  The recently revised small-$x$ helicity evolution, resumming the
double-logarithmic factor, $\alpha_s\ln^2(1/x)$, allows for the study of
helicity distributions of quarks and gluons at small Bjorken $x$, corresponding
to high center-of-mass energy. In this work, we calculate the moderate-$x$
initial conditions in the regime, $\alpha_s \ln^2(1/x)\sim 1$, for the
small-$x$ helicity evolution using a light-front valence quark model of the
proton, which provides additional physical information about the target. The
perturbative emission and absorption of a gluon by the valence quarks are also
included. The results, given in Eqs. (35), provide a new set of initial
conditions with a significantly reduced number of free parameters than
conventional models. Consequently, the predictive power of small-$x$ helicity
evolution is expected to improve once the initial conditions from this work are
incorporated.
