{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:DAIY4W6IAF2VQ6ID4I2OJ67Y7S","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":"189e604139de255fc7a127a22788b8012f81162406e29646f435f8284459881f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2012-12-11T10:02:14Z","title_canon_sha256":"3affdcf066a028073f75bae47d3c761db66aac112c7584755487cc6899cdd6dd"},"schema_version":"1.0","source":{"id":"1212.2364","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1212.2364","created_at":"2026-05-18T02:55:36Z"},{"alias_kind":"arxiv_version","alias_value":"1212.2364v2","created_at":"2026-05-18T02:55:36Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1212.2364","created_at":"2026-05-18T02:55:36Z"},{"alias_kind":"pith_short_12","alias_value":"DAIY4W6IAF2V","created_at":"2026-05-18T12:27:01Z"},{"alias_kind":"pith_short_16","alias_value":"DAIY4W6IAF2VQ6ID","created_at":"2026-05-18T12:27:01Z"},{"alias_kind":"pith_short_8","alias_value":"DAIY4W6I","created_at":"2026-05-18T12:27:01Z"}],"graph_snapshots":[{"event_id":"sha256:411dba6d38f9ec41e89f67c2420ed68d6a3b1fffbc199f9b5793fdcd3358073f","target":"graph","created_at":"2026-05-18T02:55:36Z","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 state conditions under which the set S(k) of k-rational points on a del Pezzo surface S of degree 1 over an infinite field k of characteristic not equal to 2 or 3 is Zariski dense. For example, it suffices to require that the elliptic fibration over the projective line induced by the anticanonical map has a nodal fiber over a k-rational point. It also suffices to require the existence of a point in S(k) that does not lie on six exceptional curves of S and that has order 3 on its fiber of the elliptic fibration. This allows us to show that within a parameter space for del Pezzo surfaces of d","authors_text":"Cecilia Salgado, Ronald van Luijk","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2012-12-11T10:02:14Z","title":"Density of rational points on del Pezzo surfaces of degree one"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1212.2364","kind":"arxiv","version":2},"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":"sha256:2204203d3fa212386c015ab157ac8b67303e67b199333172ab0ab9a2000d8a77","target":"record","created_at":"2026-05-18T02:55:36Z","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":"189e604139de255fc7a127a22788b8012f81162406e29646f435f8284459881f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2012-12-11T10:02:14Z","title_canon_sha256":"3affdcf066a028073f75bae47d3c761db66aac112c7584755487cc6899cdd6dd"},"schema_version":"1.0","source":{"id":"1212.2364","kind":"arxiv","version":2}},"canonical_sha256":"18118e5bc80175587903e234e4fbf8fc9e19a3c06bb613e3c66b008b8a06fe32","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"18118e5bc80175587903e234e4fbf8fc9e19a3c06bb613e3c66b008b8a06fe32","first_computed_at":"2026-05-18T02:55:36.527800Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:55:36.527800Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Ee5KJszvQm9IpYFw/KYrZR3EGQtQoyr5JNzWvDHZak4QMHBIIHZJFkOiiBoz4X/bLy4pMT8mBQDpfTPpAJUwDg==","signature_status":"signed_v1","signed_at":"2026-05-18T02:55:36.528467Z","signed_message":"canonical_sha256_bytes"},"source_id":"1212.2364","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2204203d3fa212386c015ab157ac8b67303e67b199333172ab0ab9a2000d8a77","sha256:411dba6d38f9ec41e89f67c2420ed68d6a3b1fffbc199f9b5793fdcd3358073f"],"state_sha256":"43227d1a72d0aa89ed95ff7f92fc76601995f2372818288d748d766d457bf737"}