Infinite Self-Referential Temporal Causal Spectral Chain Structure C; Causal Dynamics: ω-Categories and Higher Curvature Framework

The dynamization of causal structures is one of the core challenges in quantumgravity theories. Based on the mathematical framework of temporal ω-categories,this paper rigorously reconstructs causal structures as morphism spaces of highercategories and establishes a formal theoretical system of causal dynamics. By introducing k-morphism curvature and its self-similar scaling law, it is proved thatclassical causal structures can emerge from the limit of infinite nesting. This framework unifies key parameters such as the causal coupling constant and curvatureexponent as functions of the scaling factor λ, and predicts characteristic secondarypeak structures in the gravitational wave spectrum, non-Gaussian imprints of causalfluctuations, and log-periodic oscillations in the cosmic microwave background. Theresults provide a mathematically self-consistent and testable theoretical foundationfor understanding the causal structure problem in quantum gravity.