Frobenius liftability conjecture for cusp singularities

A cusp singularity is a normal surface singularity whose minimal resolution has exceptional divisor a cycle of rational curves.

Frobenius liftability conjecture. Every cusp singularity is $F$-liftable.

Cusp singularities are always $F$-pure, and the conjecture proposes the analogous Frobenius liftability property. The paper provides no resolution of this expectation.