Source labels openChecked July 26, 2026

Green's Open Problem 51: One Half

Suppose that $A \subset \mathbb{F}_2^n$ has density $\alpha > 1/2 - C/\sqrt{n}$ . Does $A + A$ contain a subspace of co-dimension $O_C(1)$ ? [Sa11, Question 5.1]

Combinatorics AMS 5 AMS 11

Mathematical statement

Suppose that $A \subset \mathbb{F}_2^n$ has density $\alpha > 1/2 - C/\sqrt{n}$ . Does $A + A$ contain a subspace of co-dimension $O_C(1)$ ? [Sa11, Question 5.1]

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_51.one_half

Canonical source

Complete statement target, proof intentionally absentLean 4

theorem green_51.one_half :    answer(sorry) ↔ ∀ (k : ℝ), 0 < k →      ∃ (c : ℕ), ∀ᶠ (n : ℕ) in atTop,        ∀ (α : ℝ), α > (1/2 : ℝ) - k / sqrt (n : ℝ) → α ≤ 1 →          n ≤ guaranteedMaxCosetDim n α + 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

Pinned Formal Conjectures sourceformalization Green's Open Problemsbackground