Defect Cartan Gravity IV: Intrinsic Fifth–Force Suppression from Trace Torsion

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 algebraic
auxiliary 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 a
free 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, we
show that in Jordan frame the theory is equivalent (at the linearized level around the GR
point) to a massive Brans–Dicke model with
ω0 = 1
a − 2
3
, αY = 1
2ω0 + 3 = a − 2
3
3a , m2
0 = a − 2
3
12 κ β a , λ0 = m−1
0 .
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 in
slip/lensing observables, one transition near k ∼ am0 (scalar-mediated) and a second near
k ∼ ξ−1 (defect network), providing a nontrivial closure check against Solar-System bounds
and the GW amplitude-friction sector.