Frobenius minimal ED-degree conjecture for Segre-Veronese varieties

Let $V$ be a vector space, let $\mathbf{d}$ and $\mathbf{n}$ denote the multi-indices defining the Segre-Veronese variety, and consider

$$\mathcal{V}_{\mathbf{d},\mathbf{n}}\subset\mathbb{P}(S^{\mathbf{d}}V).$$

Let $Q_F$ be a Frobenius inner product on $S^{\mathbf{d}}V^{\mathbb{R}}$, and let $Q$ be any positive definite symmetric bilinear form on $S^{\mathbf{d}}V^{\mathbb{R}}$. The ED degree with respect to a metric $Q$ is denoted by $\operatorname{EDdegree}_Q$, and the generic ED degree by $\operatorname{gEDdegree}$.

Frobenius minimal ED-degree conjecture. One has

$$\operatorname{EDdegree}_Q(\mathcal{V}_{\mathbf{d},\mathbf{n}})\geq\operatorname{EDdegree}_{Q_F}(\mathcal{V}_{\mathbf{d},\mathbf{n}}).$$

Equivalently, the maximum defect of ED degree of $\mathcal{V}_{\mathbf{d},\mathbf{n}}$ is

$$\operatorname{gEDdegree}(\mathcal{V}_{\mathbf{d},\mathbf{n}})-\operatorname{EDdegree}_{Q_F}(\mathcal{V}_{\mathbf{d},\mathbf{n}}).$$

This conjecture is the general claim motivating the paper. The examples preceding it show that the generic ED degree can grow with the format while the Frobenius ED degree can remain smaller; no resolution is given in the supplied text.