  The Kepler mission enabled us to look at the intrinsic population of
exoplanets within our galaxy. In period-radius space, the distribution of the
intrinsic population of planets contains structure that can trace planet
formation and evolution history. The most distinctive feature in period-radius
space is the radius cliff, a steep drop-off in occurrence between
$2.5-4$R$_\oplus$ across all period ranges, separating the sub-Neptune
population from the rarer Neptunes orbiting within 1 au. Following our earlier
work to measure the occurrence rate of the Kepler population, we characterize
the shape of the radius cliff as a function of orbital period ($10-300$ days)
as well as insolation flux (9500S$_\oplus$ -- 10S$_\oplus$). The shape of the
cliff flattens at longer orbital periods, tracking the rising population of
Neptune-sized planets. In insolation, however, the radius cliff is both less
dramatic and the slope is more uniform. The difference in this feature between
period- and insolation-space can be linked to the effect of EUV/X-ray versus
bolometric flux in the planet's evolution. Models of atmospheric mass loss
processes that predict the location and shape of the radius valley also predict
the radius cliff. We compare our measured occurrence rate distribution to
population synthesis models of photoevaporation and core-powered mass-loss in
order to constrain formation and evolution pathways. We find that the models do
not statistically agree with our occurrence distributions of the radius cliff
in period- or insolation-space. Atmospheric mass loss that shapes the radius
valley cannot fully explain the shape of the radius cliff.
