A Nonlinear Idempotent Capacity-Constrained Spectral Operator: Definition and Application

This preprint introduces a new definition of a nonlinear yet idempotent capacity-constrained spectral operator. The distinctive feature of this framework is that the operator reproduces Kolmogorov’s -5/3 spectral law without requiring any additional assumptions or auxiliary hypotheses. The idempotent property emerges intrinsically from the operator’s construction, ensuring robustness under capacity constraints. We provide a formal derivation, highlight the operator’s nonlinear structure, and demonstrate how the Kolmogorov scaling law arises naturally as an application. This result suggests broader implications for turbulence modeling, spectral analysis, and computational approaches to complex systems.