{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:X2XQD26CITS44ZHNAA6CQM2H5H","short_pith_number":"pith:X2XQD26C","schema_version":"1.0","canonical_sha256":"beaf01ebc244e5ce64ed003c283347e9d8e5ade0d5fdb8e1e02cbcacac632426","source":{"kind":"arxiv","id":"1504.05969","version":3},"attestation_state":"computed","paper":{"title":"Smoothing Toric Fano Surfaces Using the Gross-Siebert Algorithm","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Thomas Prince","submitted_at":"2015-04-22T20:04:16Z","abstract_excerpt":"A toric del Pezzo surface $X_P$ with cyclic quotient singularities determines and is determined by a Fano polygon $P$. We construct an affine manifold with singularities that partially smooths the boundary of $P$; this a tropical version of a Q-Gorenstein partial smoothing of $X_P$. We implement a mild generalization of the Gross-Siebert reconstruction algorithm - allowing singularities that are not locally rigid - and thereby construct (a formal version of) this partial smoothing directly from the affine manifold. This has implications for mirror symmetry: roughly speaking, it implements half"},"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":"1504.05969","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2015-04-22T20:04:16Z","cross_cats_sorted":[],"title_canon_sha256":"b2da9c05365fe50f29dadc1f58dbf68d4937b11d746dc7a450fce9c9c4488dea","abstract_canon_sha256":"6ff1b81ed2077049f4d24e4ea6d49e9daaca87255b420153da69fe83cab55edc"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:12:57.283149Z","signature_b64":"dwr40IK5YOfC89nhx4I6rJWLMTayO2YbRglyKZP4Wap1zNwLpfbdj/1tGWVOHXuvQK0KRiGehCS7//48pElVCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"beaf01ebc244e5ce64ed003c283347e9d8e5ade0d5fdb8e1e02cbcacac632426","last_reissued_at":"2026-05-18T00:12:57.282486Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:12:57.282486Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Smoothing Toric Fano Surfaces Using the Gross-Siebert Algorithm","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Thomas Prince","submitted_at":"2015-04-22T20:04:16Z","abstract_excerpt":"A toric del Pezzo surface $X_P$ with cyclic quotient singularities determines and is determined by a Fano polygon $P$. We construct an affine manifold with singularities that partially smooths the boundary of $P$; this a tropical version of a Q-Gorenstein partial smoothing of $X_P$. We implement a mild generalization of the Gross-Siebert reconstruction algorithm - allowing singularities that are not locally rigid - and thereby construct (a formal version of) this partial smoothing directly from the affine manifold. This has implications for mirror symmetry: roughly speaking, it implements half"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1504.05969","kind":"arxiv","version":3},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"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":"1504.05969","created_at":"2026-05-18T00:12:57.282592+00:00"},{"alias_kind":"arxiv_version","alias_value":"1504.05969v3","created_at":"2026-05-18T00:12:57.282592+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1504.05969","created_at":"2026-05-18T00:12:57.282592+00:00"},{"alias_kind":"pith_short_12","alias_value":"X2XQD26CITS4","created_at":"2026-05-18T12:29:47.479230+00:00"},{"alias_kind":"pith_short_16","alias_value":"X2XQD26CITS44ZHN","created_at":"2026-05-18T12:29:47.479230+00:00"},{"alias_kind":"pith_short_8","alias_value":"X2XQD26C","created_at":"2026-05-18T12:29:47.479230+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/X2XQD26CITS44ZHNAA6CQM2H5H","json":"https://pith.science/pith/X2XQD26CITS44ZHNAA6CQM2H5H.json","graph_json":"https://pith.science/api/pith-number/X2XQD26CITS44ZHNAA6CQM2H5H/graph.json","events_json":"https://pith.science/api/pith-number/X2XQD26CITS44ZHNAA6CQM2H5H/events.json","paper":"https://pith.science/paper/X2XQD26C"},"agent_actions":{"view_html":"https://pith.science/pith/X2XQD26CITS44ZHNAA6CQM2H5H","download_json":"https://pith.science/pith/X2XQD26CITS44ZHNAA6CQM2H5H.json","view_paper":"https://pith.science/paper/X2XQD26C","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1504.05969&json=true","fetch_graph":"https://pith.science/api/pith-number/X2XQD26CITS44ZHNAA6CQM2H5H/graph.json","fetch_events":"https://pith.science/api/pith-number/X2XQD26CITS44ZHNAA6CQM2H5H/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/X2XQD26CITS44ZHNAA6CQM2H5H/action/timestamp_anchor","attest_storage":"https://pith.science/pith/X2XQD26CITS44ZHNAA6CQM2H5H/action/storage_attestation","attest_author":"https://pith.science/pith/X2XQD26CITS44ZHNAA6CQM2H5H/action/author_attestation","sign_citation":"https://pith.science/pith/X2XQD26CITS44ZHNAA6CQM2H5H/action/citation_signature","submit_replication":"https://pith.science/pith/X2XQD26CITS44ZHNAA6CQM2H5H/action/replication_record"}},"created_at":"2026-05-18T00:12:57.282592+00:00","updated_at":"2026-05-18T00:12:57.282592+00:00"}