A DICHOTOMY FOR THE DIMENSION OF SRB MEASURE

The paper’s Main Theorem states the exact dichotomy for T(x,y)=(bx mod 1, γy+φ(x)) with analytic φ: either the SRB support is an analytic graph or dim_H(F)=dim(ω)=min{2,1+log b / log(1/γ)}, and this holds for all γ except finitely many when φ is non-constant. The statement and its proof (via a transversality dichotomy (H) vs (H*) and Hochman-type entropy growth) are clearly presented (Main Theorem and Theorem A; proof outline and Appendix establishing dim(ω)=1+α) . The candidate solution gives the same dichotomy and dimension formula and correctly links the graph case to a cohomological equation, but it compresses the core argument by appealing to Ledrappier–Young-style formulas and a generic “stable entropy equals log b” claim without the delicate entropy-growth/transversality machinery that the paper develops. Thus, while the conclusions match, the proof strategies differ materially; the paper’s proof is complete, whereas the model’s proof outline leaves key steps unsubstantiated. The finiteness of exceptional γ is also aligned with the paper (invoking the cited dichotomy between (H*) and (H)) .