Bi-Lipschitz charts at every regular point of a noncollapsed RCD(K,n) space

Claims that for every integer $n\ge2$ there is $L_n\ge1$ such that every regular point of every noncollapsed $\mathrm{RCD}(K,n)$ space, $K\in\mathbb R$, has an open neighborhood $L_n$-bi-Lipschitz homeomorphic, with the ambient distance, to an open subset of $\mathbb R^n$; the neighborhood depends on the space and the point. Corollary: an open set of full $\mathcal H^n$ measure containing all regular points carries a countable bi-Lipschitz atlas with $L_n^2$ transition maps. It does NOT claim that the regular set is open, any collapsed or non-RCD statement, or regularity of the metric tensor in the charts.

Claims that for every integer $n\ge2$ there is $L_n\ge1$ such that every regular point of every noncollapsed $\mathrm{RCD}(K,n)$ space, $K\in\mathbb R$, has an open neighborhood $L_n$-bi-Lipschitz homeomorphic, with the ambient distance, to an open subset of $\mathbb R^n$; the neighborhood depends on the space and the point. Corollary: an open set of full $\mathcal H^n$ measure containing all regular points carries a countable bi-Lipschitz atlas with $L_n^2$ transition maps. It does NOT claim that the regular set is open, any collapsed or non-RCD statement, or regularity of the metric tensor in the charts.