Abstract Gravitational-wave (GW) detections of binary black hole (BH) mergers have begun to sample the cosmic BH mass distribution. The evolution of single stellar cores predicts a gap in the BH mass distribution due to pair-instability supernovae (PISNe). Determining the upper and lower edges of the BH mass gap can be useful for interpreting GW detections of merging BHs. We use MESA to evolve single, nonrotating, massive helium cores with a metallicity of Z = 10⁻⁵, until they either collapse to form a BH or explode as a PISN, without leaving a compact remnant. We calculate the boundaries of the lower BH mass gap for S-factors in the range S(300 keV) = (77,203) keV b, corresponding to the ±3σ uncertainty in our high-resolution tabulated ¹²C(α,γ)¹⁶O reaction rate probability distribution function. We extensively test temporal and spatial resolutions for resolving the theoretical peak of the BH mass spectrum across the BH mass gap. We explore the convergence with respect to convective mixing and nuclear burning, finding that significant time resolution is needed to achieve convergence. We also test adopting a minimum diffusion coefficient to help lower-resolution models reach convergence. We establish a new lower edge of the upper mass gap as M _lower ≃ 60 − 14 + 32 M _⊙ from the ±3σ uncertainty in the ¹²C(α, γ)¹⁶O rate. We explore the effect of a larger 3α rate on the lower edge of the upper mass gap, finding M _lower ≃ 69 − 18 + 34 M _⊙. We compare our results with BHs reported in the Gravitational-Wave Transient Catalog.