Complete regularity of linear cocycles and the Baire category of the set of Lyapunov-Perron regular points

The paper proves the minimal-base all-or-meager dichotomy cleanly via the finest dominated splitting and a structural lemma: on each bundle with no further dominated splitting, either all ergodic measures have a single Lyapunov exponent (hence complete regularity) or the LP-regular set is meager; intersecting across bundles yields Theorem 4.10 and complete regularity when R = X. This is explicit in Lemma 4.14 and the proof of Theorem 4.10, which relies on their singular-value criterion (Theorem 4.12) and on an all-or-meager Birkhoff result (Theorem 4.2) . By contrast, the model’s Step 3 claims that, once a dominated splitting exists and certain exterior-power limits are constant, LP-regularity propagates from a nonmeager set to all points. That leap is not justified: dominated splitting alone does not ensure existence of pointwise growth limits for all vectors in each bundle, nor pointwise LP-regularity, without invoking the paper’s bundle-wise alternative (Lemma 4.14). The paper’s proof sidesteps this gap by applying Lemma 4.14 to each factor of the finest dominated splitting, which the model does not. Hence the model’s argument is incomplete, even though its final conclusion matches the paper’s theorem.