Millennium ProblemsGeneral topology
Poincare: Smooth Dimension Four
The four dimensional case of the smooth version of the conjecture is still open. See [Wang2017].
Mathematical statement
The four dimensional case of the smooth version of the conjecture is still open. See [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_dimension_four
theorem poincare_conjecture.variants.smooth_dimension_four : SmoothConjectureFor 4 := 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