Johnson–Holroyd–Stahl conjecture on the circular chromatic number of Kneser graphs

Let ${\rm KG}(m,n)$ denote the Kneser graph, whose vertices are the $n$-element subsets of an $m$-element set, with two vertices adjacent when the corresponding subsets are disjoint. Write $\chi(G)$ for the chromatic number and $\chi_c(G)$ for the circular chromatic number. Johnson–Holroyd–Stahl conjecture. For all $m\geq 2n+1$,

$$\chi_c({\rm KG}(m,n))=\chi({\rm KG}(m,n)).$$

Equality of the two chromatic parameters is known in several cases, including $m\leq 2n+2$ or $n=2$, but the statement was presented as a conjecture for all Kneser graphs in the source.