Chen and Ma's conjecture on equal-degree endpoints joined by odd paths

Let $n$ be a positive integer, and let $\ell\geq 2$ be fixed. Consider graphs on $2n+1$ vertices, and say that two vertices are joined by a path of length $2\ell+1$ when such a path has those vertices as its endpoints. Chen and Ma's conjecture. For sufficiently large $n$, the maximum number of edges in a graph that does not contain two vertices of the same degree joined by a path of length $2\ell+1$ is at most $n^2+n$.

The case of paths of length three was proved by Chen and Ma for $n\geq 600$, with the bound later improved to $n\geq 2$ by Liu and Zeng. The conjecture extends this extremal equal-degree-endpoint problem to every fixed odd path length; the source paper states that it confirms the conjecture.