{"id":"palomar/PALOMAR-2026-09-19-000001","url":"https://github.com/CoolRmal/NKBesicovitch/tree/e12e5981d840eb5ebdc25403691b3c63a9c7aff8","json":"https://data.palomar-registry.org/entries/PALOMAR-2026-09-19-000001-v1.json","repo":"https://github.com/CoolRmal/NKBesicovitch","tags":["math.CA","msc:42B25","msc:28A75","harmonic-analysis","besicovitch-sets","lean","hausdorff-dimension"],"score":0,"title":"NKBesicovitch","trust":"high","domain":"math.CA","source":"palomar","authors":["Yongxi Lin"],"reviews":0,"subject":"math.CA","summary":"Lean proofs of Hausdorff dimension at least n-(n-k)/p_c^k for all (n,k)-Besicovitch sets with 1 n. Here a Besicovitch set contains a translated unit k-disk in every k-dimensional direction, and p_c is the unique root in (2,3) of p^3-2p^2-2p+2=0. Building on Bourgain's arithmetic-combinatorial approach, Nets Hawk Katz and Terence Tao's New bounds for Kakeya problems (2002; preprint 2001) established the Minkowski-dimension bound 1+(n-1)/beta_c, where beta_c=p_c/(p_c-1)=1.67513... satisfies beta_c^3-4*beta_c+2=0. This is exactly n-(n-1)/p_c, so the numerical exponent itself is not new. They…","category":"research","comments":0,"disputed":false,"division":"math","mentions":0,"verified":true,"discussed":0,"published":"2026-09-19","reactions":{},"formalized":true,"formalizes":[{"title":"The projection estimate near 1.675","identifier":"","relationship":"formalizes"},{"title":"From Projection Inequalities to Mixed-Norm Local X-Ray Estimates","identifier":"","relationship":"formalizes"},{"title":"Two bounds for the X-ray transform","identifier":"doi:10.1007/s00209-009-0589-5","relationship":"adapts"},{"title":"Bounds for Kakeya-type maximal operators associated with k-planes","identifier":"arXiv:math/0512377","relationship":"adapts"}]}