Noncollapsed Ricci-curvature bi-Lipschitz embedding conjecture

Let $A$ be a subset with $\operatorname{diam}(A)\leq D$ of an $n$-dimensional complete Riemannian manifold $(M^n,g)$ with Ricci curvature

$$\operatorname{Ric}(g)\geq -(n-1)g.$$

Assume that $\operatorname{Vol}(B_1(p))>v$ for some $p\in A$. Noncollapsed Ricci embedding conjecture. There is a bi-Lipschitz embedding

$$f\colon A\to\mathbb{R}^N$$

with distortion less than $C(D,n,v)$ and image dimension $N\leq N(D,n,v)$. This weakens the lower sectional-curvature assumption to a lower Ricci-curvature bound while retaining a noncollapsing hypothesis; the source presents it as open.