Constructing metric gravity's N-body non-linear Lagrangian from iterative, linear algebraic scaling equations

A method for constructing metric gravity’s N-body Lagrangian is developed which uses iterative, liner algebraic euqations which enforce invariance properties of gravity — exterior effacement, interior effacement, and the time dilation and Lorentz contraction of matter under boosts. The method is demonstrated by obtaining the full 1/c^4 order Lagrangian, and a combination of exterior and interior effacement enforcement permits construction of the full Schwarzschild temporal and spatial metric potentials.