{"paper":{"title":"On the spherical Blaschke-Lebesgue problem","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CA","math.DG"],"primary_cat":"math.MG","authors_text":"Abigail Hall, Andriy Prymak, Chanatip Sujsuntinukul","submitted_at":"2026-06-29T22:35:59Z","abstract_excerpt":"The Blaschke-Lebesgue theorem states that the Reuleaux triangle has the smallest area among planar convex bodies of a fixed constant width. We study how small bodies of constant width can be on the unit sphere $\\mathbb S^n$ when $n$ is large. For a spherical convex body $K\\subset \\mathbb S^n$ of constant width $w\\in(0,\\pi)$, its relative effective radius is \\[\n  \\left(\\frac{\\mu_n(K)}{\\mu_n(\\mathbb B^n(w/2))}\\right)^{1/n}, \\] where $\\mu_n$ is the spherical $n$-measure and $\\mathbb B^n(w/2)$ is a geodesic ball of radius $w/2$. Let $\\sigma_n(w)$ be the infimum of the relative effective radius ove"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.30960","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/2606.30960/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"}