  This work refines arguments forbidding non-linear dynamical gravity from
appearing in the low energy effective description of field theories with local
kinematics, even for those with instantaneous long-range interactions.
Specifically, we note that gravitational theories with universal coupling to
energy -- an intrinsically non-linear phenomenon -- are characterized by
Hamiltonians that are pure boundary terms on shell. In order for this to be the
low energy effective description of a field theory with local kinematics, all
bulk dynamics must be frozen and thus irrelevant to the construction. The
result applies to theories defined either on a lattice or in the continuum, and
requires neither Lorentz-invariance nor translation-invariance.
