Title: Statistical Verification of General Perturbations by Gaussian Smoothing. Abstract: We present a novel statistical certification method that generalizes prior work based on smoothing to handle richer perturbations. Concretely, our method produces a provable classifier which can establish statistical robustness against geometric perturbations (e.g., rotations, translations) as well as volume changes and pitch shifts on audio data. The generalization is non-trivial and requires careful handling of operations such as interpolation. Our method is agnostic to the choice of classifier and scales to modern architectures such as ResNet-50 on ImageNet.