The generalized test-ideal and multiplier-ideal reduction conjecture for singular varieties

Let $X$ be a normal variety over a field $k$ of characteristic zero, let $\Delta$ be a $\mathbb{Q}$-divisor such that $K_X+\Delta$ is $\mathbb{Q}$-Cartier, and let $\mathfrak{a}$ be a nonzero ideal on $X$. Given a model of $(X,\Delta,\mathfrak{a})$ over a finitely generated $\mathbb{Z}$-subalgebra $A$ of $k$, the generalized test-ideal and multiplier-ideal reduction conjecture. There exists a Zariski-dense set of closed points $S \subseteq \operatorname{Spec} A$ such that

$$\tau(X_s,\Delta_s,\mathfrak{a}_s^{\lambda})=\mathcal{J}(X,\Delta,\mathfrak{a}^{\lambda})_s$$

for all $\lambda \in \mathbb{R}_{\geq 0}$ and all $s \in S$. Furthermore, for finitely many such triples and corresponding models over $A$, there is a dense subset of closed points for which the equality holds for every triple. This generalizes the smooth-variety conjecture by allowing singular $X$ and a boundary divisor. The supplied text gives no resolution evidence, so the conjecture is recorded as open.