Why a counterterm catalogue is not yet available

At order ${\kappa }^2$, the classical formulas use at most two factors of the switch, counting a differentiated switch as one factor. This is insertion bookkeeping, not a proof of renormalization completeness.

A future response-level catalogue must fix, at minimum:

1. the response, state, and loop convention;

2. the action and composite normalization conditions;

3. bounds on field degree, derivative order, and switch degree;

4. the permitted mass dependence and constant coefficients;

5. the admitted terms associated with the initial surface;

6. the propagation of every admitted term through the same Cauchy kernels used for the reference response.

No finite-dimensional ambiguity theorem follows merely from fixing the derivative order while permitting arbitrary functions of the switch.