Atiyah's non-vanishing conjecture for the Atiyah determinant

Let $x_1,\dots,x_n$ be distinct points in $\mathbb{R}^3$, and let $D(x_1,\dots,x_n)$ denote the Atiyah determinant constructed from them. Atiyah's non-vanishing conjecture.

$$D(x_1,\dots,x_n)\neq 0.$$

The conjecture is the first of the three conjectures formulated by Atiyah and Sutcliffe for this determinant; the paper reports numerical evidence but does not establish it in general.