Exponentially mixing SRB measures are Bernoulli

The paper proves Theorems A and B by constructing exponentially small “good boxes,” building fake center-stable foliations, and pushing exponential mixing to equidistribution of unstable manifolds before invoking Ornstein–Weiss to conclude Bernoulli, with all delicate quantitative steps made precise (e.g., Proposition 3.5 and its volume analogue, and the ‘shifting trick’) . By contrast, the candidate solution tries to deduce very weak Bernoulli (vWB) directly from decay of correlations by smoothing indicator functions of atoms of a finite generating partition. This approach overlooks key obstacles emphasized in the paper: for non-smooth measures, obtaining L1-approximations of indicators with controlled Cr/Lipschitz norms uniformly enough to make the correlation bounds effective is delicate, and the needed tradeoff between approximation error and function norms is not established. The candidate also relies on an unsubstantiated inequality linking Ornstein’s bar-distance to a simple two-block correlation bound, and it mishandles the quantifiers (fixing εk without ensuring the limit in n actually goes to 0). The paper’s method addresses precisely these issues and is correct; the model’s proof is incomplete.