  Motivated by the direct discovery of gravitational waves (GWs) from black
holes and neutron stars, there is a growing interest in investigating GWs from
other sources. Among them, GWs from cosmic strings are particularly fascinating
since they naturally appear in a large class of grand unified theories (GUTs).
Remarkably, a series of pulsar-timing arrays (PTAs) might have already observed
GWs in the nHz regime, hinting towards forming a cosmic string network in the
early universe, which could originate from phase transition associated with the
seesaw scale emerging from GUT. In this work, we show that if these
observations from PTAs are confirmed, GWs from cosmic strings, when combined
with fermion masses, gauge coupling unification, and proton decay constraints,
the parameter space of the minimal SO(10) GUT becomes exceedingly restrictive.
The proposed minimal model is highly predictive and will be fully tested in a
number of upcoming gravitational wave observatories.
