{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:DDW46XU52LJG73CCCALMKARV7W","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":"26c80bfefda794b996ba1688037c8f042d8086ca4c6d33b2070777ab4463193b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2012-05-29T15:29:13Z","title_canon_sha256":"e0045cb45ed70e1def278db62d8e7db12251eebad6acbd2f444adc655f8295fb"},"schema_version":"1.0","source":{"id":"1205.6392","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1205.6392","created_at":"2026-05-18T03:04:14Z"},{"alias_kind":"arxiv_version","alias_value":"1205.6392v2","created_at":"2026-05-18T03:04:14Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1205.6392","created_at":"2026-05-18T03:04:14Z"},{"alias_kind":"pith_short_12","alias_value":"DDW46XU52LJG","created_at":"2026-05-18T12:27:01Z"},{"alias_kind":"pith_short_16","alias_value":"DDW46XU52LJG73CC","created_at":"2026-05-18T12:27:01Z"},{"alias_kind":"pith_short_8","alias_value":"DDW46XU5","created_at":"2026-05-18T12:27:01Z"}],"graph_snapshots":[{"event_id":"sha256:36a88d246345582bc9ed603a2be367912bccde0bd2ffd3922397797410a08e85","target":"graph","created_at":"2026-05-18T03:04:14Z","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":"Let S be a smooth cubic surface defined over a field K. As observed by Segre and Manin, there is a secant and tangent process on S that generates new K-rational points from old. It is natural to ask for the size of a minimal generating set for S(K). In a recent paper, for fields K with at least 13 elements, Siksek showed that if S contains a skew pair of K-lines then S(K) can be generated from one point. In this paper we prove the corresponding version of this result for fields K having at least 4 elements, and slightly milder results for #K=2 or 3.","authors_text":"Jenny Cooley","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2012-05-29T15:29:13Z","title":"Generators for Cubic Surfaces with two Skew Lines over Finite Fields"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1205.6392","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":"sha256:24ac279f6967858b158958da475578fd6db69a71d2e00daf09a3f8538c84332d","target":"record","created_at":"2026-05-18T03:04:14Z","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":"26c80bfefda794b996ba1688037c8f042d8086ca4c6d33b2070777ab4463193b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2012-05-29T15:29:13Z","title_canon_sha256":"e0045cb45ed70e1def278db62d8e7db12251eebad6acbd2f444adc655f8295fb"},"schema_version":"1.0","source":{"id":"1205.6392","kind":"arxiv","version":2}},"canonical_sha256":"18edcf5e9dd2d26fec421016c50235fdba2d77dd132f849eb9bf0c9b36c21148","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"18edcf5e9dd2d26fec421016c50235fdba2d77dd132f849eb9bf0c9b36c21148","first_computed_at":"2026-05-18T03:04:14.059160Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:04:14.059160Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Icg0NHIS0wNXrWk4WGyn+FoscLpQL8n3FXVkYRNOh8QOOQ4477L19wyaS4PNRLyYylob0Ve9+GB8FDo8s2qRDg==","signature_status":"signed_v1","signed_at":"2026-05-18T03:04:14.059578Z","signed_message":"canonical_sha256_bytes"},"source_id":"1205.6392","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:24ac279f6967858b158958da475578fd6db69a71d2e00daf09a3f8538c84332d","sha256:36a88d246345582bc9ed603a2be367912bccde0bd2ffd3922397797410a08e85"],"state_sha256":"a21fd5a49bf6bf40b9c96d7a880d563bd0e8053556035d72e36366101294620e"}