Theorem: Normalization determines the map

The map $R_1(V_{1,g}[h];\cdot )$ is the unique map satisfying Definition def:sheet.

Proof. Existence is (eq:normalization). For another candidate and each $c$, write $\mathcal{R}(F_c)=\mathbf{\varphi }({d^{\prime }}_c)$. The difference of the two tests annihilates every spatially compact free solution. By Lemma lem:detect,

Lemma lem:graded gives equality of the output classes. No condition on the dependence of ${d^{\prime }}_c$ on $c$ is needed.

For formal series apply the same argument to every $\hslash$-coefficient.