Small-$x$ Quark and Gluon Helicity Contributions to the Proton Spin Puzzle

A small-$x$ helicity evolution has been derived in 2016-18 and received an important modification in 2022. This article discusses its general framework and summarizes the recent theoretical developments, including the asymptotic behaviors of helicity PDFs and $g_1$ structure function at small $x$. The latest fits to various polarized scattering data are also discussed. The results from this research program will provide important theoretical inputs for the future polarized small-$x$ measurements at the electron-ion collider (EIC).