Finite-value conjecture for stability thresholds in Q-Fano families

Let $\pi:X\to T$ be a projective family of varieties. Assume that $T$ is normal, every fiber $X_t$ is klt, and $-K_{X/T}$ is $\mathbb{Q}$-Cartier and ample. For a geometric point $\overline{t}$ over $t\in T$, let $\delta(X_{\overline{t}})$ denote the stability threshold of the geometric fiber. Finite-value conjecture. The function

$$T\ni t\longmapsto\delta(X_{\overline{t}})$$

takes finitely many values. Together with lower semicontinuity, this would imply openness of K-semistability in such families; the source does not report a resolution.