Source labels openChecked July 26, 2026

Ben Green's Open Problem 16

From [Schoen and Sisask] $f(N) \ll N \cdot e^{-c(\log N)^{1/7}}$ .

Combinatorics AMS 5 AMS 11

Mathematical statement

From [Schoen and Sisask] $f(N) \ll N \cdot e^{-c(\log N)^{1/7}}$ .

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_16_upper_bound

Canonical source

Complete statement target, proof intentionally absentLean 4

theorem green_16_upper_bound :    ∃ c > (0 : ℝ), (fun N ↦ (f N : ℝ)) ≪ fun N ↦ (N : ℝ) * exp (-c * (log N) ^ (1 / 7 : ℝ)) := 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

Pinned Formal Conjectures sourceformalization Ben Green's Open Problem 16background