What the witness does not exclude

The proposed replacement $\mathbf{r}\mapsto \mathbf{r}+\kappa {\mathcal{L}}_{\xi }\mathbf{r}$ is generally not an automorphism of the unchanged free carrier: for general $\xi$,

so a free solution need not map to another free solution.

However, this does not prove that every completion is impossible. A successor can change the declared interaction/gauge completion and supply additional tree terms. The supplied X-F record explicitly treats a different background-gauge, all-tree problem XF. Nothing here imports that construction, and nothing here refutes its stated narrower repair.