Source labels openChecked July 26, 2026

Ben Green's Open Problem 77

Given $n$ points in the unit disc, must there be a triangle of area at most $n^{-2+o(1)}$ determined by them?

Combinatorics AMS 5 AMS 52

Mathematical statement

Given $n$ points in the unit disc, must there be a triangle of area at most $n^{-2+o(1)}$ determined by them?

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_77

Canonical source

Complete statement target, proof intentionally absentLean 4

theorem green_77 :    answer(sorry) ↔    ∃ (o : ℕ → ℝ), Tendsto o atTop (𝓝 0) ∧      α ≪ fun n ↦ n ^ (-2 + o n) := 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 77background