Blickle–Mustaţă–Smith equality conjecture for F-pure thresholds over an algebraic closure

Let $p>0$ be a prime number and $d>0$ an integer. Write $\mathbb{F}_p$ for the finite field with $p$ elements, let $\overline{\mathbb{F}}_p$ be its algebraic closure, and set

$$A=(\overline{\mathbb{F}}_p[x_1,\dots,x_d])_{(x_1,\dots,x_d)}.$$

Let $\mathcal{T}_{d,p}$ be the set of $F$-pure thresholds of principal ideals in $F$-finite $d$-dimensional regular local rings of characteristic $p$, and let $\mathcal{T}_{d,p}^{\circ}$ be the set of $F$-pure thresholds of principal ideals in $A$.

Blickle–Mustaţă–Smith's equality conjecture.

$$\mathcal{T}_{d,p}=\mathcal{T}_{d,p}^{\circ}.$$

The paper explains that the closure of $\mathcal{T}_{d,p}^{\circ}$ in $\mathbb{R}$ equals $\mathcal{T}_{d,p}$, and studies this stronger equality conjecture. The supplied text gives no resolution status.