Learning-Calibrated Covert Power Control Under Unknown Background Noise: Exact Gaussian Calibration and Non-Gaussian Susceptibility Estimation

We study covert power control from finite idle samples when the warden knows the true background law. Learning-aware covertness bounds the probability that learned power causes the block Kullback–Leibler (KL) divergence to exceed its budget. Under matched zero-mean Gaussian sampling with unknown variance, one-sided chi-square calibration attains the target violation probability α exactly, whereas the plug-in probability approaches 1/2. A justified variance-ratio lower bound extends the guarantee to Gaussian proxy mismatch. For smooth non-Gaussian backgrounds, covert susceptibility governs the local KL expansion; a valid one-sided susceptibility bound and remainder control conditionally yield power calibration. We implement a split-cross estimator with a within-block bootstrap and empirical smoothing reserves. Independent fixed-reserve confirmation on the development mixture gave 0/100 observed violations and median power efficiency 0.944. Under matched adaptive reserves, a diagonal-corrected same-sample comparator also gave 0/100 observed violations and higher median efficiency. Two prespecified test mixtures each gave 0/100 observed violations at m=105, although the high-curvature envelope covered true susceptibility in 68/100 trials. Violations were observed in smaller-sample and light-tailed stress settings. The non-Gaussian results provide empirical evidence for the evaluated backgrounds and operating conditions.