SHARP ARITHMETIC DELOCALIZATION FOR QUASIPERIODIC OPERATORS WITH POTENTIALS OF SEMI-BOUNDED VARIATION.

The paper proves that for quasi-periodic Schrödinger operators with sampling functions of semi-bounded variation, the set S = {E : 0 < L(E) < β(α)} supports only singular continuous spectrum for a.e. phase (Theorem 1.1), via a new uniform upper bound for cocycles of bounded variation, telescopic bounds, and a sharp abstract Gordon criterion that eliminates eigenvalues; the absence of absolutely continuous spectrum on S follows from standard Kotani theory. The candidate solution reaches the same conclusion by citing Kotani (ac supported on {L=0}) and directly invoking the paper’s sharp Gordon theorem to exclude eigenvalues a.e. on S. Thus, both are correct; the paper supplies the technical core, while the model cites these results rather than rederiving them.