Prove the Brown–Erdős–Sós conjecture

Prove the Brown–Erdős–Sós conjecture concerning the asymptotic maximum size of uniform hypergraphs avoiding prescribed configurations of e edges on v vertices.

Background

The Brown–Erdős–Sós conjecture is presented as a major unresolved problem in extremal hypergraph theory. The paper defines f_t(n,v,e) as the largest size of a t-uniform hypergraph on n vertices in which no v vertices span e edges, and recalls known asymptotic results for particular parameter regimes. The conjecture concerns the remaining extremal behavior beyond those established cases.