Laminar Scaling, Renormalization, and Invariant Structures via the Ibaguner Fractal Operator & Ibaguner Constant : 0.3715

We introduce the Ibaguner Fractal Operator (IFO) as a nonlinear logarithmic renormalization operator acting on sequences, functions, and metric sets. We demonstrate that the operator induces laminar invariant regimes characterized by stable scaling exponents. A candidate scaling parameter Ibaguner Constant as λ ≈ 0.3715 is identified as an attracting fixed point under iterative renormalization. Connections to fractal geometry, distance set theory, and oscillatory biological systems are developed. The framework provides a unifying perspective on scale-invariant transitions between discrete and continuous structures.