A smooth stability check can reject a real minimum

The unchanged numerical check rejects two analytically exact minima where the slope changes, even with correct derivatives. It accepts the smooth minimum and correctly rejects the smooth nonminimum control.

Why this matters

The check predicts a correction from the slope at the current point. When that step crosses a slope change, its prediction can fail even at the true minimum. The fresh cost then rises, so the original rule rejects the point. In both counterexamples, stationarity and position-change screens pass; cost stability fails. The minima follow directly from the formulas, independently of a solver.

The saved calibration corrections also cross integration boundaries in both failed fits. That makes two-sided timing behavior a focused diagnostic target. These small analytical examples do not prove the same cause in the recorded calibration cases. They do not qualify those fits, justify loosening a limit, or establish a replacement solver.

What ran

All four deterministic software checks pass their expected outcomes. Four bounded linear solves and four fresh analytical evaluations were charged in advance. The original checker and its limits were unchanged. No native kernels, noise draws, nonlinear flight fits or protected data were used.

Exact formulas and fixed scope · Saved correction review · Next analyses.