Corollary: Unique zero-momentum prescription

Among the permitted extensions, exactly one satisfies

It is ${{\Pi }^{\mathrm{R}}}_{\mathrm{ref}}$. Equivalently, calibration sets the degree-two and degree-four Taylor tensors to zero.

This conclusion uses $m>0$. No $m\to 0$ limit is taken; it does not discharge XVI-N, produce a massless susceptibility, or match VII-H.

Proof. The gap $a>0$ makes $F_i(z)$ analytic near zero. Since $F_i(0)=0$, each term ${\mathsf{Q}}_i(p)F_i(p^2)$ begins at momentum degree six. Thus the reference satisfies (eq:zeronorm).

For a different extension, the degree-two term is $\hslash \alpha \mathsf{E}$, forcing $\alpha =0$. Independence of ${\mathsf{Q}}_2,{\mathsf{Q}}_0$ then forces $\beta =\gamma =0$ at degree four.