Carvajal–Rojas–Schwede–Tucker conjecture on positivity of the limit F-signature

Let $(R,\mathfrak{m})$ be a KLT singularity essentially of finite type over $\mathbb{C}$. For every sufficiently large prime $p$, let $\mathscr{s}_p(R)$ denote the $F$-signature of a reduction of $R$ to characteristic $p$. Carvajal–Rojas–Schwede–Tucker's conjecture. There is a constant $C>0$, independent of $p$, such that $\mathscr{s}_p(R)>C$ for all sufficiently large $p$, equivalently

$$\liminf_{p\to\infty}\mathscr{s}_p(R)>0.$$

This conjecture concerns uniform positivity of $F$-signatures in characteristic-$p$ reductions of KLT singularities. It is known for toric, finite quotient, quadric, diagonal hypersurface, full flag, and reductive quotient singularities, while the general case remains open.