The uniform Turán density of the tetrahedron

Abstract

We prove that the uniform Turán density of $K_4^{(3)}$ is equal to $1/2$. Kielak, Král', Lamaison, Liu, Shu, and Wu have recently proved the same result using combinatorial methods, while our proof is Fourier-analytic. This result answers a question of Erdős and Sós from the founding 1982 paper on this topic.