  The Standard Model, extended with three right-handed (RH) neutrinos, is the
simplest model that can explain light neutrino masses, the baryon asymmetry of
the Universe, and dark matter (DM). Models in which RH neutrinos are light are
generally easier to test in experiments. In this work, we show that, even if
the RH neutrinos are super-heavy ($M_{i=1,2,3}>10^9$ GeV) -- close to the Grand
Unification scale -- the model can be tested thanks to its distinct features on
the stochastic Gravitational Wave (GW) background. We consider an early
Universe filled with ultralight primordial black holes (PBH) that produce a
super-heavy RH neutrino DM via Hawking radiation. The other pair of RH
neutrinos generates the baryon asymmetry via thermal leptogenesis, much before
the PBHs evaporate. GW interferometers can test this novel spectrum of masses
thanks to the GWs induced by the PBH density fluctuations. In a more refined
version, wherein a $U(1)$ gauge symmetry breaking dynamically generates the
seesaw scale, the PBHs also cause observable spectral distortions on the GWs
from the $U(1)$-breaking cosmic strings. Thence, a low-frequency GW feature
related to DM genesis and detectable with a pulsar-timing array must correspond
to a mid- or high-frequency GW signature related to baryogenesis at
interferometer scales.
