Infinite Self-Referential Temporal Causal Spectral Chain Structure E; Time-Spectrum Duality in Spectral Chain Quantum Gravity: Self-Referential Isomorphism and Fixed-Point Framework

The origin of time and the emergence of geometry are core challenges in quantum gravity. This paper establishes a rigorous duality between the time dimensionand the spectral dimension based on the self-referential structure of temporal ωcategories. By proving that the limit structures of the two dimensions satisfy a fixedpoint equation, the mathematical rigor of ”bidirectional emergence” is achieved.This framework uniformly derives the key exponents in time-spectrum duality asfunctions of the scaling factor λ, predicting characteristic modulation effects ingravitational wave signals and the cosmic microwave background. The results provide a self-consistent theoretical foundation for understanding the time-geometryunification problem in quantum gravity.