THE COORDINATE FUNCTIONS OF THE HEIGHWAY DRAGON CURVE

The paper proves dim_B Xθ = dim_B Yθ = 1 − (log cos α)/(log 2) by explicit dyadic mesh counting: a uniform upper bound on oscillations in each dyadic column (Lemma 3.2) and a uniform lower bound via angle-combinatorics for rational α, then approximation for irrational α (Theorem 2.2), see the statement and proof outline in the text around Theorem 2.2 and Lemmas 3.2, 3.5, 3.6 . The candidate solution obtains the same formula using a de Rham-type functional equation for the complex parametrization and uniform oscillation bounds on dyadic intervals, then counts squares to get N_{2^{-n}} ~ (4r)^n and the same dimension. The two arguments are coherent but distinct: the paper avoids relying on an explicit self-similarity of the parametrization (remarking this property is not available in general beyond the Levy case) and instead uses careful covering/separation estimates, whereas the candidate’s proof leverages the exact two-map self-similarity of the limit curve and convex-hull width bounds. No contradiction was found; minor presentational clarifications would strengthen the paper but do not affect correctness.