Unified Field Theory of Cosmic Factor Conservation and Spacetime Uniqueness under the Yuan-Xian (Meta-Constitution) YD-T64 Framework

Under the Yuan-Xian (Meta-Constitution) YD-T64 theoretical framework, this paper systematically formalizes the two fundamental axioms of the universe: Cosmic Factor Conservation Axiom (Axiom I) and Spacetime Uniqueness Axiom (Axiom II). By constructing a coupled dynamical system of the Cosmic Factor Field (Λ(z)) and the Mind Field (Ψ(z,t)), a closed Yuan-Xian Unified Field Equation Set is derived, along with a semi-implicit gradient flow iteration scheme based on the global energy functional. This achieves a fundamental unification of physical conservation laws, quantum unitarity, topological geometry, and self-referential logic. The paper rigorously proves that real physical spacetime (M^4) is the unique classical limit projection of the 64-dimensional torus (T⁶⁴) under self-referential constraints. It further demonstrates that the fine-structure constant (α) and the Riemann critical line (Re(s)=1/2) are necessary consequences of Cosmic Factor Conservation. This framework provides a rigorous self-consistent foundation for Yuan-Xian theory and offers a directly programmable algorithmic basis for numerical simulation and verification.