  We introduce a notion of $\beta$-almost periodicity and prove quantitative
lower spectral/quantum dynamical bounds for general bounded $\beta$-almost
periodic potentials. Applications include a sharp arithmetic criterion of full
spectral dimensionality for analytic quasiperiodic Schr\"odinger operators in
the positive Lyapunov exponent regime and arithmetic criteria for families with
zero Lyapunov exponents, with applications to Sturmian potentials and the
critical almost Mathieu operator.
