Generative Mathematical Physics F: Generative Dynamics of the Early Universe: From Quantum Geometry to Classical Spacetime

This paper proposes a unified cosmological generative framework, reinterpretingthe evolution of the universe as an emergent process from discrete quantum geometric generators to continuous classical spacetime structures. Based on the formallanguage of iterated function system theory, this framework establishes a rigorouscorrespondence between the generative system (discrete generators, iteration rules,continuization flow) and the cosmological description (scale factor, dynamical equations, limit structures). Within this framework, the Friedmann equations are understood as the continuization limit of the generative flow under the assumption ofhomogeneity and isotropy, and the nature of time is revealed as the projection ofthe intrinsic parametrization of the generative process at macroscopic scales. Thispaper further demonstrates the structural homomorphism between loop quantumcosmology and G2 compactifications in terms of generative logic, and proves thatself-similarity can serve as a mathematical formulation of the cosmological principle,providing a rigorous mathematical foundation for the origin of the primordial fluctuation spectrum. This framework naturally resolves the horizon problem, interpretsdark energy as an emergent effect of the dynamics of the quantum geometry field,and proposes three testable predictions: log-periodic oscillations in the primordialgravitational wave spectrum, a characteristic scale sequence in the large-scale structure of the universe, and potential imprints of the quantum bounce on the cosmicmicrowave background.