Seamless Connection between the Uniqueness of Cosmic Spacetime and the Closed-Chain Homotopy Closed Loop — A Yuanxian-Theoretic Proof Based on the T⁶⁴ Ontology

**[Manifestation layer]** The cosmos is a living organism; \(T⁶⁴\) is the form of the cosmic living organism. This paper completes the seamless-connection proof of “uniqueness of cosmic spacetime” and “closed-chain homotopy closed loop” within the Yuanxian-Theory framework. **Layer distinction** \[{Mathematical assertions and ontological interpretations must be stratified.}\] Four layers are strictly distinguished: - **Ontological thesis**: the cosmos is a living organism; \(T⁶⁴\) is the form of the cosmic living organism.- **Law layer**: uniqueness of cosmic spacetime (L1), closed-chain homotopy closed loop (L2), single-point steady state (L3, derived by joint application of L1 and L2), homology-class reduction lemma, equivalence theorem.- **Entrance-formulation choice layer**: form of the projection-operator sequence, concrete mode of expression of the homology-group structure, tolerance convention for projection-layer readings (all replaceable).- **Interpretation layer** (unfolding of the ontology-layer manifestation): three physical corollaries (incompatibility of parallel universes; topological origin of global-phase uniqueness; global tracing of local-phase single-valuedness). **Core results** Uniqueness of cosmic spacetime and closed-chain homotopy closed loop are two structural properties of the law layer. Their joint application inside the bounded-yet-infinite \(T⁶⁴\) ontology yields the single-point steady state. Through the homology-class reduction mechanism of the 35-step dimensional-reduction cascade they appear as the bidirectional projected expressions of one and the same fixed-point convergence structure. The non-trivial homology classes retained inside \(T⁶⁴\) are fully preserved as global conserved charges, while all closed chains on the three-dimensional projection level converge to the unique fixed point—“the ontology has structure, the projection has uniqueness”. **Criterion**: The ontological thesis does not depend on external verification; its criterion is “read correctly / read incorrectly”, which is self-evident. Truth precedes; verification follows. --- **【显影层】** 宇宙是生命体;\(T⁶⁴\) 是宇宙生命体的形态。 本文完成「宇宙时空唯一」与「闭链同伦闭环」在元宪理论框架内的无缝衔接证明。 **层次区分** \[{数学断言与本体论解释必须分层。}\] 严格区分四个层次: - **本体论定论**:宇宙是生命体;\(T⁶⁴\) 是宇宙生命体的形态。- **规律层**:宇宙时空唯一(L1)、闭链同伦闭环(L2)、单点稳态(L3,由 L1 与 L2 联立导出)、同调类规约引理、等价定理。- **入口性表述选择层**:投影算子序列形式、同调群结构的具体表述方式、投影层读数容差约定(均可替换)。- **解释层**(本体层显影展开):三条物理推论(平行宇宙不相容;宇宙全局相位唯一性的拓扑根源;局部相位单值性的全域溯源)。 **核心结论** 宇宙时空唯一与闭链同伦闭环是规律层的两条结构性性质。二者在有界无限的 \(T⁶⁴\) 本体中联立,导出单点稳态。通过 35 步降维链的同调类规约机制,二者呈现为同一不动点收敛结构的双向投影表达。\(T⁶⁴\) 本体中保留的非平凡同调类作为全局守恒荷被完整保留,三维投影层面的所有闭链收敛至唯一不动点——这正是「本体有结构,投影有唯一」的元宪核心图景。 **判据**:本体层定论不依赖外部验证,其判据是「读对/读错」,自明。真理先行,验证在后。