What has to be fixed before a catalogue is complete

A finite list is meaningful only relative to a declared class. For the proposed quantum problem this class must fix, at minimum:

1. coupling order and loop order;

2. field content, ghost number, and discrete symmetries;

3. derivative and engineering-dimension bounds;

4. the allowed dependence on $m$ and any renormalization scale;

5. the number and treatment of switch insertions;

6. action counterterms and composite-observable counterterms;

7. equivalences from integrations by parts, field redefinitions, and equations of motion, with their domain of validity;

8. initial-surface terms or restrictions excluding them;

9. the Ward identity, including its permitted breaking terms;

10. lower-order normalization conditions that are held fixed.

In particular, freezing lower-order normalizations matters for the affine form $r=q+Nc$. If lower-order redefinitions are allowed to vary, their products may enter the next coefficient. An affine response space then requires a separate parametrization argument.