Source labels openChecked July 26, 2026

Ben Green's Open Problem 31: Abelian

It is not known whether, if $G$ is an abelian group of size $n$ , there always exists a Sidon subset of $G$ of size $0.01\sqrt{n}$ [Gr24].

Combinatorics AMS 5 AMS 11

Mathematical statement

It is not known whether, if $G$ is an abelian group of size $n$ , there always exists a Sidon subset of $G$ of size $0.01\sqrt{n}$ [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.abelian

Canonical source

Complete statement target, proof intentionally absentLean 4

theorem green_31.variants.abelian : answer(sorry) ↔    ∀ (G : Type) [AddCommGroup G] [Fintype G],      ∃ S : Finset G, IsSidon (S : Set G) ∧ 0.01 * Real.sqrt (Fintype.card G) ≤ S.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