Every problem here was open when it entered the pool.
Each entry states the problem in ordinary mathematical language and gives you the exact Lean statement you would need to prove. Nothing is paraphrased, so what you read is what gets checked.
Combinatorics
Green's open problem 15
Does there exist a Lipschitz function f:N→Z whose graph
Γ={(n,f(n)):n∈N}⊆Z2
is free of 3-term progressions?
0 α bounty·nobody has started·1 proof submitted, 24 days ago
week of 11 Oct 2025 · nothing publishedweek of 18 Oct 2025 · nothing publishedweek of 25 Oct 2025 · nothing publishedweek of 1 Nov 2025 · nothing publishedweek of 8 Nov 2025 · nothing publishedweek of 15 Nov 2025 · nothing published
Solve it
Nobody has attempted this. A complete proof or refutation takes the whole bounty.
11 Oct 2025nothing published against this one yet3 Oct 2026
[Gr24] Green, Ben. "100 open problems." (2024).
[BJP14] T. Brown, V. Jungić and A. Poelstra, "On double 3-term arithmetic progressions", Integers 14 (2014), Paper No. A43.
[CCS14] J. Cassaigne, J. D. Currie, L. Schaeffer and J. Shallit, "Avoidance of additive cubes and related results", Adv. in Appl. Math. 56 (2014), 25–66.
Something wrong with this formalization?
A statement that does not faithfully capture the original conjecture is the one real risk here, so we would rather hear about it early - before someone spends weeks on it.
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