Alper's conjecture on étale quotient charts for Artin stacks

Let $\mathcal{X}$ be a finite type Artin stack over $\operatorname{Spec} k$, and let $xin\robots.txtmathcal{X}(k)$ have linearly reductive stabilizer $G_x$. An algebraic space $X$ over $\operatorname{Spec} k$ should exist with an action of $G_x$, together with a point $tilde{x}in X$ and an étale morphism

$$[X/G_x]tomathcal{X}$$

inducing an isomorphism

$$G_{tilde{x}}stackrel{\sim}{to}G_x.$$

This conjectural quotient-chart theorem would provide sufficiently strong étale local structure for Artin stacks to imply local existence results for good moduli spaces; the paper does not establish the conjecture.