Brue–Pigati–Semola local biHölder regularity conjecture for RCD spaces

Let $(X,\mathsf{d},\mathscr{H}^3)$ be an $\operatorname{RCD}(-2,3)$ space such that every blow-up is homeomorphic to $\mathbb{R}^3$.

Brue–Pigati–Semola conjecture. $(X,\mathsf{d})$ is locally biHölder homeomorphic to a smooth, complete Riemannian manifold $(M^3,g)$.

The conjecture asks whether the topological manifold recognition result can be improved to give a more regular homeomorphism. Its status is not specified in the source.