The spherical skeleton conjecture for factorial affine spherical varieties

Let $X$ be a factorial affine spherical $G$-variety with a $G$-fixed point. The invariant $\wp(X)$ is defined by

$$\wp(X) = \sup\left\{\sum_{D\in\Delta}\langle\rho(D),\vartheta\rangle: \vartheta\in(\lambda+\mathcal{T})\cap\operatorname{cone}(\mathcal{M}^+)\right\}-\operatorname{rank}X.$$

Spherical skeleton conjecture. We have

$$\wp(X) \leq \dim X-\operatorname{rank}X,$$

where equality holds if and only if $X$ is isomorphic to an affine space. This is the factorial affine restriction of the conjecture on spherical skeletons; its status is not resolved in the supplied source.