Entropy Selection and Shape Drift for Gaussian Lattice Minima

For each perfect strictly eutactic lattice, we determine the large-parameter Gaussian energy minimum in a fixed neighborhood of its shape. The minimizing shape moves by order t^(-1), and the leading energy coefficient is the exponential of the maximum entropy of an isotropic probability measure on the shortest vectors. We give an explicit negative correction of order t^(-1) to this coefficient. Uniform localization and a summable tail estimate justify minimization of the expansion. Globally, among unit-covolume lattices, the formula selects Hermite-optimal classes first by the entropy coefficient and then by the squared drift. Poisson summation gives the corresponding small-parameter formula. An exact nine-dimensional cyclic-group example has 160 shortest vectors but optimized coefficient strictly below 160, with an integer/rational certificate. Classical packing theory, entropy duality, the cyclic-group construction and prior fixed-lattice optimality results are credited. The results concern Bravais lattices, not arbitrary point configurations; AIM Problem 1.34 and the full dataset record AIM-GEOMETRY-0093 are not closed. This is an AI-assisted, self-audited, unrefereed preprint; no independent review, formal certification or absolute priority is claimed.