Zariski-closedness conjecture for diminished base loci of generalized klt pairs

Let $(X,\Delta+M)$ be a generalized klt pair, and let $K_X+\Delta+M$ be its generalized log canonical divisor. The diminished base locus $B_{\rm -}(K_X+\Delta+M)$ is the stable base locus obtained after arbitrarily small ample perturbations.

Generalized diminished-base-locus conjecture. The diminished base locus

$$B_{\rm -}(K_X+\Delta+M)$$

is Zariski closed in $X$.

This conjecture extends the corresponding statement for ordinary klt pairs and is introduced in connection with termination of flips with scaling. Its general validity remains open.