Known-answer tests for an internal timing boundary
The saved corrections cross a timing boundary in both failed fits and in neither successful control. Before new native calculations, test whether the existing numerical check can reject a mathematically exact minimum when the slope changes at a boundary.
Small software qualification
Use four analytical one-parameter cases on the fixed interval −1 ≤ u ≤ 1:
- A smooth minimum with residuals
[15, b(u−c)], atc = 0. - A boundary-shaped minimum with residual
15 + b|u−c|, atc = 0. - The same minimum translated to
c = 0.25. - A smooth residual
15 + bu, evaluated at zero although its minimum is at −1.
Use b = 0.00005. The minima follow directly from the formulas, independently
of any optimizer. Supply the correct right-hand derivative at each kink and
verify both one-sided derivatives separately. Call the original, unchanged
stability checker once per case, with an analytical evaluator and its existing
cost, stationarity and position-change limits.
These are ordinary deterministic software checks: at most four bounded linear solves and four fresh analytical evaluations, one thread, no native calls, aircraft observations, noise draws or nonlinear fits. Preserve rejection as an expected outcome where the original check cannot certify a known minimum.
Interpretation
An exact counterexample would identify a limitation of the smooth numerical check. It would not prove that the saved aircraft-simulation failures have the same cause, justify accepting them, or qualify a replacement solver. Native two-sided derivative tests still require their own reviewed finite plan.