  We study fractal dimension properties of singular Jacobi operators. We prove
quantitative lower spectral/quantum dynamical bounds for general operators with
strong repetition properties and controlled singularities. For analytic
quasiperiodic Jacobi operators in the positive Lyapunov exponent regime, we
obtain a sharp arithmetic criterion of full spectral dimensionality. The
applications include the extended Harper's model where we obtain arithmetic
results on spectral dimensions and quantum dynamical exponents.
