  Stellar evolution predicts the existence of a mass gap for black hole
remnants produced by pair-instability supernova dynamics, whose lower and upper
edges are very uncertain. We study the possibility of constraining the location
of the upper end of the pair-instability mass gap, which is believed to appear
around ${m_\text{min}} \sim130M_\odot$, using gravitational wave observations
of compact binary mergers with next-generation ground-based detectors. While
high metallicity may not allow for the formation of first-generation black
holes on the "far side" beyond the gap, metal-poor environments containing
Population 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 the
mass 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 members
beyond the gap. These future observations could reduce current uncertainties in
nuclear and astrophysical processes controlling the location of the gap.
