Avila’s Acceleration via Zeros of Determinants, and Applications to Schrödinger Cocycles

The paper proves the stated zero-count/acceleration estimate rigorously via an annular Riesz representation and carefully chosen radii, culminating in Theorem 1.2 with the ε^{-1} n^{-γ} rate at radius ε/2, and a more general Theorem 4.1 giving an ε^{-2} n^{-γ1} rate away from endpoints. The model’s write-up misstates the scope and strength of the finite-scale comparison (claiming uniform t^{-1} bounds for all t≤ε and “super-polynomial” closeness J_n(t)≈L(E,t)), conflates un with vn when comparing to L, and implicitly assumes boundary zero-freeness at the evaluation radius without addressing how to avoid it. It also cites (in effect) the very theorems to be proved in order to conclude the main estimate. Hence the paper’s argument is correct and complete, while the model’s proof is incomplete and partially incorrect, despite reaching the correct final inequality at t=ε/2.