Inverse Local Singularity Detection from Adjacent Derivative Ratios: Resonance Inversion, Staircase Deflation, and Canonical Germ Recovery

Key Points

• The central aim is to develop techniques for detecting and classifying local singularities using adjacent derivative ratios.
• Utilized derivative-order ladders for analysis
• Derived resonance inversion formulas for classification
• Established schemes for singular staircase deflation
• Demonstrated recovery of canonical germ structures from derivatives
• Achieved exact recovery of canonical germ structures from finite derivative ratios
• Established stable recovery laws for local singularities
• Provided a systematic inverse classification of singularities