The plateau theorem

The theorem is stronger than a statement restricted to $h=0$ or $h=K{\xi }^{\prime }$: no field equation for $h$ is required.

of the first-order statement. Theorem thm:first alone proves neither second-order covariance, independence of $(g,U)$, independence of the dressing prescription, a full gravitational gauge quotient, nor a quantum Ward identity. Second-order covariance is established separately below; the other claims are not made.