{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:DHK2LITRCOGCIVM2BEKF2ZU2S7","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":"a7b8c9a4ed45bc7a99961db093af5af5a7f285dab5f2629e7599c0e8b9df9c6d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2019-02-15T00:02:00Z","title_canon_sha256":"ec4d8b79cb1c02a73f703b9c507dd4e77c482c19cbf6a49f7c7d39b7255cae60"},"schema_version":"1.0","source":{"id":"1902.05645","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1902.05645","created_at":"2026-07-05T03:25:27Z"},{"alias_kind":"arxiv_version","alias_value":"1902.05645v1","created_at":"2026-07-05T03:25:27Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1902.05645","created_at":"2026-07-05T03:25:27Z"},{"alias_kind":"pith_short_12","alias_value":"DHK2LITRCOGC","created_at":"2026-07-05T03:25:27Z"},{"alias_kind":"pith_short_16","alias_value":"DHK2LITRCOGCIVM2","created_at":"2026-07-05T03:25:27Z"},{"alias_kind":"pith_short_8","alias_value":"DHK2LITR","created_at":"2026-07-05T03:25:27Z"}],"graph_snapshots":[{"event_id":"sha256:d3f85d59d965b541422d467d850ab0055ec5b227c498a9c0e3289a0a4cc83f97","target":"graph","created_at":"2026-07-05T03:25:27Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/1902.05645/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"The degree of irrationality of a projective variety $X$ is defined to be the smallest degree rational dominant map to a projective space of the same dimension. For abelian surfaces, Yoshihara computed this invariant in specific cases, while Stapleton gave a sublinear upper bound for very general polarized abelian surfaces $(A, L)$ of degree $d$. Somewhat surprisingly, we show that the degree of irrationality of a very general polarized abelian surface is uniformly bounded above by $4$, independently of the degree of the polarization. This result disproves part of a conjecture of Bastianelli, D","authors_text":"Nathan Chen","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2019-02-15T00:02:00Z","title":"Degree of irrationality of very general abelian surfaces"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1902.05645","kind":"arxiv","version":1},"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":"sha256:59a2bde8164ebd1fadbcafe02fdc795c38dfb760f93b983f1e0bc4bb88c4b3d9","target":"record","created_at":"2026-07-05T03:25:27Z","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":"a7b8c9a4ed45bc7a99961db093af5af5a7f285dab5f2629e7599c0e8b9df9c6d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2019-02-15T00:02:00Z","title_canon_sha256":"ec4d8b79cb1c02a73f703b9c507dd4e77c482c19cbf6a49f7c7d39b7255cae60"},"schema_version":"1.0","source":{"id":"1902.05645","kind":"arxiv","version":1}},"canonical_sha256":"19d5a5a271138c24559a09145d669a97d391aa7bef939cca0ea7c5dddb1bce7b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"19d5a5a271138c24559a09145d669a97d391aa7bef939cca0ea7c5dddb1bce7b","first_computed_at":"2026-07-05T03:25:27.853081Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T03:25:27.853081Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"t0S0uk13Jd14wQ3tNvudAQqqgjayBpY8fcZzZimWkhD2WLFTxtNR27pKa4UkIJhvc34bhF+ASXHExFBLJyJ9AQ==","signature_status":"signed_v1","signed_at":"2026-07-05T03:25:27.853493Z","signed_message":"canonical_sha256_bytes"},"source_id":"1902.05645","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:59a2bde8164ebd1fadbcafe02fdc795c38dfb760f93b983f1e0bc4bb88c4b3d9","sha256:d3f85d59d965b541422d467d850ab0055ec5b227c498a9c0e3289a0a4cc83f97"],"state_sha256":"64c506ec0f9e5eeb459de9cfcc0433a444c59256c7722e3a5bb809a551e56401"}