  In Yang-Mills theory, the cumulants of the na\"ive lattice discretization of
the topological charge evolved with the Yang-Mills gradient flow coincide, in
the continuum limit, with those of the universal definition. We sketch in these
proceedings the main points of the proof. By implementing the gradient-flow
definition in numerical simulations, we report the results of a precise
computation of the second and the fourth cumulant of the $\mathrm{SU}(3)$
Yang-Mills theory topological charge distribution, in order to measure the
deviation from Gaussianity. A range of high-statistics Monte Carlo simulations
with different lattice volumes and spacings is used to extrapolate the results
to the continuum limit with confidence by keeping finite-volume effects
negligible with respect to the statistical errors. Our best result for the
topological susceptibility is $t_0^2\chi=6.67(7)\times 10^{-4}$, while for the
ratio between the fourth and the second cumulant we obtain $R=0.233(45)$.
