{"paper":{"title":"A 4/7-limit law for the largest interpoint distance in a rotational ellipsoid","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Norbert Henze","submitted_at":"2026-05-23T15:37:56Z","abstract_excerpt":"Let $M_n$ denote the largest interpoint distance among independent random points $X_1,\\dots,X_n$ uniformly distributed in a compact set in $\\mathbb{R}^d$. Weak limit laws for $M_n$ are known in several geometric settings, in particular for ellipsoids with a unique major axis. In this paper we treat the simplest nontrivial case in which the largest semi-axis is not unique, namely the rotational ellipsoid $\\{(x_1,x_2,x_3)\\in\\mathbb{R}^3: (x_1^2+x_2^2)/h^2 + x_3^2/a^2 \\le 1\\}$, where $0<a<h$. The diameter of this ellipsoid is attained by all antipodal pairs on the equatorial circle, so the extrem"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2605.24627","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2605.24627/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}