Gan–Loh–Sudakov triangle extremal conjecture

Let $G$ be a graph on $n$ vertices with maximum degree $d$. Write

$$n=q(d+1)+r,\qquad 0\le r\le d.$$

Here $q$ and $r$ are the quotient and remainder in the division of $n$ by $d+1$. Gan–Loh–Sudakov's conjecture. The number of triangles in $G$ is at most

$$q{d+1 \choose 3}+{r \choose 3}.$$

The paper's abstract states that this conjecture is resolved by the paper itself, so the claimed bound is a theorem rather than an open conjecture.