McKernan–Shokurov conjecture for generalized pairs

Let $d$ be a positive integer and $\epsilon$ a positive real number. Let $(X,B+\mathbf{M})$ be a generalized pair of dimension $d$ and let $\pi:X\to Z$ be a contraction between projective normal varieties. Assume $(X,B+\mathbf{M})$ is $\epsilon$-lc, $X$ is of Fano type over $Z$, and $K_X+B+\mathbf{M}_X\sim_{\mathbb{R},Z}0$. Let $B_Z$ denote the discriminant part of the canonical bundle formula for $(X,B+\mathbf{M})$ over $Z$. Generalized McKernan–Shokurov conjecture. There exists a positive real number $\delta$, depending only on $d$ and $\epsilon$, such that $B_Z\le 1-\delta$. The source states this generalized conjecture and records that it holds in dimension $2$ and for relative-dimension-one fibrations, while the general case remains open.