Distance Laplacian integrality conjecture for cyclic-group power graphs

Let $n\geq 2$ be an integer, and let $\mathcal{P}(\mathbb{Z}_{n})$ denote the power graph of the cyclic group $\mathbb{Z}_{n}$. Write $\partial_{1}^{L}$ for the relevant distance Laplacian eigenvalue of this graph. The graph is distance Laplacian integral when all its distance Laplacian eigenvalues are integers. Distance Laplacian integrality conjecture. The following statements are equivalent:

1. $\partial_{1}^{L}$ of $\mathcal{P}(\mathbb{Z}_{n})$ is an integer.
2. $\mathcal{P}(\mathbb{Z}_{n})$ is distance Laplacian integral.
3. $n$ is either a prime power or a product of two distinct primes.

This conjecture gives an arithmetic characterization of distance Laplacian integrality for power graphs of finite cyclic groups. The supplied text does not state whether it has been resolved.