The equality formulation of the Lonely Runner Conjecture

For $n\in\mathbb{N}$, let $\kappa(n)$ be the quantity defined in the paper by

$$\kappa(n)=\inf_{a\in\mathbb{I}^n}\lambda_n(a).$$

The equality formulation.

$$\kappa(n)=\frac{1}{n+1}$$

for all $n\in\mathbb{N}$. This is presented as an equivalent formulation of the Lonely Runner Conjecture, since the paper establishes the upper bound $\kappa(n)\leq1/(n+1)$. The conjecture is open in general.