  We develop the covariant phase space formalism allowing for non-vanishing
flux, anomalies and field dependence in the vector field generators. We
construct a charge bracket that generalizes the one introduced by Barnich and
Troessaert and includes contributions from the Lagrangian and its anomaly. This
bracket is uniquely determined by the choice of Lagrangian representative of
the theory. We then extend the notion of corner symmetry algebra to include the
surface translation symmetries and prove that the charge bracket provides a
canonical representation of the extended corner symmetry algebra. This
representation property is shown to be equivalent to the projection of the
gravitational equations of motion on the corner, providing us with an encoding
of the bulk dynamics in a locally holographic manner.
