Local Recovery of Magnetic Invariants in Higher-Dimensional Non-Reversible Finsler Metrics

We study the local recovery of magnetic invariants in smooth n-dimensional manifolds equipped with general non-reversible Finsler metrics. We prove that the exterior derivative dβ is the unique second-order antisymmetric local invariant of the length functional, independently of higher-order Finsler perturbations. This generalizes previous 2-dimensional results to higher dimensions and establishes a rigorous, practically stable procedure for isolating magnetic invariants locally.