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

Key Points

• The aim is to develop a global inverse geometry framework for multi-ratio maps applied in dynamical-decoupling spectroscopy.
• Reformulated the multi-ratio inverse problem as finite moment recovery for positive two-atom measures.
• Derived global fiber topology and proved injectivity for three symmetric ratios.
• Analyzed persistent rank-collapse on the diagonal stratum and discussed conditions for overdetermined observations.
• Established equivalence between DD ratio measurements and generalized power moments.
• Successfully characterized consistency conditions for observations beyond the expected range.