Jonsson–Mustaţă's weak and strong conjectures for asymptotic log canonical thresholds

Let $X$ be a regular algebraic variety over a field of characteristic zero. Let $\mathfrak{a}_{\bullet}$ be a graded sequence of ideals on $X$, and let $\mathfrak{q}$ be a nonzero ideal on $X$ such that $\mathrm{lct}^{\mathfrak{q}}(\mathfrak{a}_{\bullet})<\infty$. A valuation $v\in\mathrm{Val}_X^*$ computes $\mathrm{lct}^{\mathfrak{q}}(\mathfrak{a}_{\bullet})$ when

$$\mathrm{lct}^{\mathfrak{q}}(\mathfrak{a}_{\bullet})=\frac{A(v)+v(\mathfrak{q})}{v(\mathfrak{a}_{\bullet})}.$$

Algebraic version of Jonsson–Mustaţă's conjecture. There exists a quasi-monomial valuation $v\in\mathrm{Val}_X^*$ that computes $\mathrm{lct}^{\mathfrak{q}}(\mathfrak{a}_{\bullet})$.

This is a conjecture on the structure of valuations computing asymptotic jumping numbers. The source presents it as closely related to further Jonsson–Mustaţă conjectures; its resolution status is not specified here.