Classical Entanglement: Parametric Geometry and Non-Parametric Synthesis of Asymptotic Laws

This review develops a unified geometric framework for synthesizing global asymptotic laws, termed classical entanglement. The central tool is the entanglement operator, a Minkowski–La metric blend that couples asymptotic regimes through an index a>1, producing a nonlinear global state whose intermediate region is metrically non-separable and cannot be written as a linear combination of its limits. The framework reveals a universal transition knee whose curvature scales linearly with a, independent of amplitudes or local scales. We show that this geometric mechanism encompasses Orlicz norms, weighted Hölder metrics, and iterated Hölder constructions, the latter being structurally isomorphic to self-similar root approximants. A conceptual “Rosetta Stone” links practitioner terminology, geometric meta-language, and functional-analytic structures, clarifying how classical entanglement unifies empirical blending, metric curvature, and Calderón-type interpolation. Applications to turbulence (Darcy friction factor), fractional dynamics, and scale-dependent diffusion illustrate how classical entanglement provides stable, asymptotically consistent global states across multi-scale systems.