QMU Gravitational Field Theory IV: Post-Newtonian Closure Geometry and the Eddington Parameters

This paper develops the post-Newtonian weak-field projection of QMU Gravitational Field Theory from the scalar closure potential \[Ψ_c = -GM/c^2 r.\] Using this dimensionless closure potential as the natural expansion parameter, the paper derives the temporal and spatial metric projections required for comparison with the Parameterized Post-Newtonian framework. The closure geometry yields the Eddington parameters \[γ = 1,β = 1,\] thereby recovering the standard first post-Newtonian weak-field tests: gravitational redshift, first-order light deflection, Shapiro radar time delay, and perihelion precession. The paper also expresses these recoveries in closure-ledger form, showing that no additional phenomenological constants are required beyond those established in the preceding scalar QMU gravitational papers. The scalar sector is thereby shown to preserve the tested weak-field structure of gravitation while leaving rotational closure, stress-energy transport, compact-object rotation, and gravitational-wave energetics for subsequent work.