Relative derivatives and punctured products

Put $M_{\times }={\mathbb{R}}^4\setminus \{0\}$. The standard off-diagonal Feynman wavefront relation gives, at each singular $z\in M_{\times }$, only one time orientation for the nonzero covectors of $\mathcal{S}$. This is the relation stated after equation (77) in FR (Section 7); see also BDH (Proposition 26). No wavefront statement at $z=0$ is needed here.