{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:AEH7EZKNCEHVYVHJY2TFB7LLCK","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":"014760ba20d64e938f030ae4f3674546bbc8c6a2ea3a16a3cebc3d1a217408bb","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2017-02-09T03:13:22Z","title_canon_sha256":"099e04b75ac203da99fefa8232ec2b00ef5dd5c50e84db939cc668f022e3d84e"},"schema_version":"1.0","source":{"id":"1702.02687","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1702.02687","created_at":"2026-05-18T00:51:02Z"},{"alias_kind":"arxiv_version","alias_value":"1702.02687v1","created_at":"2026-05-18T00:51:02Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1702.02687","created_at":"2026-05-18T00:51:02Z"},{"alias_kind":"pith_short_12","alias_value":"AEH7EZKNCEHV","created_at":"2026-05-18T12:31:05Z"},{"alias_kind":"pith_short_16","alias_value":"AEH7EZKNCEHVYVHJ","created_at":"2026-05-18T12:31:05Z"},{"alias_kind":"pith_short_8","alias_value":"AEH7EZKN","created_at":"2026-05-18T12:31:05Z"}],"graph_snapshots":[{"event_id":"sha256:44d8f4c305b115a3a0bda724f975a88d9f76fbe91e2d751aea6f08218ee4f168","target":"graph","created_at":"2026-05-18T00:51:02Z","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":"If $E$ is an elliptic curve with a point of order two, then work of Klagsbrun and Lemke Oliver shows that the distribution of $\\dim_{\\mathbb{F}_2}\\mathrm{Sel}_\\phi(E^d/\\mathbb{Q}) - \\dim_{\\mathbb{F}_2} \\mathrm{Sel}_{\\hat\\phi}(E^{\\prime d}/\\mathbb{Q})$ within the quadratic twist family tends to the discrete normal distribution $\\mathcal{N}(0,\\frac{1}{2} \\log \\log X)$ as $X \\rightarrow \\infty$.\n  We consider the distribution of $\\mathrm{dim}_{\\mathbb{F}_2} \\mathrm{Sel}_\\phi(E^d/\\mathbb{Q})$ within such a quadratic twist family when $\\dim_{\\mathbb{F}_2} \\mathrm{Sel}_\\phi(E^d/\\mathbb{Q}) - \\dim_{\\","authors_text":"Daniel Kane, Zev Klagsbrun","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2017-02-09T03:13:22Z","title":"On the Joint Distribution Of $\\mathrm{Sel}_\\phi(E/\\mathbb{Q})$ and $\\mathrm{Sel}_{\\hat\\phi}(E^\\prime/\\mathbb{Q})$ in Quadratic Twist Families"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1702.02687","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:eb3832594a12ada263c5f0a850b16db38c4bd4d4bdb05bcda919413c08603bb8","target":"record","created_at":"2026-05-18T00:51:02Z","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":"014760ba20d64e938f030ae4f3674546bbc8c6a2ea3a16a3cebc3d1a217408bb","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2017-02-09T03:13:22Z","title_canon_sha256":"099e04b75ac203da99fefa8232ec2b00ef5dd5c50e84db939cc668f022e3d84e"},"schema_version":"1.0","source":{"id":"1702.02687","kind":"arxiv","version":1}},"canonical_sha256":"010ff2654d110f5c54e9c6a650fd6b12a35bc14e08fbb26c13c5ccd56963070d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"010ff2654d110f5c54e9c6a650fd6b12a35bc14e08fbb26c13c5ccd56963070d","first_computed_at":"2026-05-18T00:51:02.704306Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:51:02.704306Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ca7u7J1z1+c/J31Ka44o/wNabgooYvZNEPusTBx3jhSfjDcTzSpFQj9dEvHV7HMQ4OiExiT4+Yx0mrbyX8niBg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:51:02.704782Z","signed_message":"canonical_sha256_bytes"},"source_id":"1702.02687","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:eb3832594a12ada263c5f0a850b16db38c4bd4d4bdb05bcda919413c08603bb8","sha256:44d8f4c305b115a3a0bda724f975a88d9f76fbe91e2d751aea6f08218ee4f168"],"state_sha256":"96bb33e7f0095f04416bcc12f0a68bc692a89133932c9ccf0cef70a3a6d6167c"}