The mutation-compatible semibrick pair completion conjecture

Let $\Lambda$ be a finite-dimensional algebra, and let $\mathcal{S}_p,\mathcal{S}_n\in\mathsf{sbrick}\Lambda$. A semibrick pair is $\mathcal{S}_p\sqcup\mathcal{S}_n[1]$ satisfying

$$\operatorname{Hom}(\mathcal{S}_p,\mathcal{S}_n)=0=\operatorname{Ext}(\mathcal{S}_p,\mathcal{S}_n).$$

It is mutation compatible if, for every $S\in\mathcal{S}_p$ and $S'\in\mathcal{S}_n$, every minimal left $\mathsf{Filt} S$-approximation $g_{S'}:S'\to E$ is either a monomorphism or an epimorphism. Mutation-compatible semibrick pair completion conjecture. Every mutation compatible semibrick pair is completable, meaning that it is a subset of a 2-simple minded collection.

This conjecture asserts that the stated monomorphism-or-epimorphism condition is the only obstruction to completing a semibrick pair to a 2-simple minded collection. The source gives no resolution status, so the conjecture is treated as open.