Repeated black-hole mergers in dense stellar clusters are a plausible mechanism to populate the predicted gap in black hole masses due to the pair-instability supernova process. These hierarchical mergers carry distinct spin characteristics relative to first-generation black holes. We introduce an astrophysically motivated model in the joint space of effective inspiral and precessing spins, which captures the dominant spin dynamics expected for hierarchical mergers. We find decisive evidence for a transition at m_{1}=46.2_{-7.2}^{+12.6}M_{⊙}, above which the population is nearly entirely hierarchical, a location consistent with the anticipated onset of the pair-instability gap. We also infer a global peak in the hierarchical merger rate at m_{1}=15.7_{-1.1}^{+3.2}M_{⊙}. The existence of low- and high-mass subpopulations of higher-generation black holes suggests the contribution of both near-solar-metallicity and metal-poor star clusters to the hierarchical merger population. Our results reinforce the growing evidence for detailed, mass-dependent substructure in the spin distribution of the binary black hole population.