Wavefront, contacts, and admission

A wavefront theorem for a physical limit requires a stated closed cone and uniform localized Fourier bounds outside it. Finite-scale smoothness of $C_{\delta }$ does not provide those bounds.

Properness controls pushforward after a distribution exists. Extension results require their own growth and microlocal conditions Dang,BF; they do not by themselves identify a raw smoothing limit or its physical normalization.

Under the inherited contact hypothesis, collision-supported contacts vanish on the retained separated patch. An eventual nonzero physical fixed-test defect there could not be removed by those contacts. No such physical defect is proved by the scalar family.