Dimension-uniform coefficient extraction from nonlinear curl

Let L(x) = sum_r x_r X_r, where the X_r are real symmetric m by m matrices and sum_r X_r^2 is bounded above by K times the identity for a fixed finite K. For the Gaussian inverse Mills ratio q, we prove that the mean squared row curl of q(L) controls both the lack of full symmetry of the coefficient tensor and the sum of all squared coefficient commutators. After division by m, the estimate has a modulus independent of the dimension, bounded by C_K/log(e/t) when the normalized curl energy t is small. The proof compares divided differences at x and -x and controls a cutoff on all tensor indices by Gaussian operator moments. We also construct a fully symmetric tensor with a controlled operator-energy bound and controlled algebraic residual.