Blind group selection consistency conjecture

Let $\mathcal{G}$ be a library of candidate groups, let $\mathbf{x}$ be a single observation, let $\psi(G,\mathbf{x})$ be the spectral concentration criterion, and let $\delta(G,\mathbf{R})$ be the sample commutativity residual for population covariance $\mathbf{R}$. Define the optimal group by

$$G^*=\arg\min_{G\in\mathcal{G}}\delta(G,\mathbf{R}).$$

Blind group selection consistency conjecture. The spectral-concentration selector is consistent at high signal-to-noise ratio:

$$\Pr\!\left[\arg\max_{G\in\mathcal{G}}\psi(G,\mathbf{x})=G^*\right]\to 1\quad\text{as }\operatorname{SNR}\to\infty.$$

This would provide a blind, single-snapshot method for selecting the group whose action best matches the covariance, without knowing $\mathbf{R}$. The supplied text gives no evidence that the claim has been proved or disproved.