Exclusive Grassmannian pair canonical-dual conjecture

Let $F$ be a frame for $\mathbb{F}^n$. A dual of $F$ forms an exclusive Grassmannian pair with $F$ if it is the only dual frame satisfying the paper's Grassmannian coherence minimization condition. Exclusive Grassmannian pair conjecture. If $F$ forms an exclusive Grassmannian pair with one of its duals, then that dual must be the canonical dual frame of $F$.

The paper motivates this claim using examples: one frame has a unique minimizing dual, while another has at least two minimizing duals. It presents the assertion as a conjecture about the special structure required for exclusivity.