Finite-coefficient conjecture for numerically trivial generalized pairs

Let $d$ be a positive integer and let $\Gamma\subset [0,+\infty)$ be a DCC set. A projective lc generalized pair $(X,B,\mathbf{M})$ consists here of a projective generalized pair of dimension $d$ that is log canonical. Assume that $B\in\Gamma$, $\mathbf{M}\in\mathrm{Nef}^0(\Gamma)$, and

$$K_X+B+\mathbf{M}_X\equiv 0.$$

Finite-coefficient conjecture. There exists a finite set $\Gamma_0\subset\Gamma$, depending only on $d$ and $\Gamma$, such that $B\in\Gamma_0$ and $\mathbf{M}\in\mathrm{Nef}^0(\Gamma_0)$.

This is a boundedness statement for the coefficients and nef-part coefficients of numerically trivial projective lc generalized pairs in fixed dimension. The supplied text gives no resolution status or further evidence, so the conjecture is recorded as open.