The approximation conjecture for quasi-compact and quasi-separated algebraic stacks

Let $X$ be a quasi-compact and quasi-separated algebraic stack. An approximation of $X$ is a factorization

$$X\to X_0\to \operatorname{Spec} \mathbb{Z}$$

where $X\to X_0$ is affine and $X_0$ is of finite presentation over $\operatorname{Spec} \mathbb{Z}$. Approximation conjecture. If $X$ is a quasi-compact and quasi-separated algebraic stack, then $X$ has an approximation. Approximation would extend finite-presentation models beyond the classes of stacks for which the relevant approximation results are already known. The statement is presented as a conjecture in the source, and its resolution is not established in the supplied text.