C2: what is defined away from collisions

Formally, the required coefficient is

The $H$ contraction exists by the inherited product theorem. The joint time-ordered contraction requires a separate argument.

Keep the difference grouped as in (eq:formal-two-line). Expanding it into separate mixed products of $H$ and ${G_{\mathrm{act}}}^{\mathrm{A}}$ can introduce undefined intermediate products even when a grouped boundary-value expression exists.