Resolution of singularities for quasi-excellent schemes

Let $\bar{X}$ be a reduced, separated, Noetherian, quasi-excellent scheme. A proper birational morphism

$$\pi:\bar{X}'\to\bar{X}$$

should exist such that $\bar{X}'$ is regular, $\pi$ is an isomorphism over the regular locus of $\bar{X}$, and the exceptional divisor $\pi^{-1}(\bar{X}_{\mathrm{sing}})$ is an snc divisor in $\bar{X}'$.

Resolution conjecture. There exists such a morphism $\pi$.

The conjecture is a form of resolution of singularities and would yield smooth compactifications with snc boundary in the setting of smooth schemes over perfect fields. It is known when $\bar{X}$ has dimension at most $3$, but remains open in higher dimensions.