Input statement: Binary handoff

Constructed: the vertex functional, the selected tree-level binary causal composition, its properness and compact microcausal kernel, its inherited-root overlap, and the free-differential display.

Proved obstructed: the literal normalization $R_1({\mathcal{V}}_g;\mathcal{O})={\mathcal{V}}_g{\star }_H\mathcal{O}$ on ordered supports, when combined with the specified retarded definition and contraction grading.

Unresolved through the requested quantum order: the joint two-line extension in the frozen counterterm class. Neither a failed wavefront criterion nor an unconstructed extension is called a no-go.

The carrier remains ${\mathcal{E}}_H$. No quotient by ${\mathcal{N}}_W$ is released.

These statements are inputs from XIII-B XIIIB.