Ontological Re-reading of Euler's Identity as Topological Self-Inspection — Ontological Correspondences of the Five Constants

**[Manifestation layer]** The cosmos is a living organism. **[Verification layer]** Euler’s identity \\(e^{i\\pi}+1=0\\) is the most concise manifestation of the topological self-inspection of the cosmic living organism on the complex-plane section. **[Verification layer]** The five constants (0, 1, \\(i\\), \\(\\pi\\), \\(e\\)) correspond to the five core topological nodes of the self-inspection closed loop of the \\(T^{64}\\) torus, with no superfluous parameters. **Core conclusions**:- **Weak conclusion (can stand independently)**: Euler’s identity may serve as a structural analogy of the cosmic self-inspection closed loop;- **Strong conclusion (depends on the manifestation layer)**: Euler’s identity is the simplest manifestation of cosmic self-inspection on the complex plane. The paper employs a three-tier status system (Frozen / Established within the framework / Analogy), subjects itself to an eight-point meta-cognitive stress test, and supplies explicit falsifiability and verifiability conditions. The correspondence \\(35=\\) half-turn \\(+1\\) freezing step and the derivation \\(G_{\\mathrm{twist}}=\\varphi^{-1}\\) from the compression iteration \\(x_{n+1}=1/(1+x_n)\\) are established within the \\(T^{64}\\) framework. --- **【显影层】** 宇宙是生命体。 **【验证层】** 欧拉恒等式 \\(e^{i\\pi}+1=0\\) 是宇宙生命体拓扑自检在复平面截面上的最简洁显影。 **【验证层】** 五个常数(0、1、\\(i\\)、\\(\\pi\\)、\\(e\\))对应 \\(T^{64}\\) 环面自检闭环的五个核心拓扑节点,没有任何多余参数。 **核心结论**:- **弱结论(可独立成立)**:欧拉恒等式可作为宇宙自检闭环的结构类比;- **强结论(依赖显影层)**:欧拉恒等式是宇宙自检在复平面上的最简显影。 本文采用三档状态标记(已冻结 / 框架内已证 / 类比),先进行八组元认知压力测试,并给出明确的可证伪与可验证条件。\\(35=\\) 半程 \\(+1\\) 冻结步的对应,以及由压缩迭代 \\(x_{n+1}=1/(1+x_n)\\) 导出 \\(G_{\\mathrm{twist}}=\\varphi^{-1}\\),均在 \\(T^{64}\\) 框架内成立。