short_16","alias_value":"5YNC443KKCKEYIEX","created_at":"2026-05-18T12:25:58Z"},{"alias_kind":"pith_short_8","alias_value":"5YNC443K","created_at":"2026-05-18T12:25:58Z"}],"graph_snapshots":[{"event_id":"sha256:7890085934e96ffe755dfd7399da9b6b07bbea1d49221f29138b14b6f39555fc","target":"graph","created_at":"2026-05-18T04:42:44Z","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 ramified covers of the projective plane. Given a smooth projective surface S and a generic enough projection of S to the projective plane, we get a cover of the plane ramified over a plane curve. The branch curve is usually singular, but is classically known to have only cusps and nodes as singularities for a generic projection.\n  Several questions arise. First, what is the_geography_ of branch curves among all nodal-cuspidal curves? Second: what is the_geometry_ of branch curves? In other words, how can one distinguish a branch curve from a non-branch curve with the same numerical in","authors_text":"Maxim Leyenson, Michael Friedman","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2009-03-19T16:26:52Z","title":"On ramified covers of the projective plane I: Segre's theory and classification in small degrees, with Appendix by Eugenii Shustin"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0903.3359","kind":"arxiv","version":7},"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":"sha256:019c360e80e70c8b04f07443e0d0036016e593eb2abe8c2d180cce65e08484f6","target":"record","created_at":"2026-05-18T04:42:44Z","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":"2fa6afd81e935718810baa680d7eac16c639cb2a1fa4633691cef66b7c7ddf7d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2009-03-19T16:26:52Z","title_canon_sha256":"a1d66511a5df9d5a4fb5894e13e0f75ae24f94e223eaa2c8a274238f3acc86b0"},"schema_version":"1.0","source":{"id":"0903.3359","kind":"arxiv","version":7}},"canonical_sha256":"ee1a2e736a50944c2097443b2c2adc785dfa5fe4e4fa36c368bafa57da131741","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ee1a2e736a50944c2097443b2c2adc785dfa5fe4e4fa36c368bafa57da131741","first_computed_at":"2026-05-18T04:42:44.742698Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:42:44.742698Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"N5hUF+nYRYgXWDrEnlwZuEbJg3QGirHBBJapbbGxynYhgMScapzMirGW96QTTK/X5wuzn7tsEwfCesuOKwI1Aw==","signature_status":"signed_v1","signed_at":"2026-05-18T04:42:44.743386Z","signed_message":"canonical_sha256_bytes"},"source_id":"0903.3359","source_kind":"arxiv","source_version":7}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:019c360e80e70c8b04f07443e0d0036016e593eb2abe8c2d180cce65e08484f6","sha256:7890085934e96ffe755dfd7399da9b6b07bbea1d49221f29138b14b6f39555fc"],"state_sha256":"3c52245c5b53b79a8672588978dcf38ff88b2b3fc628e01002f10245ffa7400d"}