Separating hypergraph Turán densities

Abstract Determining the Turán densities of hypergraphs is a notoriously difficult problem at the core of combinatorics. Although Turán posed this problem in 1941, the value of remains unknown for all . Prior to this work, it was not even known whether holds for general and , and the best‐known bounds on are far from implying anything close to this. We prove that , for all , and provide general criteria to distinguish the Turán densities of two hypergraphs. As a corollary, we also obtain that , for all . For , this was previously proved by Markström, answering a question by Erdős.