Smooth-edge approximation

The prescribed-wavefront topology in the last assertion can be taken to be the normal topology used for distributional operations in BDHtopology. The assertion only requires that its inclusion into distributions be continuous.

At fixed $ϵ$, the source equation is

rather than the unswitched equation on the whole future half-space. Thus a fixed nonzero edge width changes the coordinate prescription. Proposition prop:smoothing establishes a distributional sharp limit for linear smearings, not a sharp limit inside the declared insertion domain and not a theorem for the bilinear composite or its retarded products.