Source labels openChecked July 26, 2026

Ben Green's Open Problem 2

Let $A \subset \mathbf{Z}$ be a set of $n$ integers. Is there a set $S \subset A$ of size $(\log n)^{100}$ such that the restricted sumset $S \hat{+} S$ is disjoint from $A$ ?

Number theory AMS 11

Mathematical statement

Let $A \subset \mathbf{Z}$ be a set of $n$ integers. Is there a set $S \subset A$ of size $(\log n)^{100}$ such that the restricted sumset $S \hat{+} S$ is disjoint from $A$ ?

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_2

Canonical source

Complete statement target, proof intentionally absentLean 4

theorem green_2 : answer(sorry) ↔    ∀ᶠ n : ℕ in atTop, ∀ A : Finset ℤ, A.card = n →      (maxRestrictedSumAvoidingSubsetSize A : ℝ) ≥ (Real.log n) ^ 100 := 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 Green, Ben. "100 open problems." (2024).background