A proof of the rational exponents conjecture

The rational exponents conjecture of Erdős and Simonovits asserts that for every rational $r\in [1,2]$ there exists a graph $H$ such that $\mathrm{e}\mathrm{x}(n,H)=\mathrm{\Theta }(n^r)$. We present a proof of this conjecture claimed by Epoch AI, explaining how it builds upon ideas and methods developed by many researchers.