Malkoun's determinant conjecture for the symplectic-group construction

Let $\mathfrak{t}\simeq\mathbb{R}^n$ be a Cartan subalgebra for $G=Sp(n)$, and let $\Delta$ be the non-regular locus. For $\mathbf{x}\in(\mathfrak{t}\otimes\mathbb{R}^3)\setminus\Delta$, let $D_{Sp(n)}(\mathbf{x})$ be the normalized determinant constructed from the polynomials $p_a,q_a$ and their Hopf lifts.

Malkoun's conjecture 2 for $Sp(n)$. For every such configuration,

$$|D_{U(n)}(\mathbf{x})|\geq 1.$$

The displayed claim appears to use $D_{U(n)}$ although the surrounding construction defines $D_{Sp(n)}$; the supplied text gives no resolution status.