The Favard-length decay exponent of the four-corner Cantor set is at least 1/4
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bounds were 1/6 (Nazarov-Peres-Volberg, 2010) and 1/5 (Marshall, arXiv:2509.02882 v2, 2026, whose v1 claim of 1/4 was withdrawn).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…
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