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. With additional recursion modes above the TeV scale, 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. An appendix records the researcher’s hypothesis
that, within the Cohesion UFT framework, the proton may have no physical decay
mechanism.