  We present state-of-the-art results from a lattice QCD calculation of the
nucleon axial coupling, $g_A$, using M\"obius Domain-Wall fermions solved on
the dynamical $N_f = 2 + 1 + 1$ HISQ ensembles after they are smeared using the
gradient-flow algorithm. Relevant three-point correlation functions are
calculated using a method inspired by the Feynman-Hellmann theorem, and
demonstrate significant improvement in signal for fixed stochastic samples. The
calculation is performed at five pion masses of $m_\pi\sim \{400, 350, 310,
220, 130\}$~MeV, three lattice spacings of $a\sim\{0.15, 0.12, 0.09\}$~fm, and
we do a dedicated volume study with $m_\pi L\sim\{3.22, 4.29, 5.36\}$. Control
over all relevant sources of systematic uncertainty are demonstrated and
quantified. We achieve a preliminary value of $g_A = 1.285(17)$, with a
relative uncertainty of 1.33\%.
