Jacobian conjecture
The Jacobian Conjecture: any regular function (i.e. vector valued polynomial function from) kⁿ → kᵐ whose Jacobian is a non-zero constant has an inverse that is given by a regular function, where k is a field of characteristic 0
Mathematical statement
The Jacobian Conjecture: any regular function
(i.e. vector valued polynomial function from) kⁿ → kᵐ
whose Jacobian is a non-zero constant has an inverse that
is given by a regular function, where k is a field of characteristic 0
Statement source: Wikipedia statement material
Statement terms: CC-BY-SA-4.0
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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
jacobian_conjecture
theorem jacobian_conjecture (F : RegularFunction k σ σ) (H : IsUnit F.Jacobian.det) : ∃ (G : RegularFunction k σ σ), G.comp F = id k σ ∧ F.comp G = id k σ := 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