The uniform reduction conjecture for test and multiplier ideals

Let $\mathfrak{a}\subset{\mathbf Z}[x_1,\ldots,x_n]$ be an ideal as above, let $\mathfrak{a}_p$ be its reduction modulo $p$, and let $\tau(\mathfrak{a}_p^\lambda)$ and $\mathcal{J}(\mathfrak{a}^\lambda)_p$ denote the corresponding test ideal and reduced multiplier ideal. Uniform reduction conjecture. There is an infinite set of primes $S$ such that

$$\tau(\mathfrak{a}_p^\lambda)=\mathcal{J}(\mathfrak{a}^\lambda)_p$$

for every $\lambda\in{\mathbf R}_{\geq 0}$ and every $p\in S$. This strengthens the threshold-equality conjecture; Hara–Yoshida proved equality for each fixed $\lambda$ and all sufficiently large primes, but the source does not give a resolution of the simultaneous assertion.