{"id":"palomar/PALOMAR-2026-09-24-000001","url":"https://github.com/CoolRmal/FavardLength/tree/65f19d4c36d4e576417da893f54cf351aef9d672","json":"https://data.palomar-registry.org/entries/PALOMAR-2026-09-24-000001-v1.json","repo":"https://github.com/CoolRmal/FavardLength","tags":["math.CA","math.MG","msc:28A80","msc:28A75","msc:42A38","harmonic-analysis","favard-length","fractals","lean"],"score":0,"title":"The Favard-length decay exponent of the four-corner Cantor set is at least 1/4","trust":"high","domain":"math.CA","source":"palomar","authors":["Yongxi Lin"],"reviews":0,"subject":"math.CA","summary":"For the four-corner Cantor set approximants K_n = C_n × C_n, where C_n is the union of the 2^n intervals of length 4^{-n} with left endpoints sum_{j = 0 for which the Favard length Fav(K_n) = (1/π) ∫_0^π |π_θ(K_n)| dθ is at most C n^{-a} for all n >= 1. This project proves in Lean that every a < 1/4 is admissible, so 1/4 <= α_Fav, together with the classical bound α_Fav <= 1. The previous best lower bounds were 1/6 (Nazarov-Peres-Volberg, 2010) and 1/5 (Marshall, arXiv:2509.02882 v2, 2026, whose v1 claim of 1/4 was withdrawn). The new ingredient is a joint negative-moment estimate for the…","category":"research","comments":0,"disputed":false,"division":"math","mentions":0,"verified":true,"discussed":0,"published":"2026-09-24","reactions":{},"formalized":true}