  We consider a minimal non-supersymmetric $SO(10)$ Grand Unified Theory (GUT)
model that can reproduce the observed fermionic masses and mixing parameters of
the Standard Model. We calculate the scales of spontaneous symmetry breaking
from the GUT to the Standard Model gauge group using two-loop renormalisation
group equations. This procedure determines the proton decay rate and the scale
of $U(1)_{B-L}$ breaking, which generates cosmic strings and the right-handed
neutrino mass scales. Consequently, the regions of parameter space where
thermal leptogenesis is viable are identified and correlated with the fermion
masses and mixing, the neutrinoless double beta decay rate, the proton decay
rate, and the gravitational wave signal resulting from the network of cosmic
strings. We demonstrate that this framework, which can explain the Standard
Model fermion masses and mixing and the observed baryon asymmetry, will be
highly constrained by the next generation of gravitational wave detectors and
neutrino oscillation experiments which will also constrain the proton lifetime.
