Resolve the case \(d=s-1\) of the modified conjecture

Resolve the case \(d=s-1\) of the modified uniform Erdős–Frankl–Pach conjecture.

Background

The general modified conjecture remains unresolved beyond the cases established in the paper. The authors single out the parameter regime $d=s-1$ as already requiring ideas beyond the methods developed in the paper, making it a concrete unresolved subcase.