Structural Multi-Fragility and Observable Swallowtail Precursors in Reduced Inverse Geometry

This paper introduces SW2 as an operational screening framework for structural multi-fragility in reduced inverse geometry. Instead of claiming an exact A4A_4A4 normal form, it defines a canonical Fisher-spectrum screen based on multi-soft depth, weak-mode competition, and weakest-direction switching. The framework is tested on reheating P17/P16 grids and a corrected DD/Q11 same-operating-point scan, showing that multi-soft precursor structure is not reheating-only but depends on the chosen operational population, Fisher metric, and screening convention.