Discrete singularity conjecture for four-dimensional noncollapsed Ricci limit spaces

Let $(X^4,\mathsf{d})$ be a noncollapsed Ricci limit space, and consider the set of points whose tangent-cone cross-sections are not homeomorphic to $S^3$. Discrete singularity conjecture. This set of points $x\in X^4$ should be discrete. In dimension four, the known result gives only that this set is zero-dimensional, while discreteness remains the proposed strengthening.