C1: the scope proposition

For reference in the proof, X-B's defect formula is

both terms of which are elements $\hat{\varphi }(d)$.

-goals (recorded, not inferred).

1. No quantum metric propagator: no bidistribution in two metric slots is present in ${\mathfrak{S}}_A$.

2. No gravitational action and no graviton vertex: no functional of degree zero in $\phi$ is formed.

3. No loop: no object contains a kernel contracted against itself; the only two-point kernels are applied to smooth compact sources.

4. No hidden contraction: by Proposition prop:scope(iii) the constructed classes do not depend on ${\Delta }_{+}$.

5. No second-order quantum map: ${\rho }_{2,g}$ is displayed in X-B as classical input and is not an object of Proposition prop:scope.

6. Branch B (Section sec:branchB) is a different construction. Treating a graviton line as latent in $R_1$ would contradict (N1)–(N4).