Shokurov's effective moduli-part conjecture for Fano type fibrations

Let $f\colon X\to Y$ be a proper surjective morphism with connected fibers between normal varieties, with $X/Y$ of relative Fano type. Let $\Delta$ be a $\mathbb Q$-divisor on $X$ such that

$$K_X+\Delta=f^*L$$

for some $\mathbb Q$-divisor $L$ on $Y$. Write

$$K_X+\Delta=f^*(K_Y+R+B),$$

where $R$ is the discriminant part and $B$ is the moduli part.

Shokurov's conjecture. If $(X,\Delta)$ is $\epsilon$-log terminal, then there exists $\delta=\delta_{m,n}(\epsilon)>0$ and an effective moduli part $B$ such that $(Y,R+B)$ is $\delta$-log terminal.

This is a stronger refinement of the epsilon-delta conjecture, incorporating the discriminant and moduli parts supplied by subadjunction. Its resolution status is not specified in the supplied text.