A Cosmological Modification to Energy from Mach-Hamilton Consistency

If Mach's Principle explains the Newtonian inertial reaction to acceleration then the role of the 'fixed stars' should also be manifest through Hamilton's formulation of mechanics. This consistency may be achieved if the expression for relativistic energy contains a cosmological coefficient that is (currently) equal to one. The presence of the required cosmological term exactly identifies the rest energy of a body as its gravitational potential energy due to the mass of the Universe.