The Gödel-IFO (Ibaguner Fractal Operator) Correspondence: A Functorial Bridge Between Logic and Fractal Geometry

<p>This work establishes a rigorous, functorial correspondence between formal systems in logic and fractal geometries, providing a unified resolution to Gödelian incompleteness, quantum measurement, and strategic equilibrium. We define the **Ibaguner Embedding Functor** ι that maps a formal system F and its propositions to a fractal manifold M F. We prove that the logical status of a proposition S is determined by the Hausdorff dimension of the singularity set of its image under the universal operator U : provable (dim H < 3), independent (dim H = 3), or contradictory (dim H > 3). This dimension is not arbitrary but is derived as the critical dimension for information loss in the functor ι. The framework is constructively verified using a formally specified fractal lattice gauge theory, providing a pathway to experimental validation</p>