Symplectic Atiyah-Sutcliffe determinant lower-bound conjecture

Let $\mathcal{C}_m(\mathbb{R}^3)$ and the symplectic determinant $D_S:\mathcal{C}_m(\mathbb{R}^3)\to\mathbb{C}$ be defined from the Hopf-lift polynomials $p_\alpha$ using the order $1<\bar{1}<\cdots<m<\bar{m}$. Symplectic determinant conjecture. For every $\mathbf{x}\in\mathcal{C}_m(\mathbb{R}^3)$,

$$|D_S(\mathbf{x})|\geq1.$$

This is the symplectic analogue of the Atiyah-Sutcliffe determinant lower bound and is stronger than the symplectic LIC. The source gives no resolution.