Polynomial-Time Optimal Group Selection via the Double-Commutator Eigenvalue Problem

arXiv:2605.00834v1 Announce Type: new Abstract: The algebraic diversity framework replaces temporal averaging over multiple observations with algebraic group action on a single observation for second-order statistical estimation. The central open problem in this framework is $\textit{group selection}$: given an $M$-dimensional observation with unknown covariance structure, find the finite group whose spectral decomposition best matches the covariance. Naive enumeration of all subgroups of the sy...