A necessary distinction: source response versus variational map

This is a concrete version of the distinction emphasized in the supplied X-G record XG. It does not invalidate the retarded equation or the direct identity (eq:jet). It excludes a stronger unqualified variational interpretation of the unchanged off-shell source law.

Switching a local density before Euler differentiation instead produces derivative-of-$\sigma$ terms. They are generally nonzero in the onset layer and are not silently included in (eq:response). They can propagate to later observations. What is used in the plateau variation is the separate fact that $Q^{(1)}[K\xi ]$ has support where $\sigma =1$, not a claim that all onset effects vanish.

We therefore use the phrase equation-level retarded response. No variational Bogoliubov map, Peierls-intertwining theorem, or time-ordered family is released.