Reference 1 introduced the gravitational closure law R(u) = s/Σ(u) with Σ(u) = uφ +b uq + c, φ = (1 + √5)/2, q = 2 ln φ/φ, b = φ6 − 2, c = (4 ln φ − 1)/φ, s = 16φ + 1. Theparent action carries two independent source couplings into the displacement field: the matter-side coupling βm acting on ρm, and the branch-local gauge-side coefficient βZ (u) acting onFµν F µν . Linearizing the scalar equation around the D = 0 recovery branch and imposingclosure-consistency with the three-channel decomposition fixes the ratio(βZ /βm)eff (u) = ΣE (u)ΣD (u) = b uq−φ, q − φ = −1.0232,recovering the natural-unit value βZ /βm = b only at u = 1. The running ratio is parametricallysuppressed at solar-system u ∼ 108 (by uq−φ ∼ 10−8) and amplified at deep-MOND u ∼ 10−3(by uq−φ ∼ 103). This collapses three apparently independent statements of the framework —thesmallness of the post-Newtonian residue, the parametric suppression of laboratory δαEM/αEMrelative to the unscreened amplitude b βm δD, and the relative weight of EM stress-energy asa D-source in galactic and cluster environments—into one closure-derived running ratio. Thealgebra, predictions, and benchmarks of Reference 1 are unchanged; the present note removesa previously implicit reading of the constant b as a universal terrestrial gauge-coupling weight.
James P Higginson (Thu,) studied this question.