Practical universality conjecture for the Sequential GEVP

Let $\mathbf{R}$ be a Hermitian positive-definite matrix arising from a broad class of physical signal models, and let $\mathcal{B}$ be a basis. Let $\operatorname{Aut}(\mathbf{R})$ denote the automorphism group of $\mathbf{R}$, and consider the Sequential GEVP with group-theoretic deflation at $\tau=0$. Practical universality conjecture. There exists a basis $\mathcal{B}$ for which the Sequential GEVP recovers $\operatorname{Aut}(\mathbf{R})$ in full. Identifying such a basis from $\mathbf{R}$ alone, or characterizing the bases for which this holds, remains an open basis-design problem. The procedure is known to be sound, but completeness is not established in general.