Gorenstein reduction conjecture for positive F-signature

Let $(R,\mathfrak m)$ be a $d$-dimensional Gorenstein local domain essentially of finite type over $\mathbb{C}$. Gorenstein positivity conjecture. If $\operatorname{Spec} R$ has klt singularities, then $s(R)>0$. This is the Gorenstein case of the local $F$-signature positivity conjecture; the paper proves that positivity in dimension $d+1$ for this Gorenstein case would imply the general conjecture in dimension $d$, but the assertion itself remains open.