We formalize a stabilized Ibaguner Fractal Operator (IFO) compression-collapse framework in which classical divergent exponential-hyperbolic cascades are replaced by bounded nonlinear compression and logarithmic compactification. The resulting operator produces finite complex collapse states instead of singular divergence. We define the IFO Omega state as a normalized asymptotic limit and prove existence, boundedness, and magnitude-phase separation laws. Numerical parameter sweeps confirm logarithmic scaling, phase stability, and compression plateaus across high-dimensional fields. This establishes an Omega attractor principle for stabilized IFO dynamics.
SİNAN İBAGÜNER (Thu,) studied this question.