Where is the lower edge of the pair-instability mass gap?

Pair-instability and pulsational pair-instability supernovae predict no black holes from single-star collapse between $M_{\mathrm{low}} \sim 45 \text{ to } 65\,M_{\mathrm{sun}}$ and $M_{\mathrm{high}} \sim 120 \text{ to } 130\,M_{\mathrm{sun}}$, with $M_{\mathrm{low}}$ sensitive to the $12\mathrm{C}(\alpha,\gamma)16\mathrm{O}$ rate and rotation. Determine $M_{\mathrm{low}}$ and whether gap events (GW190521; GW231123 with components $\sim 100 \text{ to } 140\,M_{\mathrm{sun}}$ and spins $\sim 0.8 \text{ to } 0.9$) are hierarchical mergers, stellar-merger products, or evidence of a higher gap edge. Answer: inferred $M_{\mathrm{low}}$ and a classification of gap events.

A population-level detection of the drop in the mass function together with spin signatures that separate hierarchical from first-generation black holes.