Semisimplicity conjecture for convolution complexes

Let $D$, $V$, and $V'$ be as above, and let $K_1\cdot K_2\cdot\ldots\cdot K_m$ be a convolution complex in

$$\mathscr D^-_{\mathbf G}(\mathbf E_{\Omega}(D,V,V')),$$

where each $K_a$ is either $\mathscr E^{(n),\Omega}_{\bullet}$ or $\mathscr F^{(n),\Omega}_{\bullet}$. Semisimplicity conjecture. The complexes $K_1\cdot K_2\cdot\ldots\cdot K_m$ are bounded and semisimple.

This conjecture is needed to construct the algebra of classes of simple perverse sheaves arising as direct summands of these complexes and to establish the geometric realization of the modified quantum algebra. The source explicitly assumes it for the remainder of the section; no resolution status is supplied here.