The process of pion production in AA collisions at central rapidities with a large transverse momentum in the region kinematically forbidden for reactions with free nucleons (cumulative production) is analyzed. It is shown that in this region the dominant contribution is from the flucton–flucton interaction, leading to the emission of a quark, which then fragments into a pion. The asymptotic behavior of the inclusive cross-section at high initial energies near the kinematic boundary of the process is calculated and quark counting rules for the inclusive cross-section in this region are formulated. The found patterns can be tested in the MPD and SPD experiments at the NICA collider.