An Inverse Spectral Ladder from Wrapped-Defect Energies on a Compact Fiber

We consider periodic transport on a compact one-dimensional fiber and isolate a reduced wrapped-defect model in which excitation energies are given by a curvature-penalized line functional. For closed curves of length ℓ_n = n L_χ, we prove that the minimal renormalized excitation energy is E_n^exc = 2π² B / (n L_χ). This yields an exact inverse spectral ladder and, after division by c², an inverse mass ladder m_n = M_0 / n. The result is rigorous within the reduced model. We also state explicitly the assumptions required to connect this model to compact-fiber transport frameworks.