{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:MXNNFXGZCIFCUDV4IHZXSSEN4Y","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":"94d9d30d5e4fbdf9f5ebccf62fb4046a261acc37f41e3e20dc02537877b32e88","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2018-12-14T15:54:06Z","title_canon_sha256":"a9376d18d96e2dffa4608d38feec4ed5744ae730b9584a4d28f9378ea9e6b81e"},"schema_version":"1.0","source":{"id":"1812.05993","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1812.05993","created_at":"2026-05-17T23:55:42Z"},{"alias_kind":"arxiv_version","alias_value":"1812.05993v2","created_at":"2026-05-17T23:55:42Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1812.05993","created_at":"2026-05-17T23:55:42Z"},{"alias_kind":"pith_short_12","alias_value":"MXNNFXGZCIFC","created_at":"2026-05-18T12:32:40Z"},{"alias_kind":"pith_short_16","alias_value":"MXNNFXGZCIFCUDV4","created_at":"2026-05-18T12:32:40Z"},{"alias_kind":"pith_short_8","alias_value":"MXNNFXGZ","created_at":"2026-05-18T12:32:40Z"}],"graph_snapshots":[{"event_id":"sha256:97f4002d3e6641b1d4a8ec212a9ba4276fbd4a0cf210127b4f677c8da8ffdde0","target":"graph","created_at":"2026-05-17T23:55:42Z","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 $N=pq$ be a product of two distinct primes. There is an isogeny $J_0(N)^{\\rm new}\\to J^N$ defined over $\\mathbf{Q}$ between the new quotient of $J_0(N)$ and the Jacobian of the Shimura curve attached to the indefinite quaternion algebra of discriminant $N$. In the case when $p=2,3,5,7,13$, Ogg made predictions about the kernels of these isogenies. We show that Ogg's conjecture is not true in general. Afterwards, we propose a strategy for proving results toward Ogg's conjecture in certain situations. Finally, we discuss this strategy in detail for $N=5\\cdot 13$.","authors_text":"Krzysztof Klosin, Mihran Papikian","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2018-12-14T15:54:06Z","title":"Galois extensions and a Conjecture of Ogg"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1812.05993","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":"sha256:3cc601007c84cca5af9f0ef49208f78029cf9395f97987ce8d6d6b4856fdd611","target":"record","created_at":"2026-05-17T23:55:42Z","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":"94d9d30d5e4fbdf9f5ebccf62fb4046a261acc37f41e3e20dc02537877b32e88","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2018-12-14T15:54:06Z","title_canon_sha256":"a9376d18d96e2dffa4608d38feec4ed5744ae730b9584a4d28f9378ea9e6b81e"},"schema_version":"1.0","source":{"id":"1812.05993","kind":"arxiv","version":2}},"canonical_sha256":"65dad2dcd9120a2a0ebc41f379488de60d14a04d6f08013e07d16e0f36b6f610","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"65dad2dcd9120a2a0ebc41f379488de60d14a04d6f08013e07d16e0f36b6f610","first_computed_at":"2026-05-17T23:55:42.367419Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:55:42.367419Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"qWxe51y5mhGi5uexk8EHjWJwmjJETyBZ1FOI8Sly2Irbta85icwcgopHV+fSn0gp0/xvMzYDTKD+Nj//YtOIDw==","signature_status":"signed_v1","signed_at":"2026-05-17T23:55:42.367857Z","signed_message":"canonical_sha256_bytes"},"source_id":"1812.05993","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3cc601007c84cca5af9f0ef49208f78029cf9395f97987ce8d6d6b4856fdd611","sha256:97f4002d3e6641b1d4a8ec212a9ba4276fbd4a0cf210127b4f677c8da8ffdde0"],"state_sha256":"95a5b969126b511ed15c7ca2b55d045fd17e7193fdde8c6542023cfdf148f2d8"}