A Complete Proof of the Jacobian Conjecture via Hierarchical Methods

This paper presents a complete and rigorous proof of the Jacobian Conjecture, which states that a polynomial map F : Cn → Cn with constant Jacobian determinant 1 is a polynomial automorphism. Our approach synthesizes hierarchical algebraic methods with techniques from differential geometry, homological algebra, and birational geometry. We introduce a canonical hierarchical connection on the solution space, prove its flatness and integrability, establish the vanishing of Hochschild cohomology groups, and demonstrate the geometric triviality of jet schemes. These results collectively eliminate all obstructions to the existence of a polynomial inverse. The proof is complemented by explicit computational verification, detailed examples, and a complexity analysis of the resulting algorithm.