Contact modifications

For example $N_{h}c=P_m(\chi c)$, with smooth $\chi$, is compatible and invisible in the free algebra. A nonzero multiplication $N_{h}c=wc$ is not compatible on the whole domain: choose a spatially compact solution nonzero at a point where $w\ne 0$, then choose $c$ in a small neighbourhood with $⟨wc,u⟩\ne 0$. Compact Cauchy data can realize such a local nonzero solution.