What question did this study set out to answer?

The aim is to develop a caustic theory for generic fold-cusp stratifications and address structural issues during branch collisions.

April 16, 2026Open Access

Caustic Uniformization of Coordinate-Free Renormalized Tail Orbits: Fold--Cusp Collision Normal Forms, Stokes-Filtered Monodromy, and Finite-Window Recovery

View Full Paper

Ask AI

Bookmark

The aim is to develop a caustic theory for generic fold-cusp stratifications and address structural issues during branch collisions.
Proves an Airy uniformization theorem near codimension-one fold walls after branch renormalization.
Demonstrates the Pearcey law near codimension-two cusp points on specific control scales.
Establishes a Stokes-filtered monodromy class through matrix cocycle gluing and local Airy profiles.
Derives a finite-window detector theorem for asymptotic distinction of regular and singular regimes.
The collision packet converges to a universal Airy profile with holomorphic amplitude fields.
Introduces an obstruction to global smooth simple-pole atlas existence via cohomological analysis.
Quantitatively recovers local parameters in different regimes with specific accuracy metrics.

No takes yet. Share an insight, caveat, or question.

Develops caustic theory for fold-cusp interactions, highlighting implications for local control parameters.

Mohammad Abu-Ghuwaleh (2026) studied this question.

View Full Paper

Ask AI

Bookmark