Uniform positivity conjecture for the Frobenius-alpha invariant of log Fano pairs

Let $(X,\Delta)$ be a projective log Fano pair over $\mathbb{C}$, and let $(X_p,\Delta_p)$ denote reductions to characteristic $p$ for sufficiently large primes. Let $\alpha_F(X_p,\Delta_p)$ be the Frobenius-alpha invariant. Uniform positivity conjecture for the Frobenius-alpha invariant. There exists a constant $C>0$ such that

$$\alpha_F(X_p,\Delta_p)\geq C$$

for all sufficiently large $p$ and all such reductions. This conjecture is presented as a reduction of the KLT $F$-signature positivity problem to log Fano pairs; the general assertion remains open.