ABSOLUTELY CONTINUOUS SPECTRUM FOR CMV MATRICES WITH SMALL QUASI-PERIODIC VERBLUNSKY COEFFICIENTS

The paper proves Theorem 1.1 via quantitative almost reducibility for SU(1,1) Szegő cocycles, a Johnson-type characterization of the spectrum, and measure estimates that yield pure a.c. spectrum and at most one eigenvalue per gap; the steps are coherent and supported in the text. The model’s writeup conflates the renormalized and unrenormalized Szegő cocycles, introduces an incorrect diagonal gauge, and crucially asserts full reducibility to rotations for all spectral parameters on Σ (far stronger than what is proved/needed, and not established). Its limiting-absorption argument depends on that unproved global reducibility. Hence the model’s proof is incorrect, while the paper’s argument is correct.