  One of the most significant advances by NASA's ${\mathit Kepler}$ Mission was
the discovery of an abundant new population of highly irradiated planets with
sizes between the Earth and Neptune. Subsequent analysis showed that at ~1.5
Earth radii there is a transition from a population of predominantly rocky
super-Earths to non-rocky sub-Neptunes, which must have substantial volatile
envelopes. Determining the origin of these highly irradiated rocky planets will
be critical to our understanding of low-mass planet formation and the frequency
of potentially habitable Earth-like planets. These short-period rocky
super-Earths could simply be the stripped cores of sub-Neptunes, which have
lost their envelopes due to atmospheric photo-evaporation or other processes,
or they might instead be a separate population of inherently rocky planets,
which never had significant envelopes. Using models of atmospheric
photo-evaporation, we show that if most bare rocky planets are the evaporated
cores of sub-Neptunes then the transition radius should decrease as surveys
push to longer orbital periods, since on wider orbits only planets with smaller
less massive cores can be stripped. On the other hand, if most rocky planets
formed after their disks dissipate then these planets will have formed without
initial gaseous envelopes. In this case, we use N-body simulations of planet
formation to show that the transition radius should increase with orbital
period, due to the increasing solid mass available in their disks. Moreover, we
show that distinguishing between these two scenarios should be possible in
coming years with radial velocity follow-up of planets found by TESS. Finally,
we discuss the broader implications of this work for current efforts to measure
$\eta_{\mathrm{\oplus}}$, which may yield significant overestimates if most
rocky planets form as evaporated cores.
