Bi-Lipschitz Coordinates at Regular Points of Noncollapsed RCD Spaces

We resolve the regular-point bi-Lipschitz conjecture in the noncollapsed setting. For every integer n ≥ 2 and every real K, every regular point of a noncollapsed $\mathrm{RCD}(K,n)$ space has an open neighborhood bi-Lipschitz homeomorphic to an open subset of ℝ${}^n$. The bi-Lipschitz constant depends only on n, and the neighborhood uses the restricted ambient distance.