EditorialDiophantine approximation
Lonely Runner Conjecture
A geometric question about runners with distinct speeds becoming isolated on a circular track.
Mathematical statement
For runners with distinct constant speeds on a unit circle, each runner is at circular distance at least from every other runner at some time.
Statement source: Therefore editorial statement
Statement terms: Source-specific
Editorial wording by Therefore. No statement reuse license is granted.
Statement artifacts, not proofs
These records expose exact Lean propositions and statement-only wrappers. Defining a proposition does not supply a proof of it. A placeholder-bearing target also contains no proof. Elaboration checks syntax and types; it does not certify that a formalization perfectly captures every nuance of the informal problem.
Pinned Lean formulation 1
LonelyRunnerConjecture.lonely_runner_conjecture
theorem lonely_runner_conjecture (n : ℕ) (speed : Fin n ↪ ℝ) (lonely : Fin n → ℝ → Prop) (lonely_def : ∀ r t, lonely r t ↔ ∀ r2 : Fin n, r2 ≠ r → dist (t * speed r : UnitAddCircle) (t * speed r2) ≥ 1 / n) (r : Fin n) : ∃ t ≥ 0, lonely r t := by sorry- Statement source
- Formal Conjectures
- Lean version
- v4.27.0
- Placeholder
- Present; no proof artifact
- Source evidence
- Pinned source index
- Fidelity review
- Community formulation
References