Contributor workspace
Sign in to claim tasks, verify results and earn reputation. Browsing is open to everyone.
Sign inRosenfeld (arXiv:2509.14111, September 2025) proves the conjecture for 8 runners with a computer verification built on bounds for a minimal counterexample. Trakulthongchai (arXiv:2511.22427, November 2025) refines the method with a sieve and proves 9 and 10 runners; Rosenfeld separately proves 9 (arXiv:2512.01912, December 2025). Sungkawichai and Trakulthongchai (arXiv:2604.23906, April 2026; version 2 on 1 September 2026) prove 11, 12 and 13 runners. These papers state the conjecture with one runner fixed at speed 0 and k moving runners, so their k = 10, 11, 12 correspond to 11, 12 and 13 runners in the Formal Conjectures statement, which counts every runner.
The 8 to 10 runner cases have more than one independent write-up, and the 9 and 10 paper reports a journal version (its v2 comment); the 11 to 13 runner cases rest on one preprint. None has a Lean-checked proof, and no independent rerun of the searches was found.
Verification broken into steps anyone can take. Pick an open one, do it, and submit what you found below. Matching how a check is settled earns +8; catching a failure earns +20.
Reproduce each case with the authors' code or an independent implementation, for the finite-checking reduction of Tao and Malikiosis–Santos–Schymura.
Two separate computer-assisted proofs of the 9-runner case were posted four days apart (Trakulthongchai on 27 November 2025, refining Rosenfeld's 8-runner method, and Rosenfeld on 1 December 2025) and reach the same conclusion.
The Combinatorics committee has no members yet, so this claim can be machine-checked and verified by anyone but not committee-reviewed.
No verifications yet.
Sign in to verify.
The Formal Conjectures statement is in place; a Lean proof of a fixed case would turn a preprint into a checked result.