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Stellar evolution predicts the existence of a mass gap for black holeremnants produced by pair-instability supernova dynamics, whose lower and upperedges are very uncertain. We study the possibility of constraining the locationof the upper end of the pair-instability mass gap, which is believed to appeararound ${m_\text{min}} \sim130M_\odot$, using gravitational wave observationsof compact binary mergers with next-generation ground-based detectors. Whilehigh metallicity may not allow for the formation of first-generation blackholes on the "far side" beyond the gap, metal-poor environments containingPopulation III stars could lead to such heavy black hole mergers. We show that,even in the presence of contamination from other merger channels,next-generation detectors will measure the location of the upper end of themass gap with a relative precision close to $\Delta{m_\text{min}}/{m_\text{min}} \simeq 4\% (N_\text{det}/100 )^{-1/2}$ at 90%C.L., where $N_\text{det} $ is the number of detected mergers with both membersbeyond the gap. These future observations could reduce current uncertainties innuclear and astrophysical processes controlling the location of the gap.

Beyond the far side: Observing black hole mergers beyond the pair-instability mass gap with next-generation gravitational wave detectors