Remark: What this does and does not say

In the jet module the null relations split into two kinds: universal relations, with all ${\beta }_{\gamma }(a)=0$ as smooth functions, which hold for every coefficient and never produce a defect; and annihilator relations, with some ${\beta }_{\gamma }(a)\ne 0$ but ${\beta }_{\gamma }(a)T^{\circ }=0$, which are the only source of a nonzero defect (Proposition prop:example). The supplied identity (eq:inheritednull) is of the first kind in this module. For the actual graph this classification is not available: $\mathsf{Rec}$ is defined on two elements only (D0.2), and the record does not say whether $\ker \mathsf{Rec}$ contains annihilator relations. The statement “the inherited identity carries no defect” is proved here for (eq:ajet) in the jet module and is not transferred to (eq:inheritednull) in ${\mathcal{P}}_{\mathrm{int}}$.