Gaussian variance monotonicity for de-regularized MMD

For a centered one-dimensional Gaussian target and the Gaussian kernel, we prove the strict sign inequality governing the variance in the Gaussian moment approximation to de-regularized maximum mean discrepancy (DrMMD) flow. The result holds for every target variance $s>0$, every finite regularization parameter $\lambda>0$, and every current variance $0<v<s$, removing the target statement's restriction $s>2$. The proof reduces the Gaussian expectations to a weighted power-series curve. Every finite initial block of its coordinates has a strictly negative directional inner product toward the target. A truncated negative-binomial mean bound proves this fact for positive curve parameters; a polynomial boundary identity proves it for zero and negative parameters. Summation by parts then handles all nonnegative decreasing spectral weights, including the DrMMD resolvent. The Gaussian moment variance consequently increases to its target. The analytic argument does not rely on the accompanying computations.