Finite transformation of the cubic response

Comparing with X-A's law $k^{\prime }=k+{\mathcal{L}}_{\xi }h+K\zeta +\frac{1}{2}{\mathcal{L}}_{\xi }K\xi$ at $(h,k)=(\gamma ,u_3[\gamma ])$: the response supplies the covariant term ${\mathcal{L}}_{\xi }\gamma$, the quadratic flow term through (eq:flat), and a definite second-order parameter $\zeta ={\zeta }_{\mathrm{gf}}[s_{\xi }]$. Gauge fixing does not break the second-order law; it selects $\zeta$. The selected $\zeta$ is not compactly supported in $U$, which is why a remainder survives in Section sec:F3.