What question did this study set out to answer?

The aim is to develop a global inverse geometry framework for multi-ratio maps applied in dynamical-decoupling spectroscopy.

June 10, 2026Open Access

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.

Abstract

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.

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

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Abstract

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