The Grand Unification Scale and Proton Decay in the Cohesion Unified Field Theory

The GUT group paper identified SO(10) as the grand unified group of the Cohesion UFTand established that MGUT is the density threshold DGUT at which all three recursionmode frequencies become equal. This paper derives MGUT numerically and calculatesthe resulting proton decay lifetime. The calculation uses the one-loop renormalisationgroup equations — identified in the running couplings paper as the density-dependenceof the recursion mode frequencies — with the Standard Model particle content below theelectroweak scale and the additional recursion modes required for exact unification aboveit. The Standard Model alone gives near-unification at ∼ 1014–1016 GeV but the threecouplings do not meet exactly; the SM proton lifetime estimate at this scale is τp ∼ 1030–1033 years, excluded by Super-Kamiokande. With additional recursion modes above theTeV scale (corresponding to the MSSM particle content), the three couplings convergeprecisely at MGUT ≈ 2 × 1016 GeV with αGUT ≈ 1/25, giving τp ∼ 6 × 1034 years forp → e+π0 — consistent with the Super-Kamiokande bound (τp > 1.6 × 1034 years) andwithin reach of Hyper-Kamiokande. The numerical MGUT is derived from the runningcoupling equations, not from an independent R(Dst) calibration; the Cohesion UFTprovides the geometric interpretation of why these density thresholds exist where theydo