Uniformly Accurate EDMD Generators Can Give Unbounded Auxiliary Optima

We construct noiseless data for which extended dynamic mode decomposition (EDMD) converges uniformly to the true generator on a fixed polynomial auxiliary space, while the associated unregularized auxiliary optimum is minus infinity instead of 1. For dx/dt = -x^5 on [-1,1], we use quadratic auxiliaries and a degree-six dictionary. The regression has full column rank. The theorem holds for every N >= 9 Chebyshev-node design and, almost surely, for all sufficiently large iid datasets from the full-support arcsine measure. A uniform negative-derivative certificate holds for every 0 < tau <= 2^(-26), while the operator error is bounded by 156 tau in the stated coefficient norm. Adding the valid constraint U >= 0 makes the approximate value finite but still incorrect. The qualitative strict-feasibility obstruction is known from Bramburger and Fantuzzi; this note gives an actual exact-flow realization and elementary regularization bounds. It does not close the general optimal-value error-estimation problem or contradict prior convergence theorems. This is an unrefereed, AI-assisted preprint without an absolute priority claim.