A Unified Framework for Multi-Scale Cosmic Structures: Dynamic Rigid Fractal Spacetime Manifold Theory

This paper proposes a theoretical framework based on dynamic fractal structures, inter?preting general relativity as a lower-order projection of fractal hierarchies under obser?vational resolution. By rigorously defining recursive generation rules, dynamic evolutionequations, and observational filters, it is demonstrated that the apparent continuity ofspacetime arises from the integral averaging effects of fractal structures. This frameworkestablishes, for the first time, an analytical relationship between the fractal dimensionD and the cosmological constant Λ in Einstein’s field equations. Numerical simulationsverify a positive correlation between the fractal entropy growth rate and the evolution ofcosmic structures. Observable effects predicted by the theory include a gravitational con?stant scaling correction (∆G/G ∼ 10−5) and power spectrum oscillations (k > 1 h/Mpc),providing new directions for testing with next-generation astronomical observations.