  The Adler-Weisberger sum rule for the nucleon axial-vector charge, $g_A$,
offers a unique signature of chiral symmetry and its breaking in QCD. Its
derivation relies on both algebraic aspects of chiral symmetry, which guarantee
the convergence of the sum rule, and dynamical aspects of chiral symmetry
breaking---as exploited using chiral perturbation theory---which allow the
rigorous inclusion of explicit chiral symmetry breaking effects due to
light-quark masses. The original derivations obtained the sum rule in the
chiral limit and, without the benefit of chiral perturbation theory, made
various attempts at extrapolating to non-vanishing pion masses. In this paper,
the leading, universal, chiral corrections to the chiral-limit sum rule are
obtained. Using PDG data, a recent parametrization of the pion-nucleon total
cross-sections in the resonance region given by the SAID group, as well as
recent Roy-Steiner equation determinations of subthreshold amplitudes,
threshold parameters, and correlated low-energy constants, the Adler-Weisberger
sum rule is confronted with experimental data. With uncertainty estimates
associated with the cross-section parameterization, the Goldberger-Treimann
discrepancy, and the truncation of the sum rule at $\mathcal{O}(M_\pi^4)$ in
the chiral expansion, this work finds $g_A = 1.248 \pm 0.010 \pm \ 0.007 \pm
0.013$.
