ANDERSON LOCALIZATION FOR THE QUASI-PERIODIC CMV MATRICES WITH VERBLUNSKY COEFFICIENTS DEFINED BY THE SKEW-SHIFT

The paper proves (i) L(z) ≥ -(1/4) log(1−λ^2) for the Szegő cocycle with skew–shift Verblunsky coefficients at large coupling and (ii) Anderson localization for most frequencies and a.e. phases, via an initial-scale estimate derived from a determinantal/CMV-structure formula, a quantitative LDT with exp(-N^σ) tails, the avalanche principle, and semi-algebraic elimination. These ingredients and statements are explicit in Theorems 2.1–2.2 and Proposition 3.3 and their proofs. By contrast, the model’s Step A invokes a Herman-type complexification to obtain the initial positivity and even claims one can “shrink λ0 so that c⋆ ≥ 1,” which is logically invalid since that constant is independent of λ; the model also misstates the LDT tail as exp(-c (log n)^2) instead of the paper’s exp(-N^σ). While the model’s conclusions overlap with the paper’s, key proof steps are incorrect or unsupported.