Source labels openChecked July 26, 2026

Green's Open Problem 36

Do the following exist, for arbitrarily large $n$ ? An abelian group $H$ with $|H| = n^{2+o(1)}$ , together with subsets $A_1, ..., A_n, B_1, ..., B_n$ satisfying $|A_i||B_i| \ge n^{2-o(1)}$ and $|A_i + B_i| = |A_i||B_i|$ , such that the sets $A_i + B_i$ are d...

Combinatorics AMS 5 AMS 20

Mathematical statement

NOTE: according to [CKS05, 4.1], the conditions should be $A_i + B_j$ disjoint from $A_j + B_k$ for $i \neq k$ . See green_36.variants.cks05.

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_36

Canonical source

Complete statement target, proof intentionally absentLean 4

theorem green_36 :    answer(sorry) ↔      ∀ ε > (0 : ℝ), ∃ᶠ n in atTop,        ∃ (H : Type) (_ : AddCommGroup H) (_ : Finite H) (A B : Fin n → Finset H),          (n : ℝ) ^ (2 - ε) ≤ Nat.card H ∧ Nat.card H ≤ (n : ℝ) ^ (2 + ε) ∧          (∀ i, (n : ℝ) ^ (2 - ε) ≤ (A i).card * (B i).card) ∧          Green36Property A B := 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 Problems #36background