{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:OWEUWXENIPOYJ2XG4BFVTJQRJO","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":"2c66a3747461abd9f72affb41298fddf02d3416702c1626bdc3d8e3a1691f86c","cross_cats_sorted":["math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2015-10-29T03:25:46Z","title_canon_sha256":"0f174e982ac91d3e3766979a7ed5c4940ec70566024d6aa22e2dfa6d7b45e4b6"},"schema_version":"1.0","source":{"id":"1510.08556","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1510.08556","created_at":"2026-05-17T23:59:03Z"},{"alias_kind":"arxiv_version","alias_value":"1510.08556v3","created_at":"2026-05-17T23:59:03Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1510.08556","created_at":"2026-05-17T23:59:03Z"},{"alias_kind":"pith_short_12","alias_value":"OWEUWXENIPOY","created_at":"2026-05-18T12:29:34Z"},{"alias_kind":"pith_short_16","alias_value":"OWEUWXENIPOYJ2XG","created_at":"2026-05-18T12:29:34Z"},{"alias_kind":"pith_short_8","alias_value":"OWEUWXEN","created_at":"2026-05-18T12:29:34Z"}],"graph_snapshots":[{"event_id":"sha256:4797007e0db915b86bbb472b7661a17d87bb9923c9a23d4c8e0ba826847713b3","target":"graph","created_at":"2026-05-17T23:59:03Z","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 establish the equality of classical and tropical curve counts for elliptic curves on toric surfaces with fixed $j$-invariant, refining results of Mikhalkin and Nishinou--Siebert. As an application, we determine a formula for such counts on $\\mathbb P^2$ and all Hirzebruch surfaces. This formula relates the count of elliptic curves with the number of rational curves on the surface satisfying a small number of tangency conditions with the toric boundary. Furthermore, the combinatorial tropical multiplicities of Kerber and Markwig for counts in $\\mathbb P^2$ are derived and explained algebro-g","authors_text":"Dhruv Ranganathan, Yoav Len","cross_cats":["math.CO"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2015-10-29T03:25:46Z","title":"Enumerative geometry of elliptic curves on toric surfaces"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1510.08556","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:fcc1e997b2dd62a0e0074f04e064801d3c200888d388ae9840b68d573a772374","target":"record","created_at":"2026-05-17T23:59:03Z","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":"2c66a3747461abd9f72affb41298fddf02d3416702c1626bdc3d8e3a1691f86c","cross_cats_sorted":["math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2015-10-29T03:25:46Z","title_canon_sha256":"0f174e982ac91d3e3766979a7ed5c4940ec70566024d6aa22e2dfa6d7b45e4b6"},"schema_version":"1.0","source":{"id":"1510.08556","kind":"arxiv","version":3}},"canonical_sha256":"75894b5c8d43dd84eae6e04b59a6114ba1199220a5f99bdff0ee85b586f607bd","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"75894b5c8d43dd84eae6e04b59a6114ba1199220a5f99bdff0ee85b586f607bd","first_computed_at":"2026-05-17T23:59:03.990964Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:59:03.990964Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"lKl849JtZlysFXpkpRYxCS49YVJNCKmn6wGGxDw1tHjL0reGiAXTpDv2/DeFgKME3GJBn3l9vsGeNpFTGE4pCw==","signature_status":"signed_v1","signed_at":"2026-05-17T23:59:03.991354Z","signed_message":"canonical_sha256_bytes"},"source_id":"1510.08556","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:fcc1e997b2dd62a0e0074f04e064801d3c200888d388ae9840b68d573a772374","sha256:4797007e0db915b86bbb472b7661a17d87bb9923c9a23d4c8e0ba826847713b3"],"state_sha256":"5acbeb98a82151c6ab053c12b8d268bc1d125d46279abab2f7cbeba0bf011fc5"}