Contractibility conjecture for cores of relative Artin complexes

Let $A_S$ be an Artin group, and let $S'ubset S$ be almost spherical. Let $\Delta_{S,S'}$ denote the relative Artin complex spanned by vertices of types indexed by $S'$. Assume that the Dynkin diagrams for $S'$ and $S$ are connected and have no $\infty$-labeled edges. Core contractibility conjecture. The relative Artin complex $\Delta_{S,S'}$ is contractible. This conjecture would imply the $K(\pi,1)$-conjecture for all Artin groups; its resolution is presented as part of the proposed strategy.