Hidden-State Privacy Has an Empty Middle

ArXi:2605.24042v1 Announce Type: cross Of $1{,}536$ Gaussian release covariances we tested for single-layer hidden-state privacy, zero achieve both moderate utility and moderate privacy against an adaptive retrieval attacker. We prove a complementary Fisher-ball lower bound: every full-rank Gaussian release at $O(1)$ Fisher utility admits a direction whose Mahalanobis signal grows linearly in hidden width, ruling out uniform Gaussian safety in the class and matching the empirical empty middle.