{"id":"palomar/PALOMAR-2026-10-21-000006","url":"https://github.com/mrklwk/kakeya-two-scale-lean/tree/1eba4ec16c6894aa2390b1c1bcb7d2c0e1c5a46c","json":"https://data.palomar-registry.org/entries/PALOMAR-2026-10-21-000006-v2.json","repo":"https://github.com/mrklwk/kakeya-two-scale-lean","tags":["math.CA","math.CO","msc:42B25","msc:28A75","kakeya-sets","geometric-measure-theory","harmonic-analysis","minkowski-dimension"],"score":0,"title":"Two-scale Kakeya upper Minkowski lower bound","trust":"high","domain":"math.CA","source":"palomar","authors":["Mark Lewko"],"reviews":0,"subject":"math.CA","summary":"We prove that every bounded Kakeya set in Rⁿ, n ≥ 4, has upper Minkowski dimension at least 0.597n. Here a Kakeya set contains a unit line segment in every direction. This improves the asymptotic coefficient c_KT = 1/α = 0.596968283237… in the Katz–Tao bound 1 + c_KT(n−1), where α is the unique root of α³−4α+2 = 0 in (1,2). The proof combines arithmetic estimates for line segments with geometric estimates for tubes at two different widths.","category":"research","comments":0,"disputed":false,"division":"math","mentions":0,"verified":true,"discussed":0,"published":"2026-10-21","reactions":{},"formalized":true,"formalizes":[{"title":"New Kakeya estimates using Gromov's algebraic lemma","identifier":"arXiv:1908.05314v4","relationship":"adapts"},{"title":"New bounds for Kakeya problems","identifier":"arXiv:math/0102135","relationship":"adapts"},{"title":"Generalized arithmetic Kakeya","identifier":"arXiv:2411.13395","relationship":"adapts"}]}