{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:QJDQ727MVV24RP3YJXFP7LJOQB","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":"03330697bfd799194ebcb1c08c9153acb0e95ad05fca393116c9f41cb98b9941","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2013-07-29T19:24:31Z","title_canon_sha256":"956545abb98bb0057d19a91ac497fc5b8c94970f3726ef52127606242797859f"},"schema_version":"1.0","source":{"id":"1307.7691","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1307.7691","created_at":"2026-05-18T02:55:58Z"},{"alias_kind":"arxiv_version","alias_value":"1307.7691v3","created_at":"2026-05-18T02:55:58Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1307.7691","created_at":"2026-05-18T02:55:58Z"},{"alias_kind":"pith_short_12","alias_value":"QJDQ727MVV24","created_at":"2026-05-18T12:27:57Z"},{"alias_kind":"pith_short_16","alias_value":"QJDQ727MVV24RP3Y","created_at":"2026-05-18T12:27:57Z"},{"alias_kind":"pith_short_8","alias_value":"QJDQ727M","created_at":"2026-05-18T12:27:57Z"}],"graph_snapshots":[{"event_id":"sha256:1329087c8505a241205e2a5c9e33ad6af2ada88bf4d8a07a88b04eaaef475920","target":"graph","created_at":"2026-05-18T02:55:58Z","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 an elliptic curve over Q with prime conductor p. For each non-negative integer n we put K_n:=Q(E[p^n]). The aim of this paper is to estimate the order of the p-Sylow group of the ideal class group of K_n. We give a lower bounds in terms of the Mordell-Weil rank of $E(\\Q)$. As an application of our result, we give an example such that p^{2n} divides the class number of the field $K_n$ in the case of $p=5077$ for each positive integer n.","authors_text":"Fumio Sairaiji, Takuya Yamauchi","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2013-07-29T19:24:31Z","title":"On the class numbers of the fields of the p^n-torsion points of certain elliptic curves over Q"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1307.7691","kind":"arxiv","version":3},"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":"sha256:96f327917702b8295d8b0a5381fb8ffe843bdec9604b82b69f8cea82a3910182","target":"record","created_at":"2026-05-18T02:55:58Z","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":"03330697bfd799194ebcb1c08c9153acb0e95ad05fca393116c9f41cb98b9941","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2013-07-29T19:24:31Z","title_canon_sha256":"956545abb98bb0057d19a91ac497fc5b8c94970f3726ef52127606242797859f"},"schema_version":"1.0","source":{"id":"1307.7691","kind":"arxiv","version":3}},"canonical_sha256":"82470febecad75c8bf784dcaffad2e80636c1dc1b328efccb7437afa60ce020e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"82470febecad75c8bf784dcaffad2e80636c1dc1b328efccb7437afa60ce020e","first_computed_at":"2026-05-18T02:55:58.971928Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:55:58.971928Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"6HM70DuUzoiXf04YeNTZQLfzGaKXwR0c2ugomLVlsVnFzYqSP2FMSxJ/I+w0eAhchbfFEqoBHdcX3G4GHLykAw==","signature_status":"signed_v1","signed_at":"2026-05-18T02:55:58.972488Z","signed_message":"canonical_sha256_bytes"},"source_id":"1307.7691","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:96f327917702b8295d8b0a5381fb8ffe843bdec9604b82b69f8cea82a3910182","sha256:1329087c8505a241205e2a5c9e33ad6af2ada88bf4d8a07a88b04eaaef475920"],"state_sha256":"56e7c4e8eecd885251b8d9c9f3add22e20b66138276a8533e627278c6306984f"}