Hausdorff Dimension of Closure of Cycles in d-Maps on the Circle

The paper proves dimH(Em,d) = log m / log d via a lower bound using a Cantor-type subset and an upper bound by counting and covering precycles. It also establishes deg(C) = η(C) (crossing number) and the inequality η(C) ≤ dig(C) (number of distinct first digits used). The candidate solution incorrectly claims deg(C) equals the number of distinct digits used in the periodic word and consequently misidentifies Em,d as the union of digit-restricted d-adic sets. That equality is false in general (e.g., the 2-cycle {1/3, 2/3} for d=2 uses two digits but has degree 1). Although the candidate’s final dimension formula matches the paper, the core argument is flawed.