{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2009:6CAPISARPBDQMBAIS3NR3K7GZM","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":"cbf9b487ed67bc381233f9de2cc83ba5a59b0fb084793314ffdaf175dfec2fab","cross_cats_sorted":["math.NT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2009-11-02T05:33:29Z","title_canon_sha256":"9c64eb13d8bfd31d6c3e8a9cafa4983d563c0c6c1f61965d6a605ee9b8b3797b"},"schema_version":"1.0","source":{"id":"0911.0236","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0911.0236","created_at":"2026-05-18T03:54:26Z"},{"alias_kind":"arxiv_version","alias_value":"0911.0236v1","created_at":"2026-05-18T03:54:26Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0911.0236","created_at":"2026-05-18T03:54:26Z"},{"alias_kind":"pith_short_12","alias_value":"6CAPISARPBDQ","created_at":"2026-05-18T12:25:58Z"},{"alias_kind":"pith_short_16","alias_value":"6CAPISARPBDQMBAI","created_at":"2026-05-18T12:25:58Z"},{"alias_kind":"pith_short_8","alias_value":"6CAPISAR","created_at":"2026-05-18T12:25:58Z"}],"graph_snapshots":[{"event_id":"sha256:104f9f4050e22025a4f3fef41dc60472b20428c96c235ed84a49af956332939f","target":"graph","created_at":"2026-05-18T03:54:26Z","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 calculate the $ \\phi (\\hat{\\phi})-$Selmer groups $ S^{(\\phi)} (E / \\Q) $ and $ S^{(\\hat{\\varphi})} (E^{\\prime} / \\Q) $ of elliptic curves $ y^{2} = x (x + \\epsilon p D) (x + \\epsilon q D) $ via descent theory (see [S, Chapter X]), in particular, we obtain that the Selmer groups of several families of such elliptic curves can be arbitrary large.","authors_text":"Derong Qiu, Fei Li","cross_cats":["math.NT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2009-11-02T05:33:29Z","title":"On several families of elliptic curves with arbitrary large Selmer groups"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0911.0236","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:f8a5608aabdcb2847fe057e4f858ec5add4232189a8eac689c67c0cca659e776","target":"record","created_at":"2026-05-18T03:54:26Z","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":"cbf9b487ed67bc381233f9de2cc83ba5a59b0fb084793314ffdaf175dfec2fab","cross_cats_sorted":["math.NT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2009-11-02T05:33:29Z","title_canon_sha256":"9c64eb13d8bfd31d6c3e8a9cafa4983d563c0c6c1f61965d6a605ee9b8b3797b"},"schema_version":"1.0","source":{"id":"0911.0236","kind":"arxiv","version":1}},"canonical_sha256":"f080f44811784706040896db1dabe6cb1b20aa9878c8cc2d614a8d33d7c7cdc9","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f080f44811784706040896db1dabe6cb1b20aa9878c8cc2d614a8d33d7c7cdc9","first_computed_at":"2026-05-18T03:54:26.450086Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:54:26.450086Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"pYOrwkDy3vHY/h2MIPlS4Sp2BaVBtZ8VuAHpO7k7QrRrpLz/jaMj1Vr+AceRWrpQaWUs1A60Zk0trV7YU2LQCA==","signature_status":"signed_v1","signed_at":"2026-05-18T03:54:26.450693Z","signed_message":"canonical_sha256_bytes"},"source_id":"0911.0236","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f8a5608aabdcb2847fe057e4f858ec5add4232189a8eac689c67c0cca659e776","sha256:104f9f4050e22025a4f3fef41dc60472b20428c96c235ed84a49af956332939f"],"state_sha256":"6ee0ee7dfd1dad9ab4b9b98f586e89fcb99a29cd13e5ca527684ca7869881082"}