The strong real Atiyah–Sutcliffe conjecture

Let $D$ be the normalized determinant associated with a configuration in $\operatorname{Conf}_n(\mathbb{R}^2)$, and let $F_n^{\mathbb{R}}$ denote the space of projectively independent real labels. The strong real Atiyah–Sutcliffe conjecture. For every $(p_1,\dots,p_n)\in\operatorname{Conf}_n(\mathbb{R}^2)$,

$$|D(p_1,\dots,p_n)|\geq1.$$

This is the real analogue of the strong Atiyah–Sutcliffe conjecture; the supplied text gives no resolution, so the general statement remains open.