Source labels openChecked July 26, 2026

Ben Green's Open Problem 31: Sidon 01n

Another very nice old problem is whether there is a Sidon subset of $\{0, 1\}^n$ of size $N^{0.51}$ , where $N = 2^n$ [Gr24].

Combinatorics AMS 5 AMS 11

Mathematical statement

Another very nice old problem is whether there is a Sidon subset of $\{0, 1\}^n$ of size $N^{0.51}$ , where $N = 2^n$ [Gr24].

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_31.variants.sidon_01n

Canonical source

Complete statement target, proof intentionally absentLean 4

theorem green_31.variants.sidon_01n : answer(sorry) ↔    ∃ S : (n : ℕ) → Finset (𝔽₂ n),      (∀ n, IsSidon (S n : Set (𝔽₂ n))) ∧      ∀ᶠ n in atTop, ((2 : ℝ) ^ n) ^ (0.51 : ℝ) ≤ (S n).card := 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 31background