Fractal Holographic Emergent String Theory (FHEST) PART G Mapping of Fractal Cartan Formulas to Traditional Cartan Formulas

This paper explores the mapping relationship between the fractal Cartan for?mula and the traditional Cartan formula within the framework of Fractal Holo?graphic Emergent String Theory (FHEST). By introducing fractal dimension cor?rection factors, non-local differential operators, and curvature integral terms, weestablish a rigorous mapping between the fractal Cartan formula and traditionalgeometric frameworks. This mapping not only preserves the mathematical struc?ture of classical theories but also reveals the regulatory role of multi-scale geometryon physical laws through fractal correction terms. We validate the restoration ofthis mapping in the classical limit, the consistency of fractal field equations, andexperimental observability, demonstrating its physical self-consistency.