Loss of rapid velocity decay in a broad smooth class for the cutoff Boltzmann equation

We construct a spatially homogeneous, radial, nonnegative smooth solution of the full-sphere hard-sphere Boltzmann equation whose initial value is a Gaussian but whose velocity tail is a positive multiple of \(r^{-6}\) at every positive time. Mass is one, and energy and entropy have uniform finite upper bounds on a short time interval. This gives a negative answer to a literal rapid-decay continuation statement when smoothness means joint pointwise smoothness and no energy admissibility or positive-time Schwartz condition is part of the solution class. The solution itself continues smoothly in the critical weighted class: the example concerns loss of rapid velocity decay and does not establish local derivative blowup or resolve conservative continuation. The proof separates an explicit radial linear part from a nonlinear remainder with one extra power of decay, and proves nonnegativity by a compact-maximum argument. No novelty claim is made.