Gauge Coupling Unification and Proton Decay in E 8 E 8 Unification: Quantitative Analysis with Improved Threshold Corrections

Within the 𝐸8⊃𝐸6×SU(3)𝐹 unification framework, which explains the origin of three fermion generations (Paper I) and provides a quantitative derivation of the fermion mass hierarchy (Paper II), we present a detailed quantitative analysis of gauge coupling unification and proton decay with significantly improved treatment of threshold corrections. Using one-loop renormalization-group equations with inputs from precision electroweak data, and incorporating threshold corrections from the 12 exotic states whose masses are determined by the SU(3)𝐹 breaking VEV hierarchy from Paper II (𝜆=0.22±0.05), we compute the unification scale and unified coupling with reduced theoretical uncertainty. We find 𝑀GUT=(1.2−0.3+0.5)×1016 GeV and 𝛼GUT−1=40±4. From these values, the proton lifetime for the dominant decay mode 𝑝→𝜋0𝑒+ is calculated with careful propagation of all uncertainties, yielding 𝜏𝑝=(3.2−1.9+4.8)×1035 years, well within the reach of next-generation experiments (Hyper‑Kamiokande, DUNE). This provides a sharp, falsifiable test of the 𝐸8 unification program. We also discuss the connection between the exotic states responsible for threshold corrections and the first-generation mass problem identified in Paper II, showing that they can naturally generate the required 10−3 suppression for 𝑚𝑢/𝑚𝑡 via seesaw-like mixing with Planck-scale masses.