Quasimonomial valuation conjecture for controlled-growth subadditive sequences

Let $R$ be an excellent regular domain of equicharacteristic zero, let $\mathfrak b_\bullet$ be a subadditive sequence of ideals in $R$, and say that it has controlled growth when

$$\frac1jv(\mathfrak b_j)\le v(\mathfrak b_\bullet)\le\frac1j\bigl(v(\mathfrak b_j)+A(v)\bigr)$$

for every $j\ge1$ and every quasimonomial valuation $v$ on $R$. Controlled-growth subadditive valuation conjecture. If there are a maximal ideal $\mathfrak m$ in $R$ and a positive integer $p$ such that $\mathfrak m^{pj}\subseteq\mathfrak b_j$ for all $j$, then there exists a quasimonomial valuation $v$ on $R$ that computes $\operatorname{lct}(\mathfrak b_\bullet)$.

The source says this conjecture is equivalent to the corresponding graded-sequence conjecture and is known in dimensions one and two. It remains open in higher dimensions.