Compact-test field algebra

For compact field tests, impose

and the full free field equations. The contractions are $\hslash \mathbb{W}$. Finite Wick polynomials in compactly smeared linear fields are defined by finite pairings with smooth compact joint tests.

This does not admit an arbitrary singular or noncompact composite kernel. In particular, it does not yet define the native pairing of the full lapse Hessian with $W_{\mathcal{B}}$.