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We introduce a notion of $\beta$-almost periodicity and prove quantitativelower spectral/quantum dynamical bounds for general bounded $\beta$-almostperiodic potentials. Applications include a sharp arithmetic criterion of fullspectral dimensionality for analytic quasiperiodic Schr\"odinger operators inthe positive Lyapunov exponent regime and arithmetic criteria for families withzero Lyapunov exponents, with applications to Sturmian potentials and thecritical almost Mathieu operator.

Quantitative continuity of singular continuous spectral measures and arithmetic criteria for quasiperiodic Schr\"odinger operators