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) 的 YD-T^64 框架与 TCSC 公理体系, 提出了一种全新的拓扑手术证明路径。通过将任意闭 3-流形 M 嵌入 T^64 高维背景, 并利用 TCSC 对合诱导的手术进行分解, 在单连通性 (π₁ (M) =0) 的刚性约束下, 所有碎片经填充后均同胚于 S³, 重组后原流形必同胚于 S³。 使用 SageMath + SnapPy 进行计算验证, 并在 Lean 4 中完成相关形式化。 核心结论: 庞加莱猜想是 T^64 拓扑手术与单连通性刚性的必然结果。