Fiber Intersection Geometry and Global Identi ability of Multi-Ratio Maps in Dynamical-Decoupling Spectroscopy

This paper develops the global inverse geometry of multi-ratio maps in dynamical-decoupling spectroscopy. The multi-ratio inverse problem is reformulated as finite moment recovery for positive two-atom measures, establishing a direct equivalence between DD ratio measurements and generalized power moments. Using this viewpoint, we derive global fiber topology, prove injectivity modulo exchange symmetry for three symmetric ratios, analyze persistent rank-collapse on the diagonal stratum, and characterize consistency conditions for overdetermined observations.