The category conjecture for unordered Euclidean configuration spaces

Let $B(\mathbb R^n,k)$ be the unordered configuration space of $k$ points in Euclidean $n$-space, and let $\operatorname{cat}$ denote Lusternik–Schnirelmann category.

Category conjecture. For all $n$ and $k$,

$$\operatorname{cat}(B(\mathbb R^n,k))=(k-1)\cdot(n-1).$$

The paper presents this as a plausible analogue of the corresponding result for ordered configuration spaces. It would give a simple exact formula for the category of unordered Euclidean configuration spaces; the supplied source does not establish the claim or indicate a resolution.