Dynamic Rigid Fractal Spacetime Manifold Theory (DRFSMT) PART B: Mathematical Framework and Physical Applications

Fractal geometry offers a novel paradigm for describing the non-smooth structures of spacetime. Although the Dynamic Rigid Fractal Spacetime Manifold Theory (DRFSMT) has preliminarily unified phenomena such as fractal spacetime, quantum field theory, and dark energy, its mathematical foundation and experimental connections still require further development. This study focuses on three key innovations within the DRFSMT framework: (1) axiomatic definitions of the manifold based on compact coverings and connectedness; (2) fractal differential operators in the context of noncommutative geometry; (3) a parametrized dark energy model compatible with observational data. These advancements establish the computational viability of fractal physical models and their experimental validation.