{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:GDJRKSSNXME7YLSOAWOCTOQPYO","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":"267f998dae67c402facd8132cbf66395e0b27ba0459f8ed8d62c7b4256270d33","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2018-09-07T13:29:51Z","title_canon_sha256":"4781871104f76ff2340500d44468b11adaefea8e5362865568f96fb2dbf9437d"},"schema_version":"1.0","source":{"id":"1809.02462","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1809.02462","created_at":"2026-05-17T23:47:53Z"},{"alias_kind":"arxiv_version","alias_value":"1809.02462v2","created_at":"2026-05-17T23:47:53Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1809.02462","created_at":"2026-05-17T23:47:53Z"},{"alias_kind":"pith_short_12","alias_value":"GDJRKSSNXME7","created_at":"2026-05-18T12:32:25Z"},{"alias_kind":"pith_short_16","alias_value":"GDJRKSSNXME7YLSO","created_at":"2026-05-18T12:32:25Z"},{"alias_kind":"pith_short_8","alias_value":"GDJRKSSN","created_at":"2026-05-18T12:32:25Z"}],"graph_snapshots":[{"event_id":"sha256:e8f302563f5a0f0066bd01be0bcc694bba10260d9b39e3f35afb9619577c0f46","target":"graph","created_at":"2026-05-17T23:47:53Z","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":"Let $f:\\mathbb{C}^2 \\to \\mathbb{C}$ be a polynomial map. Let $\\mathbb{C}^2 \\subset X$ be a compactification of $\\mathbb{C}^2$ where $X$ is a smooth rational compact surface and such that there exists a morphism of varieties $\\Phi :X\\to \\mathbb{P}^1$ which extends $f$. Put $\\mathcal{D}=X\\setminus \\mathbb{C}^2$; $\\mathcal{D}$ is a curve whose irreducible components are smooth rational compact curves and all its singularities are ordinary double points. The dual graph of $\\mathcal{D}$ is a tree. We are interested in this tree, and we analyse its complexity in terms of the genus of the generic fib","authors_text":"Daniel Daigle, Pierrette Cassou-Nogues","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2018-09-07T13:29:51Z","title":"Structure of the Newton tree at infinity of a polynomial in two variables"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1809.02462","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:baa472314f13a823fe47bd7f0c27b6df9e819f16df723151fcc89fa9a0eff5ad","target":"record","created_at":"2026-05-17T23:47:53Z","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":"267f998dae67c402facd8132cbf66395e0b27ba0459f8ed8d62c7b4256270d33","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2018-09-07T13:29:51Z","title_canon_sha256":"4781871104f76ff2340500d44468b11adaefea8e5362865568f96fb2dbf9437d"},"schema_version":"1.0","source":{"id":"1809.02462","kind":"arxiv","version":2}},"canonical_sha256":"30d3154a4dbb09fc2e4e059c29ba0fc396c62dd14d1565785092a4196b64a311","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"30d3154a4dbb09fc2e4e059c29ba0fc396c62dd14d1565785092a4196b64a311","first_computed_at":"2026-05-17T23:47:53.884629Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:47:53.884629Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"aomdoMWFUWDNWkdj5qcrlHDBDrWK6oOn+rnk/WweH8x1z01MFfi/Je0xymXmFs20632pVlY9g8mQXIINyLciBA==","signature_status":"signed_v1","signed_at":"2026-05-17T23:47:53.885191Z","signed_message":"canonical_sha256_bytes"},"source_id":"1809.02462","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:baa472314f13a823fe47bd7f0c27b6df9e819f16df723151fcc89fa9a0eff5ad","sha256:e8f302563f5a0f0066bd01be0bcc694bba10260d9b39e3f35afb9619577c0f46"],"state_sha256":"7d924b2d57688da491b718a9a4d0ce9ca4677db1beb281ff6662d528bdebedf7"}