Corollary: X-E's defect is a truncation defect

X-E's one-tree observable in the flat gauge is (eq:all-tree) without ${\mathsf{T}}_{\mathrm{mix}}$ and ${\mathsf{T}}_{\mathrm{self}}$. Its ${\kappa }^2$ defect $-{\kappa }^2{\hat{A}}_1[{\mathcal{L}}_{\xi }\hat{h}]$ is the negative of the variation of the omitted mixed tree, modulo $\mathfrak{J}$. The defect is independent of $(h_{\mathrm{cl}},k_{\mathrm{cl}})$ because ${\mathsf{T}}_{\mathrm{mix}}$ vanishes identically at $h_{\mathrm{cl}}=0$ while its first variation does not.