TCIE–MSSM v1.5: A Froggatt–Nielsen Origin for Yukawa Couplings in a Unifying Scalar Framework

We present TCIE–MSSM v1.5, a complete effective field theory framework in which a single light scalar field controls the cosmological variation of gauge couplings through a universal coupling f(ϕ)F2f(\phi) F^2f(ϕ)F2, while remaining consistent with all local tests of gravity via a Damour–Polyakov screening mechanism. The model embeds naturally within an SU(5)-unified extension of the MSSM and incorporates a Froggatt–Nielsen origin for the scalar dependence of Yukawa couplings. This construction replaces the previously fine-tuned continuous parameter γEW\gamma_{\mathrm{EW}}γEW with a discrete integer Froggatt–Nielsen charge nEWn_{\mathrm{EW}}nEW, thereby improving the theoretical naturalness of the framework. The theory predicts a relative variation of the fine-structure constant Δα/α(z=2)≃−2.3×10−7\Delta \alpha / \alpha (z = 2) \simeq -2.3 \times 10^{-7}Δα/α(z=2)≃−2.3×10−7, accompanied by a correlated variation of the strong coupling and a suppressed but calculable variation of the proton-to-electron mass ratio μ\muμ. All current constraints from equivalence principle tests and fifth-force searches are satisfied. The model is predictive and falsifiable by next-generation spectroscopic surveys such as ANDES/ELT and by high-precision atomic clock experiments.