Running Couplings and Grand Unification in the Cohesion Unified Field Theory

The running of the Standard Model coupling constants with energy scale is one of
the most precise predictions of quantum field theory. In the Cohesion Unified Field
Theory, running couplings are not an artefact of virtual particle loops: they are the
density-dependence of the recursion frequencies ωn(Dst) of the three recursion modes.
At higher probe energy, the recursion medium is sampled at higher effective density; the
recursion frequencies change with density; and therefore the coupling strengths change
with energy. The one-loop beta function coefficients bi are identified as the logarithmic
derivatives of the recursion frequency ratios with respect to the density-state variable.
The near-convergence of the three Standard Model couplings at ∼ 1014–1016 GeV is
interpreted as the approach toward a common recursion frequency threshold DGUT at
which the n = 2, n = 6, and three-slip-phase recursion modes become degenerate. At
DGUT, the distinction between quarks and leptons dissolves: fractional closures and full
closures become equivalent when all recursion mode frequencies are equal. The GUT
group is the full phase rotation symmetry of the recursion medium at DGUT. The exact
density at which unification occurs and the precise identification of the GUT group are
open problems requiring the full R(Dst) calibration.