Source labels openChecked July 26, 2026

Poincare: Smooth Other Cases

It is conjectured that the only values of $n > 4$ for which the smooth version of the conjecture holds are $n = 5, 6, 12, 56, 61$ . See Conjecture 1.17 in [Wang2017].

General topology AMS 54 AMS 57

Mathematical statement

It is conjectured that the only values of $n > 4$ for which the smooth version of the conjecture holds are $n = 5, 6, 12, 56, 61$ . See Conjecture 1.17 in [Wang2017].

Statement source: Millennium 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

poincare_conjecture.variants.smooth_other_cases

Canonical source

Complete statement target, proof intentionally absentLean 4

theorem poincare_conjecture.variants.smooth_other_cases (n : ℕ) (hn : n > 4)    (hn' : n ∉ SmoothTrueValues) : ¬ SmoothConjectureFor 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 Miln2022background Wang2017background mo296171background