  The interior structure of an exoplanet is hidden from direct view yet likely
plays a crucial role in influencing the habitability of the Earth analogues.
Inferences of the interior structure are impeded by a fundamental degeneracy
that exists between any model comprising more than two layers and observations
constraining just two bulk parameters: mass and radius. In this work, we show
that although the inverse problem is indeed degenerate, there exists two
boundary conditions that enables one to infer the minimum and maximum core
radius fraction, CRFmin and CRFmax. These hold true even for planets with light
volatile envelopes, but require the planet to be fully differentiated and that
layers denser than iron are forbidden. With both bounds in hand, a marginal CRF
can also be inferred by sampling in-between. After validating on the Earth, we
apply our method to Kepler-36b and measure CRFmin = (0.50 +/- 0.07), CRFmax =
(0.78 +/- 0.02), and CRFmarg = (0.64 +/- 0.11), broadly consistent with the
Earth's true CRF value of 0.55. We apply our method to a suite of hypothetical
measurements of synthetic planets to serve as a sensitivity analysis. We find
that CRFmin and CRFmax have recovered uncertainties proportional to the
relative error on the planetary density, but CRFmarg saturates to between 0.03
and 0.16 once delta rho/rho drops below 1-2 per cent. This implies that mass
and radius alone cannot provide any better constraints on internal composition
once bulk density constraints hit around a per cent, providing a clear target
for observers.
