SRB MEASURES FOR PARTIALLY HYPERBOLIC SYSTEMS WITH ONE-DIMENSIONAL CENTER SUBBUNDLES.

The paper proves Theorem 1 and Theorem 2 as stated (dichotomy for Lebesgue-a.e. x in U, and finiteness when all SRB measures are hyperbolic) via a detailed construction using hyperbolic times, lower bounds on entropies of empirical measures, and Propositions 6 and 7, which are explicitly presented and proved in the note . By contrast, the model’s key Step 3 asserts an unproven “upgrade” from Gibbs u-states to i-Gibbs states when ∫φi>0 (absolute continuity along W^{Fi}), whereas the paper itself poses precisely this as an open question it cannot establish (see the “Question” after Proposition 7) . The model also sketches a finiteness argument via uniform basin density that is not justified, while the paper rigorously derives finiteness from the compactness/accumulation argument in Proposition 7 . Therefore, even though the model’s final conclusions match the paper’s statements, its proof outline relies on steps that are unsupported or contradicted by the paper’s own discussion.