{"paper":{"title":"Fine approximation of convex bodies by polytopes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Dmitry Ryabogin, Fedor Nazarov, M\\'arton Nasz\\'odi","submitted_at":"2017-05-04T14:53:32Z","abstract_excerpt":"We prove that for every convex body $K$ with the center of mass at the origin and every $\\varepsilon\\in \\left(0,\\frac{1}{2}\\right)$, there exists a convex polytope $P$ with at most $e^{O(d)}\\varepsilon^{-\\frac{d-1}{2}}$ vertices such that $(1-\\varepsilon)K\\subset P\\subset K$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1705.01867","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":""},"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"}