Meunier's stability conjecture for stable Kneser hypergraphs

Let $[n]=\{1,\ldots,n\}$, and let $\mathrm{KG}^r(n,k)_{s\textup{-stab}}$ be the induced $r$-uniform Kneser hypergraph whose vertices are the $s$-stable $k$-subsets of $[n]$, where $s$-stability means $s\leq|i-j|\leq n-s$ for distinct elements $i,j$. Meunier's conjecture. If $r,s\geq2$ and $n\geq\max\{r,s\}k$, then

$$\chi\left(\mathrm{KG}^r(n,k)_{s\textup{-stab}}\right)=\left\lceil\frac{n-\max\{r,s\}(k-1)}{r-1}\right\rceil.$$

This extends Ziegler's conjecture from $r$-stable to $s$-stable Kneser hypergraphs. The source does not specify the general resolution status; it also notes that an alternative generalization was later found incorrect.