A NOTE ON DOUBLE ROTATIONS OF INFINITE TYPE

The paper proves Theorem 1: the parameter set of double rotations of infinite type has Hausdorff dimension strictly less than 3, by building a Rauzy-like renormalization (Z- and R-inductions), associating a simplicial system, verifying it is quickly escaping via Fougeron’s criterion, and invoking Fougeron’s Theorem 1.5 to obtain a strict dimension drop; Corollary 20 on length data is stated as equivalent to Theorem 1 in parameter space . The candidate solution mirrors these steps almost verbatim (renormalization → simplicial system → quickly escaping → Theorem 1.5 → transfer to (α,β,c)), with only minor cosmetic differences (calling the induction “ρ-induction” and mentioning bi-Lipschitz charts, whereas the paper asserts the equivalence of Corollary 20 and Theorem 1 directly). Hence both are correct and essentially the same proof.