The importance of studying processes involving cumulative-proton production stems from their direct relation to the formation of multiquark configurations, so-called fluctons, in a nucleus owing to nucleondensity fluctuations in which two or more nucleons occur at a distance shorter than 1 fm from one another. According to [1], multiquark configurations may arise in two different physics patterns. The first, caused by a fluctuation of the target-nucleus density, is referred to as a cold model, while the second, associated with nuclear-matter compression occurring under the effect of an incident hadron or a projectile nucleus and leading to the formation of dense quark bags, is called a hot model. It should be noted that, in early interpretations, the production of cumulative protons was related to the Fermi momenta of nucleons. However, the calculations that took into account the Fermi momentum of nucleons [2] showed that the spectrum of fast ( p> 500 MeV/c) cumulative protons cannot be described in this way. In the present study, we examine new features of the process of cumulative-proton production—in particular, we analyze the behavior of the mean multiplicity of cumulative protons as a function of the charge and mass numbers of the target nucleus. Previously, our group studied [3–5] cumulativeproton production in π −12 С, pС, 4 НеС, СС, 16 Op, and p 20 Ne collisions at primary energies in the range 3–300 GeV and, on the basis of a vast statistical data sample, confirmed the universal regularity that the slope parameter of inclusive cross sections for cumulative protons in the cumulative number β is independent of the primary energy and mass of the incident particle or nucleus. It was shown that the fraction of events involving cumulative-proton production on a carbon nucleus is sensitive to the