Takagi's log canonicity and dense sharp F-purity conjecture

Let $X$ be a normal variety over an algebraically closed field $K$ of characteristic zero, and let $D$ be an effective $\mathbb{Q}$-divisor on $X$ such that $K_X+D$ is $\mathbb{Q}$-Cartier. Let $Z=\sum_i t_i Z_i$ be a formal combination, where the $t_i$ are nonnegative rational numbers and the $Z_i$ are proper closed subschemes of $X$. Fix a point $x\in X$. Log canonicity–dense sharp $F$-purity conjecture.

1. $((X,D);Z)$ is log canonical at $x$ if and only if it is of dense sharply $F$-pure type at $x$.
2. If $(X,D)$ is log canonical at $x$, then for any model of $(X,D,Z,x)$ over a finitely generated $\mathbb{Z}$-subalgebra $B$ of $K$, there is a dense subset of closed points $W\subseteq\operatorname{Spec}B$ such that

$$\operatorname{lct}_x((X,D);Z)=\operatorname{fpt}_{x_\mu}((X_\mu,D_\mu);Z_\mu)$$

for every $\mu\in W$. The conjecture proposes an arithmetic correspondence between log canonicity and sharp $F$-purity, extending the known correspondence between klt singularities and strongly $F$-regular type. The source describes this correspondence as largely conjectural and does not state a resolution.