The log-terminality conjecture for Mori conic bundles

Let $(X,C)$ be a germ of a three-dimensional complex space along a compact reduced curve $C$, let $(S,0)$ be a germ of a two-dimensional normal complex space, and let $f\colon (X,C)\to (S,0)$ be a Mori conic bundle: $(f^{-1}(0))_{\operatorname{red}}=C$, $f_*\mathcal{O}_X=\mathcal{O}_S$, $X$ has at worst terminal singularities, and $-K_X$ is ample. For a positive integer $n$, let $D$ be a generic member of the linear system $|-nK_X|$.

Log-terminality conjecture. The divisor pair

$$\left(X, K_X+\frac{1}{n}D\right)$$

is log-terminal.

This conjecture concerns the singularities of generic anticanonical divisors in Mori conic bundles and is presented as important in the study of local structures of extremal contractions. The source does not provide evidence of a resolution, so its status is open.