What does this research mean for the field?

Key algebraic and geometric reductions of the Jacobian Conjecture, including the Bass-Connell-Wright cubic reduction and Wright nilpotent tree inversion, can be formally certified using the Lean 4 interactive theorem prover. Novelty: ClaimNovelty.SYNTHESIS. Consensus alignment: ConsensusAlignment.NEUTRAL.

What question did this study set out to answer?

To examine Smale's 16th Problem on the Jacobian Conjecture by presenting comprehensive algebraic reductions, explicit combinatorial inversion formulas, and machine-checked formal proofs.

August 29, 2026Open Access

On the Jacobian Conjecture and the Nilpotent Tree Inversion of Keller Mappings

View Full Paper

Ask AI

Bookmark

Authors

CNCharles EDOU NZE

Discussion

Member takes

Implication

Formal verification study demonstrates algebraic reductions and tree inversion formulas for Keller mappings in polynomial spaces, highlighting structural equivalences across algebraic geometry.

Key Points

To examine Smale's 16th Problem on the Jacobian Conjecture by presenting comprehensive algebraic reductions, explicit combinatorial inversion formulas, and machine-checked formal proofs.
Evaluated classical reductions and matrix stratifications, including the Bass-Connell-Wright cubic reduction, Drużkowski forms, and the Kontsevich-Dixmier Weyl algebra equivalence.
Derived Wright's combinatorial tree inversion formula based on sums over rooted trees of differential operators under nilpotent Jacobian conditions.
Formally certified the algebraic lemmas, polynomial automorphisms, and inversion formulas using the Lean 4 interactive theorem prover and Mathlib.
Proved that Keller mappings reduce to degree-1 affine bijections in dimension 1 and demonstrated the general equivalence to cubic-homogeneous forms with strictly nilpotent Jacobians.
Verified that Wright's formal inverse series truncates to a finite polynomial with degree bounded by 3^(n-1) under Jacobian nilpotency.
Achieved complete machine verification in Lean 4 with zero additional axioms, zero sorry placeholders, and zero linter warnings.

Cite This Study

Charles EDOU NZE (2026) studied this question.

synapsesocial.com/papers/6a92995f8e5d7d1fc0c1145e https://doi.org/10.5281/zenodo.22133106

View Full Paper

Ask AI

Bookmark

Implication

Formal verification study demonstrates algebraic reductions and tree inversion formulas for Keller mappings in polynomial spaces, highlighting structural equivalences across algebraic geometry.

On the Jacobian Conjecture and the Nilpotent Tree Inversion of Keller Mappings

Discussion

Member takes

Implication

Key Points

Cite This Study

On the Jacobian Conjecture and the Nilpotent Tree Inversion of Keller Mappings

Discussion

Member takes

Implication

Key Points

Cite This Study

Also Consider

Also Consider