We find the small- asymptotics of the quark helicity distribution in the large- & limit by numerically solving small- evolution equations derived in earlier works, where is the number of quark colors and is the number of quark flavors. Previously, those evolution equations were solved only in the large- limit. We find that oscillates as a function of at small , with the oscillation frequency being dependent on the number of quark flavors, . Our result may account for the apparent oscillation in the strange quark helicity distribution as a function of Bjorken . For , these oscillations disappear; this is why they were not seen in the earlier large- studies. Our work presents the most precise theoretical determination of the small- asymptotics of the quark helicity distribution based on the Wilson line approach to small- evolution. When combined with the future EIC data, our approach should allow for a precise determination of the amount of the proton spin coming from small- partons, thus contributing to the resolution of the proton spin puzzle.