Target Fidelity Is Not Numerical Fidelity Signed Bias-Discretization Alignment at Equal NFE

At equal numbers of score evaluations (NFE), Heun can converge faster to a fixed learned probability-flow ODE while Euler remains closer to the target. We prove this separation for a smooth Gaussian VP construction: numerical errors have exact orders one and two, yet Euler has strictly smaller target $W_2$ error at every sufficiently large even budget. The result persists in a one-dimensional neighborhood of smooth nonlinear fields, with a uniform budget threshold. The target-error gap decays as $M^{-1}$ and the relative advantage vanishes. Signed alignment between continuous-flow bias and Euler's leading defect determines the eventual coupled ranking. In DSM-trained GMMs, the joint ranking persists beyond the earliest checkpoint: at 2400 and 6000 updates, respectively, 6/15 and 11/15 fixed networks retain the opposite coupled target ranking throughout a common 128-2048 NFE normal-order diagnostic window, while Heun has smaller numerical error in every comparison. Oracle-assisted alignment estimates do not outperform simple target-gap extrapolation. A controlled 32-dimensional study provides additional coupled evidence; An unpaired kernel-embedding test finds no statistically certified MMD reversal. These results establish a locally robust distributional existence theorem and a controlled learned-score mechanism; Image-scale relevance remains open.