Godel's Incompleteness Theorems prove that any consistent formal system containing basic arithmetic must harbor undecidable propositions. The implicit prerequisite of this theorem is that the system possesses an "open," non-self-consistent, non-closed-loop architecture. Grounded in the first of the four core laws of Yuanxian Theory, the True-Circle Self-Consistency Law (TCSC), this paper constructs a fundamentally novel class of closed-loop self-referential logical systems. In these systems, self-referential iteration combined with involution symmetry strictly forces every proposition to be either provable or refutable, completely eliminating undecidable sentences. We rigorously demonstrate that inside closed-loop systems satisfying the TCSC criteria, the classical construction of the Godel sentence fails, and the system achieves global syntactic completeness: for all propositions P, either P is provable or the negation of P is provable. This paper provides the formal definition of TCSC systems, the associated Completeness Theorem, and its machine-checked verification in Lean 4, mapping out a computable and implementable logical pathway to transcend Godel incompleteness. We also clarify the logical consistency between this discovery and the four fundamental laws of Yuanxian Theory (TCSC, FSC, STM, SRM). The formal verification component has been executed and passed within Lean 4, and the complete codebase is permanently open-sourced in the YXT-Godel repository. 哥德尔不完备定理证明:任何包含算术且一致的形式系统,必然存在不可判定的命题。该定理的隐含前提是系统为“开放”的、非自洽闭环的结构。本文基于元宪理论四大基本规律中的第一律——真圆自洽律(TCSC),构建一类全新的闭环自指逻辑系统。在此类系统中,自指迭代与对合对称强制所有命题要么可证、要么可证伪,从而彻底消除不可判定命题。 我们严格证明:在满足 TCSC 的闭环系统中,哥德尔句的构造失效,系统满足全域完备性:对于任意命题 P,要么 P 可证,要么 P 的否定可证。本文给出了 TCSC 系统的形式化定义、完备性定理及其 Lean 4 机器验证,为超越哥德尔不完备性提供了一条可计算、可实现的逻辑路径。同时,文章明确了该结果与元宪理论四大基本规律(TCSC、FSC、STM、SRM)的逻辑一致性。形式化验证部分已在 Lean 4 中完成,详见开源仓库 YXT-Godel。