Conclusion

For the action-level switching prescription (eq:switchedaction), the first-order plateau repair extends through second order. The extension requires the genuine metric two-jet, the density-valued transformation law, the complete inverse harmonic-coordinate expansion, and fixed Cauchy data.

The mechanism is precise. On the support of an admitted gauge transformation the switched scalar operator is the natural curved operator. Outside that support the transformation is the identity. The scalar solution and the harmonic-coordinate map therefore obey the same pullback law, and their relational composition is invariant.

The larger-support first-order obstruction remains intact. Equation (eq:defect) identifies its defect, and Corollary cor:nohigherrepair explains why adding a second-order coefficient to the unchanged large-group construction cannot remove it.

What has been completed is the classical gate:

A renormalized quantum response and its complete ambiguity space require further work on the repaired object. They are not consequences of the classical cancellation alone.