Simplicial affine oriented matroid bounded-complex conjecture

Let $(E,\mathcal{L},g)$ be a simplicial affine oriented matroid, where $g$ is the distinguished element and $\mathcal{L}^{++}$ denotes its bounded complex. Simplicial bounded-complex conjecture. Then the bounded complex $\mathcal{L}^{++}$ is a ball. This is an open question attributed to Oriented Matroids and is posed here as a conjecture for simplicial affine oriented matroids. Unlike the uniform-contraction case proved earlier in the paper, no resolution is given here.