Corollary: Consistency with XIV-J's normal form

XIV-J states that $K_{\mathrm{supp}}$ has a unique finite normal form of normal order at most three along $S_{\mathrm{resp}}$, with reference ${t^{\circ }}_D={\sum }_{|\alpha |\le 3,\beta \le \alpha }(-1{)}^{|\beta |}(\genfrac{}{}{0ex}{}{\alpha }{\beta }){\mathsf{E}}_{\alpha -\beta }(v_{\alpha }{c}_{D,\beta })$ on $U\setminus N_U$ Jreference,Jconditional. Under the candidate $S_{\mathrm{resp}}\stackrel{?}{=}\{(b-a{)}^2=0,a=z\}$ of the patch, which on $V_{+}$ is $S^{+}$, Theorem thm:normalorder reproduces the normal-order bound three from XIV-H's bound $|\alpha |+|\beta |\le 2$ alone, for every completion of the undefined coefficients: one normal derivative from the outer ${\partial }_b$ and at most two from the source. The two bounds are therefore mutually consistent, and the bound three is attained by the term pattern of $K_8$, $K_9$ unless the coefficients cancel.

Proof. Theorem thm:normalorder and the cited statements.