Cross Gramian coherence lower-bound conjecture for dual frames

Let $F$ be a frame for $\mathbb{F}^n$, and let $G$ be one of its dual frames. Write $Gr(F,G)$ for their cross Gramian and let $\mu(Gr(F,G))$ denote its maximum off-diagonal magnitude. Cross Gramian lower-bound conjecture.

$$\mu(Gr(F,G)) \geq \sqrt{\frac{nk-n^2}{k^2(k-1)}}.$$

The paper gives a partial proof, but notes that one of the cases needed for the argument does not occur in its examples; the conjecture is therefore not established in full.