Gerbner–Palmer's conjecture that paths are Turán-good

Let $F$ be a graph with chromatic number $\chi(F)=k+1$. A graph $H$ is $F$-Turán-good if, for all sufficiently large $n$, the maximum number of copies of $H$ in an $n$-vertex $F$-free graph equals the number of copies of $H$ in the Turán graph $T(n,k)$.

Gerbner–Palmer's conjecture. Every path is $K_{k+1}$-Turán-good for every $k$.

The conjecture asks when the Turán graph is extremal for generalized Turán problems. In this paper, the authors state that they prove the claim for paths, so the conjecture is solved.