A Unified Dimensional Reduction Proof Framework for the Seven Millennium Prize Problems under the Yuanxian Topological Paradigm

The Seven Millennium Prize Problems have long been partitioned into isolated research territories—such as number theory, algebraic geometry, partial differential equations, quantum field theory, and computational complexity—with academia chronically lacking a unified foundational axiomatic infrastructure. Rooted in the 64-dimensional compact torus topology (T64) and the True-Circle Self-Consistency (TCSC) Axiom, Yuanxian Theory (YXT) transcends the cognitive constraints of localized, single-domain proofs. Utilizing a core four-step methodology—Topological Embedding, Operator Reconstruction, Dynamical Systemization, and Self-Consistent Adjudication—this paper achieves a global unification and reduction of the seven problems. It translates disparate mathematical and physical propositions from four-dimensional spacetime into endogenous structural constraints of a high-dimensional topological manifold, framing all target conjectures as inevitable corollaries of the ontological self-consistent survival of the cosmos. This paper systematically illuminates the paradigmatic significance of this methodology, delivers the high-dimensional topological reduction logic for the six unsolved problems (including the Riemann Hypothesis, P vs NP, and Yang-Mills Theory), and contextualizes the Poincaré Conjecture as a low-dimensional historical validation of this meta-framework. Furthermore, three distinct falsifiable criteria are formulated to secure the paradigm's empirical testability within Popperian science. This research demonstrates that the Yuanxian topological paradigm yields a rigorous, grand unified proof infrastructure, offering a viable ontological path to integrate the fragmented axiomatic architectures of contemporary mathematical sciences.