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This chapter of the proceedings for the Ninth Meeting on CPT and LorentzSymmetry is dedicated to the Hamiltonian formulation of the minimalgravitational Standard-Model Extension. Some theoretical questions associatedwith the latter shall be reviewed. First, we recall the properties of theHamiltonian, which was computed elsewhere, and discuss how it is linked to themodified Einstein equations. Second, we describe how the covariant andHamiltonian formulations are shown to be consistent with each other.

New Developments in the Hamiltonian Formulation of the Gravitational Standard-Model Extension