Timely Lonely Runner Conjecture

Ascertain whether for every integer n ≥ 1 there exists a constant N (depending only on n) such that for any set V of n positive speeds, the earliest time t0 at which the origin becomes lonely satisfies t0 ≤ N when times are normalized by the slowest speed.

Background

This conjecture strengthens the Lonely Runner claim by bounding the time to loneliness uniformly in n. It aligns with results that reduce the problem to finitely many bounded-speed instances and has been proven for n ≤ 5.

The problem connects to algorithmic and quantitative aspects of the conjecture, seeking universal temporal bounds independent of particular speed sets.