The Ω-operator in action (Eq. (2), thick solid S-shaped curve, schematic, right ordinate). Its exact shape depends on the cluster volume-density within the half-mass radius, ρ_ecl, and time, t, for stimulated evolution. Multiplying the respective operator by the initial binary population (Kroupa 1995b, thin dotted line) for a cluster with ρ_ecl = 10³ M_⊙   pc^-3, and age, t = 1, 3, and 5 Myr, respectively, results in the three semi-major axis distributions (solid histograms from top to bottom). Most of the evolution has already taken place in the first Myr, where the binary fraction decreases from 100 to 72 percent in this particular cluster. The grey thick dashed line on top of the lowest black solid line is the resulting semi-major axis distribution for a ρ_ecl = 10^3.5 M_⊙   pc^-3 cluster after 1 Myr of stimulated evolution. This shows that two clusters with densities ρ_ecl(1) < ρ_ecl(2) can evolve into the same resulting distribution when we assume t(2) < t(1) is appropriately chosen (owing to the age-density degeneracy). That is, the ρ_ecl(1) cluster at age t(1) is dynamically equivalent to the ρ_ecl(2) cluster at age t(2).