HIDDEN SUBCRITICALITY, SYMPLECTIC STRUCTURE, AND UNIVERSALITY OF SHARP ARITHMETIC SPECTRAL RESULTS FOR TYPE I OPERATORS

The uploaded paper (Ge–Jitomirskaya 2024) proves the AAJ sharp frequency transition for all type I energies/operators and, moreover, establishes all-frequency absolute continuity of the IDS for non-critical type I operators. The main tools are: T-acceleration/type I formalism, a multiplicative Jensen’s formula for the duals yielding an explicit subcritical strip on the dual center, the symplectic structure and fibered rotation numbers of that center, their relation to the IDS, and a new completeness argument that removes evenness constraints; see the Main Results and the proof road-map (Theorem 2.1; Definitions 2.2–2.3; Sections 5–8) in the uploaded PDF . The candidate solution also reaches the AAJ conclusion for type I by a different route: it sketches a localization proof for L(E)>β(α) via hidden subcriticality plus large-deviation/Green-function control and resonance elimination, and a quantitative Gordon/Kotani argument for 0<L(E)<β(α). While its localization half leans on a large-deviation framework not explicitly employed in the paper (the paper uses dual reducibility and a new completeness argument instead), its steps are consistent with current techniques and hypotheses for analytic v and type I energies. Minor imprecision: it informally equates “type I” with “first supercritical stratum,” whereas type I is defined via T-acceleration at the first turning (ω̄=1) and is used on both subcritical and supercritical sides in the paper . Overall, both reach the same AAJ universality; the paper’s proof differs materially from the model’s outline.