Atiyah-Sutcliffe's determinant bound conjecture for hyperbolic configurations

Let $C_n(H^3)$ be the configuration space of $n$ distinct points in hyperbolic $3$-space $H^3$. For $\mathbf{x}\in C_n(H^3)$, let $D(\mathbf{x})$ be the normalized Atiyah-Sutcliffe determinant formed from the direction polynomials $p_a(t)$ and the pairwise polynomials $p_{ab}(t)=t-t_{ab}$.

Atiyah-Sutcliffe's determinant bound conjecture. For every $\mathbf{x}\in C_n(H^3)$,

$$|D(\mathbf{x})|\geq 1.$$

This is the second Atiyah-Sutcliffe conjecture and strengthens the nonvanishing assertion by imposing a uniform lower bound on the normalized determinant. The supplied text gives no resolution status.