C1-Diffeomorphism Class of some Circle Maps with a Flat Interval

The uploaded paper proves the equivalence “h is C1 iff c∗u(f)=c∗u(g) and c+(f)+c′+(f)=c+(g)+c′+(g)” for Fibonacci circle maps with a flat interval and different one-sided critical exponents, using a renormalization-coordinate decomposition (Proposition 1) and a partition-based derivative scheme Dhn that converges under the stated coefficient equalities (Propositions 2 and 3) . The candidate solution proves the same equivalence with a different presentation: renormalized conjugacies Hn, a linear functional extracting the center drift, and Koebe-type distortion. The invariants and the necessity/sufficiency logic align with the paper’s statements (Main result) . Minor notational issues in the paper (e.g., c∗) do not affect correctness; both arguments are sound and compatible.