Shokurov's conjecture on generalized singularities in adjunction for Fano-type fibrations

Let $(X,B)$ be a pair and let $f:X\rightarrow Z$ be a contraction. A pair $(X,B)$ is $\epsilon$-lc when all its log discrepancies are at least $\epsilon$, and $X$ is of Fano type over $Z$ when, equivalently here, $-K_X$ is big over $Z$. Adjunction gives a generalized pair $(Z,B_Z,\mathbf M)$, where $B_Z$ is the discriminant divisor and $\mathbf M$ is the moduli $\mathbf b$-divisor, from

$$K_X+B\sim_{\mathbb R}f^*(K_Z+B_Z+M_Z).$$

Shokurov's conjecture. Fix a positive integer $r$ and a real number $0<\epsilon\leq 1$. There exists $\delta>0$ depending only on $r,\epsilon$ such that, if $\dim X-\dim Z=r$, $(X,B)$ is $\epsilon$-lc, $K_X+B\sim_{\mathbb R}0/Z$, and $X$ is of Fano type over $Z$, then the generalized pair $(Z,B_Z,\mathbf M)$ given by adjunction is generalized $\delta$-lc.

This is a uniform singularity bound for the generalized pair on the base in the canonical bundle formula, and it implies McKernan's conjecture. The source states that Birkar proved Shokurov's conjecture recently.