Effective adjunction conjecture for lc-trivial fibrations

Let $(X,B)$ be an lc pair such that $K_X+B$ is a $Q$-Cartier divisor, and let $f:(X,B)\to Z$ be an lc-trivial fibration. Let ${\mathbf D}_{\mo}$ denote its moduli b-divisor. Effective adjunction conjecture. There exists a positive integer $m$, depending only on the dimension of $X$ and the horizontal multiplicities of $B$, such that $m{\mathbf D}_{\mo}$ is a base-point free b-divisor. This is a conjecture about effectivity in the canonical bundle formula; the paper studies a variant suitable for induction and real coefficients, while the general assertion is not stated as resolved here.