Fiber Geometry of the Protocol Ratio Map: Submersion Structure, Symmetry-Induced Projected Folds, and Level-Set Design in Dynamical-Decoupling Spectroscopy

Key Points

• The study aims to analyze the fiber geometry of the protocol ratio map in dynamical-decoupling spectroscopy and explore symmetry-induced projected folds.
• Analyzed the protocol ratio map to identify fiber-geometric features.
• Examined the nature of folds and symmetry properties in the context of level-set designs.
• Developed criteria for fold-free designs based on derived structures.
• Demonstrated that the ratio map serves as a surjective submersion with smooth fibers.
• Reinterpreted a specific fold as a symmetry-induced projected fold at Rc=4/3.
• Introduced design criteria that avoid folds by leveraging symmetry-breaking properties.