{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:CTRARI2NDFUTP3NAQMJE46LTRI","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":"134ae295c8a53603d2927a1c3da648fabe4811b8a52f57bb4366d82ea8b5c63a","cross_cats_sorted":["math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2010-12-23T21:17:11Z","title_canon_sha256":"76f37417290b61854f31d2fd875d982369e709ebbc76d128e0e041003aaf8fa2"},"schema_version":"1.0","source":{"id":"1012.5305","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1012.5305","created_at":"2026-05-18T03:56:46Z"},{"alias_kind":"arxiv_version","alias_value":"1012.5305v2","created_at":"2026-05-18T03:56:46Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1012.5305","created_at":"2026-05-18T03:56:46Z"},{"alias_kind":"pith_short_12","alias_value":"CTRARI2NDFUT","created_at":"2026-05-18T12:26:06Z"},{"alias_kind":"pith_short_16","alias_value":"CTRARI2NDFUTP3NA","created_at":"2026-05-18T12:26:06Z"},{"alias_kind":"pith_short_8","alias_value":"CTRARI2N","created_at":"2026-05-18T12:26:06Z"}],"graph_snapshots":[{"event_id":"sha256:9f11f52cd2e12305456fa1963b9b3e912cc0402bfc2882dd9537670d77df4dbd","target":"graph","created_at":"2026-05-18T03:56:46Z","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":"The Severi variety parameterizes plane curves of degree d with delta nodes. Its degree is called the Severi degree. For large enough d, the Severi degrees coincide with the Gromov-Witten invariants of P^2. Fomin and Mikhalkin (2009) proved the 1995 conjecture that, for fixed delta, Severi degrees are eventually polynomial in d.\n  In this paper, we study the Severi varieties corresponding to a large family of toric surfaces. We prove the analogous result that the Severi degrees are eventually polynomial as a function of the multidegree. More surprisingly, we show that the Severi degrees are als","authors_text":"Federico Ardila, Florian Block","cross_cats":["math.CO"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2010-12-23T21:17:11Z","title":"Universal Polynomials for Severi Degrees of Toric Surfaces"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1012.5305","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":"sha256:47d7babfea6f595c28cb8f62b1089665bdf83486426d602e13c73a6841ea6539","target":"record","created_at":"2026-05-18T03:56:46Z","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":"134ae295c8a53603d2927a1c3da648fabe4811b8a52f57bb4366d82ea8b5c63a","cross_cats_sorted":["math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2010-12-23T21:17:11Z","title_canon_sha256":"76f37417290b61854f31d2fd875d982369e709ebbc76d128e0e041003aaf8fa2"},"schema_version":"1.0","source":{"id":"1012.5305","kind":"arxiv","version":2}},"canonical_sha256":"14e208a34d196937eda083124e79738a2d6dd3d48c5b7540485a3a0b814e8764","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"14e208a34d196937eda083124e79738a2d6dd3d48c5b7540485a3a0b814e8764","first_computed_at":"2026-05-18T03:56:46.315222Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:56:46.315222Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"4z/FgUlQXXMSMJh/NIoO2DBY62lwEGSI4AWWbOAyu27PoAnxd8jFDM5F9rsiHs0Kn9RerSLyiwJMQNu3FqKeAw==","signature_status":"signed_v1","signed_at":"2026-05-18T03:56:46.315772Z","signed_message":"canonical_sha256_bytes"},"source_id":"1012.5305","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:47d7babfea6f595c28cb8f62b1089665bdf83486426d602e13c73a6841ea6539","sha256:9f11f52cd2e12305456fa1963b9b3e912cc0402bfc2882dd9537670d77df4dbd"],"state_sha256":"82215d49dcdac1f9e985b2879ca7b934c23b0d732f6b9abcb13f2eeeeaab51e1"}