{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:2WU64PDS5WJXAFHFPKV3NDOJCZ","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":"df25c2a36ab40d9a41574bc2261acc2b1fa35da3a15c4c52fd2c28b2532b5c85","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2013-07-16T11:52:44Z","title_canon_sha256":"a0700d03f6357bfbd3531f8d41e4b1ad8fd4cb621e057d8f8740f9bbf5371d2e"},"schema_version":"1.0","source":{"id":"1307.4251","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1307.4251","created_at":"2026-05-18T03:05:01Z"},{"alias_kind":"arxiv_version","alias_value":"1307.4251v2","created_at":"2026-05-18T03:05:01Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1307.4251","created_at":"2026-05-18T03:05:01Z"},{"alias_kind":"pith_short_12","alias_value":"2WU64PDS5WJX","created_at":"2026-05-18T12:27:32Z"},{"alias_kind":"pith_short_16","alias_value":"2WU64PDS5WJXAFHF","created_at":"2026-05-18T12:27:32Z"},{"alias_kind":"pith_short_8","alias_value":"2WU64PDS","created_at":"2026-05-18T12:27:32Z"}],"graph_snapshots":[{"event_id":"sha256:5fbe8e251619a234b34900e749969bdb8eb97fd78f6fe80de031165a698ebc78","target":"graph","created_at":"2026-05-18T03:05:01Z","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 $E$ be the elliptic curve $y^2=x(x+1)(x+t)$ over the field $\\Fp(t)$ where $p$ is an odd prime. We study the arithmetic of $E$ over extensions $\\Fq(t^{1/d})$ where $q$ is a power of $p$ and $d$ is an integer prime to $p$. The rank of $E$ is given in terms of an elementary property of the subgroup of $(\\Z/d\\Z)^\\times$ generated by $p$. We show that for many values of $d$ the rank is large. For example, if $d$ divides $2(p^f-1)$ and $2(p^f-1)/d$ is odd, then the rank is at least $d/2$. When $d=2(p^f-1)$, we exhibit explicit points generating a subgroup of $E(\\Fq(t^{1/d}))$ of finite index in ","authors_text":"Chris Hall, Douglas Ulmer, Ricardo Concei\\c{c}\\~ao","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2013-07-16T11:52:44Z","title":"Explicit points on the Legendre curve II"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1307.4251","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":"sha256:44e26a62f5f9107316a41024e011d0c93756414620304ca9439f1ce967ce532a","target":"record","created_at":"2026-05-18T03:05:01Z","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":"df25c2a36ab40d9a41574bc2261acc2b1fa35da3a15c4c52fd2c28b2532b5c85","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2013-07-16T11:52:44Z","title_canon_sha256":"a0700d03f6357bfbd3531f8d41e4b1ad8fd4cb621e057d8f8740f9bbf5371d2e"},"schema_version":"1.0","source":{"id":"1307.4251","kind":"arxiv","version":2}},"canonical_sha256":"d5a9ee3c72ed937014e57aabb68dc9165fbe155f101d7471644d32aeaf7c5b25","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d5a9ee3c72ed937014e57aabb68dc9165fbe155f101d7471644d32aeaf7c5b25","first_computed_at":"2026-05-18T03:05:01.324018Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:05:01.324018Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"3840UkwWS7zs5LPTYzd3HOzCepP6Ec7eFovpIf1o4cil5l+04SdG1ol9hGH7qQjfd27CoRV5LEeJ4Qr4m4n5DA==","signature_status":"signed_v1","signed_at":"2026-05-18T03:05:01.324550Z","signed_message":"canonical_sha256_bytes"},"source_id":"1307.4251","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:44e26a62f5f9107316a41024e011d0c93756414620304ca9439f1ce967ce532a","sha256:5fbe8e251619a234b34900e749969bdb8eb97fd78f6fe80de031165a698ebc78"],"state_sha256":"155dedb0b3a794af9a398ca25fb91bdb15d9dcb739cda397176bf94cda24517d"}