Action classes and response classes

There are two quotients:

The response map connects them but need not be injective. A response test of a density representative tests its action class because evaluation descends to $\mathcal{V}$. A test of contact-surviving information instead tests $[m]$, not one arbitrary reference representative.

In particular, no equation-of-motion quotient, source weighting, or characteristic-product ambiguity is silently added to $\mathcal{V}$.