Corollary: Relative obstruction in the jet module

In the jet module with $Z$ finite, the relative obstruction class of any extension lift vanishes already in the class of extension changes $\{{\mathsf{Rec}}_s:\mathrm{supp}s\subset Z\}$, which is contained in XV-D's unrestricted puncture-supported class. For general $Z$ it vanishes in that class if and only if (eq:relest) holds. No separated contact witness exists for any extension lift, since every defect is supported in $Z\times \{0\}$ XVD.

Proof. Theorems thm:point and thm:relative, together with ${F_0}^T-{F_0}^{\tilde{T}}={\mathsf{Rec}}_{T-\tilde{T}}$ and XV-D's support theorem.