Rifford's Timely Lonely Runner Conjecture

For a positive speed set $V=\{v_1,\dots,v_n\}$, let $t_0$ be the smallest time in $(0,1)$ at which the origin is lonely, and normalize time by the slowest speed by setting

$$\hat t_0=t_0v_1.$$

Timely Lonely Runner Conjecture. For every $n\in\mathbb{N}$ there is $N$ such that, for every $n$-set $V$ of positive speeds,

$$\hat t_0\leq N.$$

The conjecture strengthens the Lonely Runner Conjecture by asserting a bound depending only on the number of runners. The source states that Rifford proved it for $n\leq5$; its general case remains open.