Source labels openChecked July 26, 2026

Green's Open Problem 9

Problem 9 (iii): is $r_4(\mathbf{F}_5^n) \ll N^{1-c}$ , where $N=5^n$ ?

Combinatorics AMS 5

Mathematical statement

Problem 9 (iii): is $r_4(\mathbf{F}_5^n) \ll N^{1-c}$ , where $N=5^n$ ?

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_9_iii

Canonical source

Complete statement target, proof intentionally absentLean 4

theorem green_9_iii : answer(sorry) ↔    ∃ c > (0 : ℝ), (fun (n : ℕ) ↦ ((Finset.univ : Finset (𝔽₅ n)).maxAPFreeCard 4 : ℝ))      ≪ fun (n : ℕ) ↦ ((5 : ℝ) ^ n) ^ (1 - 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, Ben. "100 open problems." (2024).background