Jonsson–Mustață's equivalent valuation-computing conjecture for subadditive sequences

Let $(\mathcal{O}_o,\mathfrak{m})$ be the local ring at $o$, let $\mathfrak{q}\subset\mathcal{O}_o$ be a nonzero ideal, and let $\mathfrak{b}_{\bullet}$ be a subadditive sequence of ideals. Assume that it has controlled growth, meaning

$$\nu(\mathfrak{b}_{\bullet})\le\frac{\nu(\mathfrak{b}_t)}{t}+\frac{A(\nu)}{t}$$

for every $t>0$ and every quasimonomial valuation $\nu$, and that for some positive integer $p$,

$$\mathfrak{m}^{pj}\subset\mathfrak{b}_j$$

for every $j$. Then

$$\mathrm{lct}^{\mathfrak{q}}(\mathfrak{b}_{\bullet})=\inf_{\nu}\frac{A(\nu)+\nu(\mathfrak{q})}{\nu(\mathfrak{b}_{\bullet})}.$$

Jonsson–Mustață's equivalent conjecture. There is a quasimonomial valuation $\nu$ on $\mathcal{O}_o$ that computes $\mathrm{lct}^{\mathfrak{q}}(\mathfrak{b}_{\bullet})$, namely

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

The source presents this as an equivalent conjecture to the graded-sequence statement and gives no resolution status. It is relevant to the algebraic formulation of the strong openness conjecture and to the existence of valuations computing asymptotic log canonical thresholds.