Definition: A matched response family

Fix:

1. a physical model, preparation, source/readout calibration, and physical boundary problem;

2. a perturbative order $N$;

3. an admitted test space $\mathcal{E}$;

4. a nonempty class ${\mathfrak{P}}_0$ of physically matched prescriptions;

5. a constructed response ${{\mathcal{R}}_{\mathcal{N}}}^{\mathsf{P}}\in {\mathcal{E}}^{\prime }$ for every $\mathsf{P}\in {\mathfrak{P}}_0$.

Every response must be expressed in the same calibrated test coordinates. Its complete difference space is

No finite-dimensionality is assumed.