Corollary: The master equation does not decide XII-F

On ${\mathfrak{F}}_W$, $(S_{\mathrm{ext}},S_{\mathrm{ext}})=0$ and $s_{\mathrm{ext}}$ is nilpotent (Theorem thm:relative), while $s_0\mathcal{O}$, the ${\kappa }^0$ part of $s_{\mathrm{ext}}\mathcal{O}$ in the kinematic rule, is the nonzero functional (eq:relO) on ${{\mathcal{C}}_{\mathrm{sol}}}^{\mathrm{bos}}$. The relative symmetry of the action is compatible with a nonzero relative variation of the displayed observable, and that variation is exactly the auxiliary pairing.