Jonsson–Mustată quasi-monomiality conjecture for log canonical thresholds

Let $X$ be a klt variety and let $\mathfrak{a}_\bullet$ be a graded sequence of ideals on $X$ with finite log canonical threshold $\operatorname{lct}(\mathfrak{a}_\bullet)$. A valuation computes this threshold if it realizes the infimum defining it. Jonsson–Mustată conjecture. (Weak version) There exists a quasi-monomial valuation that computes $\operatorname{lct}(\mathfrak{a}_\bullet)$. (Strong version) Every valuation that computes $\operatorname{lct}(\mathfrak{a}_\bullet)$ is quasi-monomial. The conjecture concerns the structure of valuations computing thresholds of graded ideal sequences and is presented as relevant because normalized-volume minimizers compute log canonical thresholds; the source gives no resolution status.