Tightness of the quadratic query lower bound

Determine whether the quadratic Robertson–Webb lower bound for complete envy-free cake cutting with arbitrary nonatomic additive valuations is asymptotically tight.

Background

For arbitrary nonatomic additive valuations, the paper compares its single-exponential upper bound with Procaccia’s Ω(n^2) lower bound. The substantial gap between these bounds leaves unresolved whether the quadratic lower bound captures the true worst-case query complexity or whether substantially larger complexity is necessary.