Ziegler's conjecture for r-stable Kneser hypergraphs

Let $KG^r(n,k)$ be the Kneser hypergraph whose vertices are the $k$-element subsets of $[n]$, and call a subset $S\subseteq[n]$ $r$-stable when any two elements $x,y\in S$ satisfy $r\leq |x-y|\leq n-r$. Let $KG^r(n,k)_{r\text{-}\mathrm{Stab}}$ be the sub-hypergraph induced by the $r$-stable vertices. Ziegler's conjecture. For all $n\geq rk$ and $r\geq2$, its chromatic number is

$$\chi\bigl(KG^r(n,k)_{r\text{-}\mathrm{Stab}}\bigr)=\left\lceil\frac{n-r(k-1)}{r-1}\right\rceil.$$

This asserts that the Alon–Frankl–Lovász chromatic-number formula remains valid after restricting to $r$-stable vertices. The source attributes the conjecture to Ziegler; no resolution status is supplied here.