With reference to the Post "Another Theorem By Changing The Question" dated 30 Dec 2022.
Adding a reference runner with arbitrary speed is like rotating the path at that speed with all the runners on it. As far as the runners are concern nothing changes. But there is this strange guy by the track, seems to be going backwards. Never seen before, must be new, a NPC!
Initiatively the proof is flawed. It could be that this added \(n+1\) runner does not start at the origin, but does that matter when his relative speed is zero.
This added runner must be half way between the lonely runner and the runner closes to him. That position may not be the starting point. But he is stationary always. Can the whole system be rotated, rotational invariant? The situation can stop and every body runs nothing should change.
What gives? Starting position.
