{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:KCVHC7JU25UKQBIZ4MHWO5QFKX","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":"10c4a0df3d4ec119f456762cd464c4ea4958450652fe8e5ff60d116eda25ead7","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2019-11-01T10:55:04Z","title_canon_sha256":"1d2002e2493227a1ee44f7d763a2518cce96db66f8deb30f1a06eca0335c2080"},"schema_version":"1.0","source":{"id":"1911.00296","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1911.00296","created_at":"2026-07-05T00:16:25Z"},{"alias_kind":"arxiv_version","alias_value":"1911.00296v1","created_at":"2026-07-05T00:16:25Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1911.00296","created_at":"2026-07-05T00:16:25Z"},{"alias_kind":"pith_short_12","alias_value":"KCVHC7JU25UK","created_at":"2026-07-05T00:16:25Z"},{"alias_kind":"pith_short_16","alias_value":"KCVHC7JU25UKQBIZ","created_at":"2026-07-05T00:16:25Z"},{"alias_kind":"pith_short_8","alias_value":"KCVHC7JU","created_at":"2026-07-05T00:16:25Z"}],"graph_snapshots":[{"event_id":"sha256:af5824b13e068644d80a9a632082b213f954d78a58129133521a2411843b548f","target":"graph","created_at":"2026-07-05T00:16:25Z","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/1911.00296/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"The degree of irrationality of a smooth projective variety $X$ is the minimal degree of a dominant rational map $X\\dashrightarrow \\mathbb{P}^{\\dim X}$. We show that if an abelian surface $A$ over $\\mathbb{C}$ is such that the image of the intersection pairing $\\text{Sym}^2NS(A)\\to \\mathbb{Z}$ does not contain $12$, then it has degree of irrationality $4$. In particular, a very general $(1,d)$-polarized abelian surface has degree of irrationality $4$ provided that $d\\nmid 6$. This answers two questions of Yoshihara by providing the first examples of abelian surfaces with degree of irrationality","authors_text":"Olivier Martin","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2019-11-01T10:55:04Z","title":"The degree of irrationality of most abelian surfaces is 4"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1911.00296","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":"sha256:5ce398d8fffc2d1cec56b2a68631e06c0de88105b8063c929804b87423c336e5","target":"record","created_at":"2026-07-05T00:16:25Z","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":"10c4a0df3d4ec119f456762cd464c4ea4958450652fe8e5ff60d116eda25ead7","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2019-11-01T10:55:04Z","title_canon_sha256":"1d2002e2493227a1ee44f7d763a2518cce96db66f8deb30f1a06eca0335c2080"},"schema_version":"1.0","source":{"id":"1911.00296","kind":"arxiv","version":1}},"canonical_sha256":"50aa717d34d768a80519e30f67760555c7f807cb70f01cf3ba26c56ddd56fdab","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"50aa717d34d768a80519e30f67760555c7f807cb70f01cf3ba26c56ddd56fdab","first_computed_at":"2026-07-05T00:16:25.659497Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T00:16:25.659497Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"wWSGEgOLLd8254cfglNpMnQPGDWGa0t1nB98Zn9qINY4d4Pd4Qh3kSVbhIT3CCXkQuHrOvGR0lD04Uop+EjLBg==","signature_status":"signed_v1","signed_at":"2026-07-05T00:16:25.660023Z","signed_message":"canonical_sha256_bytes"},"source_id":"1911.00296","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:5ce398d8fffc2d1cec56b2a68631e06c0de88105b8063c929804b87423c336e5","sha256:af5824b13e068644d80a9a632082b213f954d78a58129133521a2411843b548f"],"state_sha256":"f249d8c59b7aaa6196951767645c18e7d41ff057c43e33124e65a16a5328a632"}