Topological Decision of the Poincaré Conjecture via YD-T64 Framework

The Poincaré Conjecture asserts that every simply connected closed 3-manifold is homeomorphic to the 3-sphere S³. While Perelman proved it using Ricci flow, alternative combinatorial or topological surgery approaches remain highly valuable. This paper, based on the YuanXian Theory (YXT) YD-T64 framework and the TCSC axiom system, proposes a novel topological surgery proof strategy. By embedding any closed 3-manifold M into the high-dimensional torus T⁶⁴ and performing surgeries induced by the TCSC involution, we decompose M into simpler pieces. Under the rigidity of simple connectedness (π₁(M)=0), each piece is shown to be homeomorphic to S³ after filling. Reassembly then yields that M must be homeomorphic to S³. Computational verification is performed using SnapPy in SageMath, and key definitions and theorems are formalized in Lean 4. Core Conclusion: The Poincaré Conjecture is a necessary consequence of T⁶⁴ topological surgery and the rigidity of simple connectivity. 庞加莱猜想断言每一个单连通的闭三维流形同胚于三维球面 S³。虽然 Perelman 已通过 Ricci 流给出证明,但寻找更直接或基于组合拓扑的证明路径仍然具有重要意义。 本文基于元宪理论(YuanXian Theory, YXT)