The ANR version of Hausmann's theorem for Vietoris-Rips complexes

Let $(X,d_X)$ be a compact ANR metric space, where ANR means an absolute neighborhood retract. Let $\mathrm{VR}_r(X)$ denote the Vietoris-Rips complex at scale $r$.

ANR Vietoris-Rips conjecture. There exists $r(X)>0$ such that

$$\mathrm{VR}_r(X)\simeq X$$

for every $r\in(0,r(X)]$.

This is proposed as a version of Hausmann's theorem for compact ANR metric spaces. The source does not state whether the conjecture has been resolved.