Renormalization freedom and anomalies

Graph counting does not determine every admissible finite quantum normalization. Additional local terms can involve external coupling jets, observation-test jets, scalar fields, and background curvature data. The candidate defect is not exhausted by one schematic expression $\int (\partial \xi )\mathcal{R}[h_{\mathrm{cl}}]$.

A proof of anomaly removability must:

1. construct the actual defect;

2. derive its consistency condition;

3. classify the admissible finite normalization terms;

4. solve the cancellation equation within that class.

None of these steps follows from a failed scalar product criterion or from the absence of a particular unrenormalized background graph.

The explicit reciprocity defect of Section sec:obstruction is different. It is a classical obstruction to an exact source-preserving field-map identification, not an evaluated one-loop anomaly.