Ben Green's Open Problem 41: Exists Better Bound
Is there a better bound than the best-known bound from [KrLe25]? This is an existential version of the main problem that does not require providing the bound explicitly.
Mathematical statement
Is there a better bound than the best-known bound from [KrLe25]? This is an existential version of the main problem that does not require providing the bound explicitly.
Statement source: Green's Open Problems statement material
Statement terms: Source-specific
Source-specific terms. Therefore does not assert reuse rights beyond attributed display.
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
green_41.variants.exists_better_bound
theorem green_41.variants.exists_better_bound : answer(sorry) ↔ ∃ C : ℝ, C > 0 ∧ ∃ ε₀ > 0, ∀ ε ∈ Ioc 0 ε₀, ∃ ans : ℝ, (minCopies ε : ℝ) ≤ ans ∧ ans < Real.exp (Real.exp (Real.exp (ε ^ (-C)))) := 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