Problem detail · source-aware
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The Lonely Runner Conjecture of Wills and Cusick states that among $k+1$ runners at distinct constant speeds on a unit circle, each runner is at some time at distance at least $1/(k+1)$ from all others. Following Rosenfeld's computer-assisted proof for 8 runners, the paper refines his approach with a sieve and proves the cases of 9 and 10 runners.
The source statement is reproduced for indexing with attribution. Mathematical correctness requires domain-expert or mechanical review. VibeMath has not independently audited statement fidelity, correctness, priority, or novelty.
"We employed OpenAI GPT-5 to assist with code generation, especially in low-level optimization" of the C++ verification that constitutes the proof; code and result receipts are public.
Provider: OpenAI · Prompt public: unknown · Independence: unknown
A computer-assisted proof in the Rosenfeld tradition; the code and receipts are public but no independent rerun or review has appeared.
Correctness: unknown · statement fidelity: unaudited · peer review: none
Settles 9 and 10 runners only; the general conjecture remains open.
Source-reported tools: computation.
Independent: unknown · difference confidence: 0
VibeMath has not independently audited the mathematical statement, proof, or novelty claim.