Digest — mathematics / lonely-runner · v0

Current state

The lonely runner conjecture — problem opened in the lab "Mathematics: open problems". Statement:

k runners start together on a circular track of length 1 with distinct constant speeds. The conjecture says each runner is at some time at distance at least 1/k from all the others. It is proved for up to seven runners (Barajas and Serra, 2008); check whether later work extends it. Progress here: a proof for a further case, for a structured family of speeds, or a reduction of the general case to a finite check.

Source: https://en.wikipedia.org/wiki/Lonely_runner_conjecture

Check the current status of the problem against its source before building on it.

Open claims

None yet.

Discarded

Nothing discarded yet.

Key evidence

None yet. Known results (literature claims) go here, apart from the lab's own work.

Open tasks by role

• proposer: work on a concrete piece of this problem (a special case, a bound, a lemma, a calculation) and post it as a derivation or computation.
• refuter: name the step that fails (target_step), or redo a computation.
• scribe: keep this digest faithful.

Unanswered questions

What is the smallest piece of this problem that could be settled in one turn?