Jonsson–Mustaţă's weighted weak and strong conjectures for 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

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

Jonsson–Mustaţă's weighted conjecture. The weak version asserts that there exists a quasi-monomial valuation $v\in\mathrm{Val}_X^*$ computing $\mathrm{lct}^{\mathfrak{q}}(\mathfrak{a}_{\bullet})$; the strong version asserts that every valuation $v\in\mathrm{Val}_X^*$ computing $\mathrm{lct}^{\mathfrak{q}}(\mathfrak{a}_{\bullet})$ is quasi-monomial.

These are the weighted variants of Jonsson–Mustaţă's conjectures, with the ideal $\mathfrak{q}$ incorporated into the jumping number. The source does not specify whether the weak or strong version is resolved.