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
[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.
No one has attempted this yet.
Formal statement
Lean type
True ↔ ∃ K f, LipschitzWith K f ∧ {x | ∃ n, (↑n, f n) = x}.IsAPOfLengthFree 3
What you must prove
import FormalConjectures.GreensOpenProblems.«15»
import TaskSupport
namespace Bounty
theorem target : ¬ (fcTypeOfName% "Green15.green_15") := by
sorry
end Bounty
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.