Brick occurrence characterization of simple objects

Let $W$ be a Weyl group, let $w\in W$, and let $\mathcal{F}(w)$ be its torsion-free class. A brick is an object with division endomorphism ring. Brick occurrence characterization. If a brick $B$ appears in every brick sequence of $\mathcal{F}(w)$, then $B$ is a simple object of $\mathcal{F}(w)$.

Simple objects are known to occur in every brick sequence. The paper states that this assertion is equivalent to the semibrick extension conjecture above; the general case remains open, although the preceding conjecture is proved in types $A_n$, $D_n$, and $E_6$.