Deformation conjecture for F-purity in Q-Gorenstein rings

Let $(R,\mathfrak{m},k)$ be a local $F$-finite $\mathbb{Q}$-Gorenstein ring of prime characteristic $p>0$. Suppose that $f\in R$ is a non-zero-divisor such that $R/(f)$ is normal and $F$-pure.

Deformation conjecture for $F$-purity. Then $R$ is $F$-pure.

This conjecture concerns whether $F$-purity deforms from a normal hypersurface section to the ambient ring under a local $F$-finite $\mathbb{Q}$-Gorenstein hypothesis. The supplied source identifies a positive solution as remarkable because of the relationship between $F$-purity and log canonicity; the conjecture is recorded here as solved.