The exact maximum-stable-set conjecture for flag spheres

Let $G$ be the graph of a flag triangulation of the $(d-1)$-dimensional sphere on $n$ vertices, and let $\alpha_M(d,n)$ denote the maximum possible size of a stable set in such a graph. The exact maximum-stable-set conjecture. For all $d\ge 2$,

$$\alpha_M(d,n)=\left\lfloor\frac{n-2(d-2)}{2}\right\rfloor.$$

This gives an exact upper extremal value for stable sets in flag spheres and refines the preceding qualitative prediction that their vertex proportion cannot exceed $1/2$. The source presents the assertion as a conjecture without resolving it.