Abstract

We examine the coefficient linear in $\hslash$ left unresolved in XIII-B. The entries are the frozen switched metric–scalar vertex and the displayed second-order composite. The carrier and the off-shell lifts remain unchanged.

We replace the total-diagonal ambiguity class by a class admitting the partial collision diagonals produced by the selected pair. An eleven-branch decomposition gives a complete incidence inventory of its double cross-contractions. For the elementary parallel-line factors, we compute transverse scaling degrees, construct extensions, and identify their finite contact ambiguities.

A further joint issue must not be hidden. For a nonlocal observable, removing collision diagonals does not by itself establish the off-collision distribution. Retarded internal lines and time-ordered cross-lines admit a nonzero wavefront cancellation at distinct null-related vertices. We exhibit this cancellation explicitly. It is a failure of a sufficient product criterion, not a theorem that no joint distribution exists.

Consequently, the elementary extensions do not constitute a complete joint extension or an output admission theorem. The requested coefficient retains the ending Unresolved. Corrected ordered values, tree overlap, properness, and the exact missing microlocal obligations are separated. No gauge-consistency defect is opened.