Alon–Drewnowski–Łuczak conjecture for stable Kneser hypergraphs

For positive integers $n,k,r$ with $k\geq 2$, $r\geq 2$, and $n\geq rk$, let $KG^{r}(n,k)_{r\text{-}stab}$ be the $r$-stable $r$-uniform Kneser hypergraph, and let $KG^{r}(n,k)$ be the ordinary $r$-uniform Kneser hypergraph. Alon–Drewnowski–Łuczak conjecture.

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

The source notes that this was confirmed when $r$ is a power of $2$, but gives no resolution for general $r$.