Lean formalization toward Bugeaud Problem 10.61
A Lean 4 / Mathlib development of criteria for Bugeaud's Problem 10.61 ([Bug12, p. 222], due to Mendès France [MF67]): for a Pisot number α > 2 and the Cantor set C(α) = {(α−1) Σ_{k≥1} ε_k α^{−k} : ε_k ∈ {0,1}}, no ξ ∈ C(α) has (ξαⁿ)_{n≥1} uniformly distributed modulo one. The problem is open; what is proved here are criteria for it and two instances. Every compared statement that concludes Problem 10.61 does so for a *quadratic* setup — a real root α > 1 of X² − aX − b whose conjugate has modulus below one — and the two instances are quadratic; the arbitrary-degree material is conditional…
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