  The radius distribution of small, close-in exoplanets has recently been shown
to be bimodal. The photoevaporation model predicted this bimodality. In the
photoevaporation scenario, some planets are completely stripped of their
primordial H/He atmospheres, whereas others retain them. Comparisons between
the photoevaporation model and observed planetary populations have the power to
unveil details of the planet population inaccessible by standard observations,
such as the core mass distribution and core composition. In this work, we
present a hierarchical inference analysis on the distribution of close-in
exoplanets using forward-models of photoevaporation evolution. We use this
model to constrain the planetary distributions for core composition, core mass
and initial atmospheric mass fraction. We find that the core-mass distribution
is peaked, with a peak-mass of $\sim 4$M$_\oplus$. The bulk core-composition is
consistent with a rock/iron mixture that is ice-poor and ``Earth-like''; the
spread in core-composition is found to be narrow ($\lesssim 16\%$ variation in
iron-mass fraction at the 2$\sigma$ level) and consistent with zero. This
result favours core formation in a water/ice poor environment. We find the
majority of planets accreted a H/He envelope with a typical mass fraction of
$\sim 4\%$; only a small fraction did not accrete large amounts of H/He and
were ``born-rocky''. We find four-times as many super-Earths were formed
through photoevaporation, as formed without a large H/He atmosphere. Finally,
we find core-accretion theory over-predicts the amount of H/He cores would have
accreted by a factor of $\sim 5$, pointing to additional mass-loss mechanisms
(e.g. ``boil-off'') or modifications to core-accretion theory.
