Resolving this universality question would provide a mathematically rigorous foundation for physicists' predictions about mean-field spin glasses at their critical temperature, clarifying whether the Parisi ultrametricity picture persists, simplifies, or breaks down at the transition. It would also likely require new tools in the analysis of critical branching processes and Gaussian multiplicative chaos at the boundary of the L2 phase, advances that would immediately benefit the study of Liouville quantum gravity, random planar maps, and the Riemann zeta function on the critical line where similar log-correlated structures appear.