St. Denis Wave–Fold Transform (FURGT), For analyzing parts of the ABC equation

This paper introduces the St. Denis Wave–Fold Transform (FURGT), a geometric framework that maps scalar ratios derived from integer triples into a bounded rotational coordinate space. Using a multi-wheel system with scaling anchors and a trigonometric–logarithmic transform, the framework produces a finite analytic ceiling and demonstrates monotonicity, multi-scale stability, and structural consistency. The system provides a tool for visualizing and classifying patterns in integer-derived data without making claims about arithmetic conjectures.