  We develop a framework to relate proton number cumulants measured in
heavy-ion collisions within a momentum space acceptance to the susceptibilities
of baryon number, assuming that particles are emitted from a fireball with
uniform distribution of temperature and baryochemical potential, superimposed
on a hydrodynamic flow velocity profile. The rapidity acceptance dependence of
proton cumulants measured by the HADES Collaboration in $\sqrt{s_{\rm NN}} =
2.4$ GeV Au-Au appears to be consistent with thermal emission of nucleons from
a grand-canonical heat bath, with the extracted baryon number susceptibilities
exhibiting an hierarchy $\chi_4^B \gg -\chi_3^B \gg \chi_2^B \gg \chi_1^B$.
Naively, this could indicate large non-Gaussian fluctuations that might point
to the presence of the QCD critical point close to the chemical freeze-out at
$T \sim 70$ MeV and $\mu_B \sim 850-900$ MeV. However, the description of the
experimental data at large rapidity acceptances becomes challenging once the
effect of exact baryon number conservation is incorporated, suggesting that
more theoretical and experimental studies are needed to reach a firm
conclusion.

High Energy Physics - Phenomenology;Nuclear Experiment;Nuclear Theory