The interface, transcribed

Lemma lem:directsum is the reason the plan requires the generators of every entry before $\ker \mathsf{Rec}$ can be computed: the per-entry kernels do not suffice when images overlap, and Theorem thm:normalorder below shows that the images of the $K_6$-, $K_8$-, and $K_9$-presentations all lie in one and the same finite normal-jet space.