  We examine aspects of locality in perturbative quantum gravity and how
information can be localized in subregions. In the framework of AdS/CFT, we
consider the algebra of single-trace operators defined in a short time band. We
conjecture that, if the state has large energy variance, then this algebra will
have a commutant in the 1/N expansion. We provide evidence for this by
identifying operators that commute with the conformal field theory Hamiltonian
to all orders in 1/N, thus resolving an apparent tension with the gravitational
Gauss law. The bulk interpretation is that these operators are gravitationally
dressed with respect to features of the state rather than the boundary. We
comment on observables in certain black hole microstates and the gravitational
dressing in the island proposal.
