Definition: Coupled constraint surface

$\mathcal{C}$ is the set of formal triples $(h,k,\varphi )$, $\varphi ={\varphi }_0+\kappa {\varphi }_1+{\kappa }^2{\varphi }_2+\dots$, with ${\mathsf{E}}^{\mu \nu }[q,\varphi ]=0$ and ${\mathsf{E}}_{\varphi }[q,\varphi ]=0$ through ${\kappa }^2$ in (eq:metric-euler-expanded), with the ramp coordinates (eq:coordinate-equations) unchanged.