A New Fractal Mass Generation Mechanism Theory and Its Mathematical Framework

This paper proposes a novel mass generation mechanism based on fractal geometry andnon-perturbative curvature dynamics, aiming to provide a unified geometric and topo?logical explanation for the origin of particle mass, thereby offering an alternative to thetraditional Higgs mechanism. By introducing concepts such as fractal spacetime dis?cretization, dynamic fractal dimensions, and multi-scale coupling, the theory constructsa mathematical framework for particle mass, energy-mass relations, and modified gravita?tional field equations. The paper elaborates on key formulas, including fractal curvatureintegrals, instanton corrections, and fractal-modified Hamiltonian operators, and dis?cusses their connections to quantum gravity and black hole thermodynamic phenomena.The proposed framework not only exhibits mathematical elegance and self-consistencybut also provides new directions for future high-energy physics and gravitational experi?ments.