{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2025:RZOBEWU2Z4B7XG7RMOOVEULXWV","short_pith_number":"pith:RZOBEWU2","schema_version":"1.0","canonical_sha256":"8e5c125a9acf03fb9bf1639d525177b54c403c4cd796a039cf8b2d55bd18b14d","source":{"kind":"arxiv","id":"2506.13975","version":4},"attestation_state":"computed","paper":{"title":"Enumerating log rational curves on some toric varieties","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Carl Lian, Naufil Sakran","submitted_at":"2025-06-16T20:29:47Z","abstract_excerpt":"The genus 0, fixed-domain log Gromov-Witten invariants of a smooth, projective toric variety X enumerate maps from a general pointed rational curve to a smooth, projective toric variety passing through the maximal number of general points and with prescribed multiplicities along the toric boundary. We determine these invariants completely for the projective bundle X=P_{P^r}(O^s+O(-a)), proving a conjecture of Cela--Iribar L\\'opez. A different conjecture when X is the blow-up of P^r at r points is disproven. Whereas the conjectures were predicted using tropical methods, we give direct intersect"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"2506.13975","kind":"arxiv","version":4},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AG","submitted_at":"2025-06-16T20:29:47Z","cross_cats_sorted":[],"title_canon_sha256":"de70d902af1291e79f06b97a858064ac50c50c120cb308e6b982650d951ac69f","abstract_canon_sha256":"18916808fc82c8b59262933fbbce8d58fe1decb9becac491b0ce95ccd9c0d716"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-09T01:05:07.220467Z","signature_b64":"G1phPdKDcrmwjtfNA9PMRP3peLePTtl3eHvT/7HzfA/v9pK7h0oMZZYOoYuTu+gYH1D1jk+cI8dLMi2JztX2Dw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"8e5c125a9acf03fb9bf1639d525177b54c403c4cd796a039cf8b2d55bd18b14d","last_reissued_at":"2026-06-09T01:05:07.219899Z","signature_status":"signed_v1","first_computed_at":"2026-06-09T01:05:07.219899Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Enumerating log rational curves on some toric varieties","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Carl Lian, Naufil Sakran","submitted_at":"2025-06-16T20:29:47Z","abstract_excerpt":"The genus 0, fixed-domain log Gromov-Witten invariants of a smooth, projective toric variety X enumerate maps from a general pointed rational curve to a smooth, projective toric variety passing through the maximal number of general points and with prescribed multiplicities along the toric boundary. We determine these invariants completely for the projective bundle X=P_{P^r}(O^s+O(-a)), proving a conjecture of Cela--Iribar L\\'opez. A different conjecture when X is the blow-up of P^r at r points is disproven. Whereas the conjectures were predicted using tropical methods, we give direct intersect"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2506.13975","kind":"arxiv","version":4},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2506.13975/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"aliases":[{"alias_kind":"arxiv","alias_value":"2506.13975","created_at":"2026-06-09T01:05:07.219964+00:00"},{"alias_kind":"arxiv_version","alias_value":"2506.13975v4","created_at":"2026-06-09T01:05:07.219964+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2506.13975","created_at":"2026-06-09T01:05:07.219964+00:00"},{"alias_kind":"pith_short_12","alias_value":"RZOBEWU2Z4B7","created_at":"2026-06-09T01:05:07.219964+00:00"},{"alias_kind":"pith_short_16","alias_value":"RZOBEWU2Z4B7XG7R","created_at":"2026-06-09T01:05:07.219964+00:00"},{"alias_kind":"pith_short_8","alias_value":"RZOBEWU2","created_at":"2026-06-09T01:05:07.219964+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/RZOBEWU2Z4B7XG7RMOOVEULXWV","json":"https://pith.science/pith/RZOBEWU2Z4B7XG7RMOOVEULXWV.json","graph_json":"https://pith.science/api/pith-number/RZOBEWU2Z4B7XG7RMOOVEULXWV/graph.json","events_json":"https://pith.science/api/pith-number/RZOBEWU2Z4B7XG7RMOOVEULXWV/events.json","paper":"https://pith.science/paper/RZOBEWU2"},"agent_actions":{"view_html":"https://pith.science/pith/RZOBEWU2Z4B7XG7RMOOVEULXWV","download_json":"https://pith.science/pith/RZOBEWU2Z4B7XG7RMOOVEULXWV.json","view_paper":"https://pith.science/paper/RZOBEWU2","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2506.13975&json=true","fetch_graph":"https://pith.science/api/pith-number/RZOBEWU2Z4B7XG7RMOOVEULXWV/graph.json","fetch_events":"https://pith.science/api/pith-number/RZOBEWU2Z4B7XG7RMOOVEULXWV/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/RZOBEWU2Z4B7XG7RMOOVEULXWV/action/timestamp_anchor","attest_storage":"https://pith.science/pith/RZOBEWU2Z4B7XG7RMOOVEULXWV/action/storage_attestation","attest_author":"https://pith.science/pith/RZOBEWU2Z4B7XG7RMOOVEULXWV/action/author_attestation","sign_citation":"https://pith.science/pith/RZOBEWU2Z4B7XG7RMOOVEULXWV/action/citation_signature","submit_replication":"https://pith.science/pith/RZOBEWU2Z4B7XG7RMOOVEULXWV/action/replication_record"}},"created_at":"2026-06-09T01:05:07.219964+00:00","updated_at":"2026-06-09T01:05:07.219964+00:00"}