We calculate the effective spatial dimension d_{IR} of electron modes at critical points of 3D Anderson models in various universality classes (O,U,S,AIII). The results are equal within errors, and suggest the super-universal value d_{IR}=2.665(3)≈8/3. The existence of such a unique marker may help identify natural processes driven by Anderson localization, and provide new insight into the spatial geometry of Anderson transitions. The recently introduced d_{IR} is a measure-based dimension of Minkowski-Hausdorff type, designed to characterize probability-induced effective subsets.