The diminished-base-locus conjecture for log canonical centres in MMPs

Let $(X_1,B_1+M_1)$ be a projective $\mathbb{Q}$-factorial NQC dlt generalised pair such that $K_{X_1}+B_1+M_1$ is pseudoeffective. Consider a $(K_{X_1}+B_1+M_1)$-MMP:

$$(X_1,B_1+M_1)\dashrightarrow (X_2,B_2+M_2)\dashrightarrow (X_3,B_3+M_3)\dashrightarrow\dots.$$

Let $S$ be a log canonical centre of $(X_1,B_1+M_1)$ which belongs to $\operatorname{\mathbf{B}}_-(K_{X_1}+B_1+M_1)$. The diminished-base-locus conjecture. There exists an index $i$ such that $\pi_i$ is not an isomorphism at the generic point of the strict transform of $S$ on $X_i$.

This conjecture predicts that every log canonical centre contained in the diminished base locus is eventually affected by a step of the MMP. Its status is not resolved in the supplied source context.