Complete pure gauge

For $\xi \in {\mathfrak{g}}_p$, take the full two-jet

It vanishes near the initial surface, so both layer sources and both limiting velocities vanish there. The coordinate intertwiner gives, for every small width,

The completed coefficients have zero free class, including their limiting classes by Theorem thm:ward. This diagnostic checks the complete two-jet and the zero-layer case. It is not a replacement for the general layer proof.

The choice $h=K\xi ,k=0$ is not a second-order pure-gauge jet.