Independent admissibility requirements

Before a subtraction is used to decide the quantum limit, the chosen theory and order must determine:

1. the graph distributions and their coincidence sets;

2. the tensor structures and background/clock dependence permitted in their extensions;

3. the derivative and scaling bounds;

4. causal and local covariance conditions in the applicable renormalization framework;

5. quantum BRST/BV conditions and the relevant equation ideal;

6. allowed finite normalizations;

7. existence and tail control for their observable-level images.

This list is an admissibility contract, not a completed classification of ${\mathfrak{C}}_{\mathrm{adm}}$.

Neither successful cancellation nor failure of attachment-diagonal support alone settles admissibility.