We complete the trace–torsion elimination that Papers I–III defer and establish a locked-branch theorem: in the macroscopic spinless regime, the torsion trace is an algebraicauxiliary field whose exact elimination produces a scalar–tensor sector with a derived Brans–Dicke parameter. This converts the Yukawa fifth force in the weak-field limit from afree phenomenological amplitude into a predicted function of the locked-branch couplings.Concretely, for κ > 0, β > 0, and the committed torsion normalization with a > 2/3, weshow that in Jordan frame the theory is equivalent (at the linearized level around the GRpoint) to a massive Brans–Dicke model withω0 = 1a − 23, αY = 12ω0 + 3 = a − 233a , m20 = a − 2312 κ β a , λ0 = m−10 .Hence the fifth-force coupling is intrinsically suppressed as a ↓ 2/3 without invoking screening.We then summarize the falsifiable program-level implication: a two-scale departure inslip/lensing observables, one transition near k ∼ am0 (scalar-mediated) and a second neark ∼ ξ−1 (defect network), providing a nontrivial closure check against Solar-System boundsand the GW amplitude-friction sector.
SIKX HILTON (Tue,) studied this question.