## 1 Introduction  
Although experiments with cosmic rays simultaneously make use of several models of interactions of high-energy hadrons with the nuclei of air atoms and the subsequent development in the atmosphere of so-called extensive air showers (EAS) (nuclear-electromagnetic cascades, initiated by protons and the nuclei of primary cosmic radiation (PCR) of ultrahigh energies), none of them can accurately reproduce the entire set of experimentally observed EAS characteristics. In addition, some results accumulated in high-mountain and balloon X-ray emulsion chambers (XRECs) have not yet been explained. A decrease in the absorption rate of high-energy (\(\sim\)n\(\cdot\)10 TeV) hadronic cascades in the lead absorber of the so-called Big Ionization Calorimeter (BIC) [1; 2; 3; 4; 5] with an area of 36 m\({}^{2}\) was first discovered about fifty years ago at the Tien Shan High-mountain Scientific Station (3340 m a.s.l.) in experiments with EAS. The BIC contained a lead absorber with a thickness of 850 g/cm\({}^{2}\), which corresponds approximately to five mean free paths for proton interaction in lead (see Figure 1, [6]). Due to the large BIC's thickness, this unique experiment made it possible to study the hadronic component of EAS in detail and showed that the absorption length \(L(E_{h})\) of the hadron component and the corresponding ionization in the BIC absorber in EAS cores intensifieswith the increase in hadron energy \(E_{h}\) in the calorimeter. Figure 1 (Figure 2, [6]) shows experimental data (crossed circles). In order to explain the effect, a hypothesis on the existence of a so-called long-flying component was proposed. Later, after the discovery of charmed particles, it was shown that the above-described effect can be explained by assuming that the cross section for the production of charmed particles by hadrons reaches \(\sim\)30% of the inelastic proton-nucleus cross section. Figure 1 (Figure 2, [6]) also shows Monte Carlo simulation results [7] obtained using two versions of the charm production cross section, namely, \(\sigma_{h\to c}=0\) (empty circles) and \(\sigma_{h\to c}\approx 0.3\cdot\sigma_{h\text{-}nucleus}\) (empty squares). At the same time, charmed particles could carry away a significant fraction of the energy of interacting hadrons (see the simulation results shown in Figure 1). In high-mountain (4300 m above sea level) experiments with XRECs carried out by the _Pamir_ Collaboration [8], an unusual deceleration in the absorption of hadrons with energies \(E_{h}\gtrsim 10\) TeV was found at great depths in homogeneous lead XRECs 110 cm thick [9] (see Figure 3, [6]). In the XREC's upper part (\(t<78\)_radiation lengths, r.l._), the distribution of hadron-initiated cascade origin depths obeys the standard exponential law with index \(\lambda_{absq}^{(1)}=212\pm 19\text{g/ cm}^{2}\). However, Figure 2 (Figure 4, [6]) shows that, at more significant XREC depths (\(t>78\)_r.l._), the interaction-depth distribution changes, and the index increases to \(\lambda_{abs}^{(2)}=310\pm 36\text{ g/cm}^{2}\). Both phenomena were explained as a consequence of the high values of the cross section for the production of leading charmed hadrons at energies \(E_{Lab}\sim 50\) TeV in the Lab system. In order to explain the experimental data, both for overly intense ionization in the deep hadron calorimeter and for the overly flat distribution of hadron interaction depths in the deep XREC, it was necessary to assume that the cross section for the production of charmed particles in the fragmentation region of hadron interactions (\(\tau_{Lab}\gtrsim 0.01\)) rapidly increases with energy up to \(\sigma_{c\overline{c}}^{(NN)}\approx 2-4\text{ mb}\) at \(E_{Lab}\gtrsim 20\) TeV [6; 7; 9; 10]. During the above-mentioned experiments, the values of charm-generation cross sections measured on accelerators were equal to a few tens of microbarns. Therefore, the results obtained in cosmic rays showed that the cross section of charm generation should increase rapidly with increasing energy.