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 UFT
and established that MGUT is the density threshold DGUT at which all three recursion
mode frequencies become equal. This paper derives MGUT numerically and calculates
the resulting proton decay lifetime. The calculation uses the one-loop renormalisation
group equations — identified in the running couplings paper as the density-dependence
of the recursion mode frequencies — with the Standard Model particle content below the
electroweak scale and the additional recursion modes required for exact unification above
it. The Standard Model alone gives near-unification at ∼ 1014–1016 GeV but the three
couplings 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 the
TeV scale (corresponding to the MSSM particle content), the three couplings converge
precisely at MGUT ≈ 2 × 1016 GeV with αGUT ≈ 1/25, giving τp ∼ 6 × 1034 years for
p → e
+π
0 — consistent with the Super-Kamiokande bound (τp > 1.6 × 1034 years) and
within reach of Hyper-Kamiokande. The numerical MGUT is derived from the running
coupling equations, not from an independent R(Dst) calibration; the Cohesion UFT
provides the geometric interpretation of why these density thresholds exist where they
do