{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:QDMTPGFAJBOZSM3DGZ3KRTKQEL","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":"9de1b1618fc54e897e3787ae98a12d0ba779279e2fbe19e1ee7157e37dd4d598","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.NT","submitted_at":"2017-08-03T16:13:08Z","title_canon_sha256":"a51febd96bfe9f4c1852c9de6d76533d80f85a23e36af6bf620c831c9d94f2ad"},"schema_version":"1.0","source":{"id":"1708.01192","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1708.01192","created_at":"2026-05-18T00:25:07Z"},{"alias_kind":"arxiv_version","alias_value":"1708.01192v4","created_at":"2026-05-18T00:25:07Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1708.01192","created_at":"2026-05-18T00:25:07Z"},{"alias_kind":"pith_short_12","alias_value":"QDMTPGFAJBOZ","created_at":"2026-05-18T12:31:37Z"},{"alias_kind":"pith_short_16","alias_value":"QDMTPGFAJBOZSM3D","created_at":"2026-05-18T12:31:37Z"},{"alias_kind":"pith_short_8","alias_value":"QDMTPGFA","created_at":"2026-05-18T12:31:37Z"}],"graph_snapshots":[{"event_id":"sha256:0fb1b8bb3d68fade6bb80fec3259d43035f3a3bfd13331c0adbfd42bd29c8979","target":"graph","created_at":"2026-05-18T00:25:07Z","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":"In this paper, we consider Abelian varieties over function fields that arise as twists of Abelian varieties by cyclic covers of irreducible quasi-projective varieties. Then, in terms of Prym varieties associated to the cyclic covers, we prove a structure theorem on their Mordell-Weil group. Our results give an explicit method for construction of elliptic curves, hyper- and super-elliptic Jacobians that have large ranks over function fields of certain varieties.","authors_text":"Sajad Salami","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.NT","submitted_at":"2017-08-03T16:13:08Z","title":"The rational points on certain Abelian varieties over function fields"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1708.01192","kind":"arxiv","version":4},"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":"sha256:5e78c5f2ad6c852fcda93b7a5d57a810daf9cc06426c9a0989aad20ffa6792a3","target":"record","created_at":"2026-05-18T00:25:07Z","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":"9de1b1618fc54e897e3787ae98a12d0ba779279e2fbe19e1ee7157e37dd4d598","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.NT","submitted_at":"2017-08-03T16:13:08Z","title_canon_sha256":"a51febd96bfe9f4c1852c9de6d76533d80f85a23e36af6bf620c831c9d94f2ad"},"schema_version":"1.0","source":{"id":"1708.01192","kind":"arxiv","version":4}},"canonical_sha256":"80d93798a0485d9933633676a8cd5022feb7e698c431114cb5ea052b34c35d3b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"80d93798a0485d9933633676a8cd5022feb7e698c431114cb5ea052b34c35d3b","first_computed_at":"2026-05-18T00:25:07.589521Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:25:07.589521Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"lDqwokhROmmZJRl9SVcJJy5CYWoMGhaFgys9scclPuG3gqSe9W2xiZugxsA6PBRMiZKeNqQNPVk3ti6Hii2cDg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:25:07.590083Z","signed_message":"canonical_sha256_bytes"},"source_id":"1708.01192","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:5e78c5f2ad6c852fcda93b7a5d57a810daf9cc06426c9a0989aad20ffa6792a3","sha256:0fb1b8bb3d68fade6bb80fec3259d43035f3a3bfd13331c0adbfd42bd29c8979"],"state_sha256":"43794561b299cd028c121f8fb51bdd2dca68d8dd41ba3606627bb3bb2656041b"}