C4: Branch B is recorded and not opened

An independent quantum-metric branch would have to supply at least:

1. a quadratic graviton action, gauge fixing, and ghost sector, with the action-Hessian normalization specified;

2. graviton retarded and advanced Green operators, their transposition conventions, and support theorems;

3. a graviton Hadamard two-point matrix satisfying the chosen equations, commutator, and metric-slot wavefront condition;

4. a contraction domain in the scalar, metric, and ghost variables, including the status of $k$ and of the coordinate kernels after $h$ is quantized;

5. the mixed vertex with quantum $h$, its Wick ordering, field degrees, and coupling and $\hslash$-gradings;

6. an actual wavefront and extension analysis for the required mixed graphs and any sourced graviton tree;

7. a Ward or BRST formulation on that new domain;

8. a comparison rule specifying any intended agreement with the present scalar-only map.

None of those data is supplied here. The classical coordinate kernel is not a graviton propagator, ${\Delta }_{+}$ is not a metric two-point matrix, and joint admission with classical background slots is not a quantum-metric contraction theorem. The scalar map has no latent graviton contribution.

XII-B is a different track and is not an input. Retrieval summaries do not constitute analytical premises. This section asserts neither existence, failure, nor correction of Branch B XBii (Section C4).