Smooth residual testing can hide the relevant wavefront

This is a counterexample to a proposed inference from tested regularity, not a replacement for $K_{\mathrm{ret}}$. It satisfies the same relevant compactness and balanced-covector condition.

Smooth tests determine a distributional kernel uniquely. The proposition does not deny that fact. It shows that the regularity of every tested kernel can conceal attachment wavefront directions of the untested kernel. Those directions are precisely among the data a later joint composition must control.

Thus the tested equality of XIV-E remains valid, but it cannot supply the missing common symbol bundle or uniform characteristic composition estimates by itself.