All open problems
Source labels openChecked July 26, 2026

Green's Open ProblemsCombinatorics

Green's Open Problem 25: Upper

We conjecture that the best-known upper bound can be lowered.

Mathematical statement

We conjecture that the best-known upper bound can be lowered.

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_25.upper

Canonical source
Complete statement target, proof intentionally absentLean 4
theorem green_25.upper :    let ans := (answer(sorry) :   )    (ᶠ N in atTop, 1  ans N  ans N  N)  -- Ensure k is a valid partition size    (fun N => (ans N : )) =o[atTop] bestUpper     ¬ ᶠ N in atTop, Property25 (ans N) 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