Entropy Selection and Shape Drift for Gaussian Lattice Minima

This is the authors' abstract. We don't add key points for this paper.

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.