{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:RMUR3NGEKCB2MOPMRQ4AZ3BFWS","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":"cc431570e392f721730dd6f5592ea4a32fe896231b9f9d4b704f378cd5bb2dc9","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2018-07-19T18:51:34Z","title_canon_sha256":"7a981aedc2d7d9186bf6a507e53cd8a3893ca50f8c69b03b22bd95b2e0b7d85b"},"schema_version":"1.0","source":{"id":"1807.07604","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1807.07604","created_at":"2026-05-17T23:45:20Z"},{"alias_kind":"arxiv_version","alias_value":"1807.07604v2","created_at":"2026-05-17T23:45:20Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1807.07604","created_at":"2026-05-17T23:45:20Z"},{"alias_kind":"pith_short_12","alias_value":"RMUR3NGEKCB2","created_at":"2026-05-18T12:32:50Z"},{"alias_kind":"pith_short_16","alias_value":"RMUR3NGEKCB2MOPM","created_at":"2026-05-18T12:32:50Z"},{"alias_kind":"pith_short_8","alias_value":"RMUR3NGE","created_at":"2026-05-18T12:32:50Z"}],"graph_snapshots":[{"event_id":"sha256:66f448845e53f8f0b20d548999621148aad6cf134d2a5cbfb618e12cc3371051","target":"graph","created_at":"2026-05-17T23:45:20Z","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 $F$ be a number field unramified at an odd prime $p$ and $F_\\infty$ be the $\\mathbf{Z}_p$-cyclotomic extension of $F$. Let $A$ be an abelian variety defined over $F$ with good supersingular reduction at all primes of $F$ above $p$. B\\\"uy\\\"ukboduk and the first named author have defined modified Selmer groups associated to $A$ over $F_\\infty$. Assuming that the Pontryagin dual of these Selmer groups are torsion $\\mathbf{Z}_p[[\\mathrm{Gal}(F_\\infty/F)]]$-modules, we give an explicit sufficient condition for the rank of the Mordell-Weil group $A(F_n)$ to be bounded as $n$ varies.","authors_text":"Antonio Lei, Gautier Ponsinet","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2018-07-19T18:51:34Z","title":"On the Mordell-Weil ranks of supersingular abelian varieties in cyclotomic extensions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1807.07604","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:c4b9826704870df5a80ddc2e82f533d1c3f26d05821ba0dfa2d2796c9e4bff5b","target":"record","created_at":"2026-05-17T23:45:20Z","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":"cc431570e392f721730dd6f5592ea4a32fe896231b9f9d4b704f378cd5bb2dc9","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2018-07-19T18:51:34Z","title_canon_sha256":"7a981aedc2d7d9186bf6a507e53cd8a3893ca50f8c69b03b22bd95b2e0b7d85b"},"schema_version":"1.0","source":{"id":"1807.07604","kind":"arxiv","version":2}},"canonical_sha256":"8b291db4c45083a639ec8c380cec25b4b45de77bbdb031f382ffd8c639db90f8","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"8b291db4c45083a639ec8c380cec25b4b45de77bbdb031f382ffd8c639db90f8","first_computed_at":"2026-05-17T23:45:20.763737Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:45:20.763737Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"iN5Gse3CjoKDTh2gXBVdCeIn2Z1alAZ/mUUJGV1fjxCIGq9deYvpQgW+Peg+gEu8SzfkGM7VL5ZlnS8Se+JRBw==","signature_status":"signed_v1","signed_at":"2026-05-17T23:45:20.764399Z","signed_message":"canonical_sha256_bytes"},"source_id":"1807.07604","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c4b9826704870df5a80ddc2e82f533d1c3f26d05821ba0dfa2d2796c9e4bff5b","sha256:66f448845e53f8f0b20d548999621148aad6cf134d2a5cbfb618e12cc3371051"],"state_sha256":"dabdae4e0369f32f497967968473ba3bc7cb4deb8e45c650ed0ee11d840ef29c"}