  We present a state-of-the-art calculation of the isovector quark helicity
Bjorken-$x$ distribution in the proton using lattice-QCD ensembles at the
physical pion mass. We compute quasi-distributions at proton momenta $P_z \in
\{2.2, 2.6, 3.0\}$~GeV on the lattice, and match them systematically to the
physical parton distribution using large-momentum effective theory (LaMET). We
reach an unprecedented precision through high statistics in simulations,
large-momentum proton matrix elements, and control of excited-state
contamination. The resulting distribution with combined statistical and
systematic errors is in agreement with the latest phenomenological analysis of
the spin-dependent experimental data; in particular, $\Delta \bar{u}(x)>\Delta
\bar{d}(x)$.
