The Jacobian counterexample discovered by Claude Fable 5 has a Jacobian determinant of -2 (constant) — satisfying the conjecture's hypothesis of a nonzero constant Jacobian — yet maps three distinct points to the same image, proving the map is not injective and therefore not invertible. This directly contradicts the Jacobian conjecture's claim that every polynomial map with constant nonzero Jacobian is invertible. The counterexample's elegance — a simple, verifiable construction rather than an existence proof — makes it particularly compelling for mathematical verification.