  Monte Carlo simulations of neutron-rich matter of relevance to the inner
neutron-star crust are performed for a system of A=5,000 nucleons. To determine
the proton fraction in the inner crust, numerical simulations are carried out
for a variety of densities and proton fractions. We conclude---as others have
before us using different techniques---that the proton fraction in the inner
stellar crust is very small. Given that the purported "nuclear pasta" phase in
stellar crusts develops as a consequence of the long-range Coulomb interaction
among protons, we question whether pasta formation is possible in such
proton-poor environments. To answer this question, we search for physical
observables sensitive to the transition between spherical nuclei and exotic
pasta structures. Of particular relevance is the static structure factor
S(k)---an observable sensitive to density fluctuations. However, no dramatic
behavior was observed in S(k). We regard the identification of physical
observables sensitive to the existence---or lack-thereof---of a pasta phase in
proton-poor environments as an open problem of critical importance.
