Coupling Framework of Dynamic Calabi-Yau Manifolds with Four-Dimensional Spacetime: Complete Derivation and Analysis

This paper explores the coupling relationship between dynamic Calabi-Yau (CY)manifolds and four-dimensional spacetime. Starting from geometric definitions, wederive the evolution equations of moduli parameters and analyze their mutual influ?ence on spacetime dynamics. By constructing a rigorous mathematical framework,we provide new insights into the role of higher-dimensional manifolds in cosmology.Specifically, this paper introduces fractal dimensions and fractal measures, modi?fies the traditional uncertainty principle, and examines its applications in quantumgravity and multi-scale physical phenomena