  Superpotentials offer a direct means of calculating conserved charges
associated with the asymptotic symmetries of space-time. Yet superpotentials
have been plagued with inconsistencies, resulting in nonphysical or incongruent
values for the mass, angular momentum and energy loss due to radiation. The
approach of Regge and Teitelboim, aimed at a clear Hamiltonian formulation with
a boundary, and its extension to the Lagrangian formulation by Julia and Silva
have resolved these issues, and have resulted in a consistent, well-defined and
unique variational equation for the superpotential, thereby placing it on a
firm footing. A hallmark solution of this equation is the KBL superpotential
obtained from the first-order Lovelock Lagrangian. Nevertheless, here we show
that these formulations are still insufficient for Lovelock Lagrangians of
higher orders. We present a paradox, whereby the choice of fields affects the
superpotential for equivalent on-shell dynamics. We offer two solutions to this
paradox: either the original Lagrangian must be effectively renormalized, or
that boundary conditions must be imposed, so that space-time be asymptotically
maximally symmetric. Non-metricity is central to this paradox, and we show how
quadratic non-metricity in the bulk of space-time contributes to the conserved
charges on the boundary, where it vanishes identically. This is a realization
of the gravitational Higgs mechanism, proposed by Percacci, where the
non-metricity is the analogue of the Goldstone boson.
