The b-semi-ampleness conjecture for moduli b-divisors

Let $f:(X, B)\to Y$ be a basic slc-trivial fibration, and let $\mathbf M$ denote its moduli part, a moduli $\mathbb Q$-b-divisor on $Y$. B-semi-ampleness conjecture. The moduli part $\mathbf M$ is b-semi-ample. This conjecture extends the known b-potential nefness of the moduli part established for basic slc-trivial fibrations; whether it is b-semi-ample in general remains open.