Radion Protection from Neutrino Sourcing in KK-Reduced Entangled Relativity

This work addresses a specific consistency problem in Entangled Relativity: non-relativistic neutrinos satisfy \(L_m = 0\) on shell while having a non-zero stress-energy trace \(T ≠ 0\). In a purely four-dimensional scalar interpretation, this can source the ER dilaton at the level \(δϑ/ϑ ~ Ω_ν ~ 10⁻³\). If this scalar were directly identified with the electromagnetic fine-structure sector, it would imply a variation of \(αEM\) in tension with atomic-clock and quasar absorption constraints. We show that the Geometric Relay Theory (GRT), defined as the Kaluza-Klein reduction of Entangled Relativity from five to four dimensions, resolves this problem by separating the relevant physical channels. The compact radion \(σ = g₅₅\), which controls the electromagnetic gauge coupling through \(αEM ∝ 1/σ\), is governed by an equation proportional to \(L_m^2\). Since the on-shell neutrino matter Lagrangian vanishes, \(Lm,ν=0\), neutrinos do not directly source the radion. The direct protection is therefore exact: \((δα/α)ν,direct=0\). The remaining indirect channel, in which neutrinos modify \(R_4\) through their stress-energy tensor and thereby affect the coefficient of the radion equation, is bounded by a self-consistency argument. The indirect effect is at most a fraction \(Ω_ν/Ω_m\) of the already constrained dust-driven radion response. This gives \((δα/α)ν,indirect < 5 × 10⁻⁸\) for the minimal neutrino mass sum, safely below current observational bounds. The robust observable signature is therefore not a neutrino-induced variation of the fine-structure constant, but a small correction to the expansion history: \[ ν → δ H(z), ν δαEM. \] The predicted correction is of order \(δ H/H ~ Ω_ν ~ 10⁻³\), potentially testable with DESI, Euclid, and future cosmological surveys. A Python reproduction script i Ens provided.