The high-mass IMF index, α₃, versus the cloud-core density, ρ_cl (stars+gas). Symbols and lines as in Fig. 2. The gap between the GCs and UCDs seen in Fig. 2 vanishes and the IMF indices, α₃, now form a single sequence as a function of ρ_cl: the IMF index at the high-mass end decreases (the IMF becomes flatter) with increasing density of the objects’ progenitor cloud core. It is canonical (α₃= 2.3) below 9.5 × 10⁴ M_⊙ pc⁻³.