Mass scatter diagram (a), and BHMF (b), for a cluster representing the observed Cosmic Gems proto-stellar clusters, following ten simulation runs. In particular, the initial parameters of the gas-rich cluster are M = 3 ∙ 10⁶ M_⊙, r_h = 0.72 pc, ε = 0.35, Z ≃ 0.01 Z_⊙, and τ = 2.9 Myr, resulting in a stellar cluster after gas is depleted with M_★ = 10⁶ M_⊙ and r_h,★ = 1.15 pc. The general trend of the individual BH mass increase is Δm = (m_initial/23 M_⊙)⁶⁷ depicted as the dashed green curve in (a). In (b), α denotes the exponent of each histogram fit.