The log canonical and dense F-pure type correspondence conjecture

Let $(X,\Delta)$ be a normal variety over a field of characteristic zero, with $\Delta$ an effective $\mathbb{Q}$-divisor and $K_X+\Delta$ $\mathbb{Q}$-Cartier. Log canonical–dense F-pure type conjecture. The pair $(X,\Delta)$ is log canonical if and only if it is of dense $F$-pure type. Dense $F$-pure type is known to imply log canonicity, and the converse is described as wide open apart from special cases.