Future-Law Shape Beyond Two Moments

A one-dimensional truth-known discrete kernel compares Gaussian innovations with a moment-matched symmetric Gaussian mixture from one exact start state. Train-only symmetric whitening, hybrid Gaussian-kernel MMD, and directional excess kurtosis are scored on 100 seeds with 512 training and 512 test episodes. At separation 0.88 the null rejected in 6/100 units and the mixture was detected in 98/100. The same target with 256 episodes per pool was detected in 82/120. No entropy, committor, empirical, or biological claim is made.