The $K_n'$ formulation of the Lonely Runner Conjecture

For $n\in\mathbb{N}$, let $K_n'$ be the obstruction parameter defined in the paper, and let $\kappa(n)$ be the quantity satisfying

$$K_n'=1-2\kappa(n).$$

The $K_n'$ formulation.

$$K_n'=\frac{n-1}{n+1}$$

for every $n\in\mathbb{N}$. This is stated as equivalent to the Lonely Runner Conjecture through the relation above. It remains open in general.