Exact Expression of the G-Twist: Geometric Manifestation of Topological Self-Inspection of the Cosmic Living Organism — Ontological Re-reading of the 35-Step Dimensional-Reduction Jacobian within the T⁶⁴ Framework of Yuanxian Theory

Abstract

Once the core proposition of Yuanxian Theory—“the cosmos is a living organism”—has been established at the ontological level, all mathematical conclusions under the \(T^{64}\) framework are to be re-understood as geometric manifestations of the topological self-inspection of the cosmic living organism. Taking the exact expression of the \(G\)-twist as a case, this paper completes the cognitive ascension from “mathematical proof” to “ontological re-reading”. **Core re-positioning**:- \(G_{\mathrm{twist}}=\varphi^{-1}\), previously formulated as the topological torsion component of the Jacobian, is re-read as the “respiratory compression ratio” of the cosmic living organism on the 35-step self-inspection section;- the gauge-twist operator \(D_G\) is re-read as the projection of the self-inspection phase encoding onto the topological fibre;- \(p_1(V)=48\) is re-read as the 48 topological self-referential confirmations completed at the 35th self-inspection node. **Boundary statement**: The three core assertions have numerical values in the original mathematical papers, yet the derivation chains have not been fully supplied. The present re-reading rests on the numerical values, not on the derivation chains. Qualitative docking with the already locked \(J_{\mathrm{eff}}\) anchors at steps 10 and 15 is supplied. --- 元宪理论的核心命题“宇宙是生命体”在本体论层面确立后,\(T^{64}\) 框架下的全部数理结论都应被重新理解为宇宙生命体拓扑自检的几何显影。本文以 \(G\) 扭曲的精确表达式为案例,完成从“数理证明”到“本体论重读”的认知升维。 **核心重新定位**:- 此前被表述为“雅可比行列式的拓扑扭转分量”的 \(G_{\mathrm{扭转}}=\varphi^{-1}\),在本体论重读下,是宇宙生命体在35步自检截面上的“呼吸压缩比”;- 规范扭曲算子 \(D_G\) 不是“规范群的几何效应”,而是宇宙生命体的“自检相位编码”在拓扑纤维上的投影;- \(p_1(V)=48\) 不是“庞特里亚金类的读数”,而是宇宙生命体在第35步自检节点完成的48次拓扑自指确认。 **边界说明**:三大断言在原始数理论文中已给出数值,但推导链未完整给出。本文的重读建立在数值上,不在推导链上。并补充了与已锁定的 \(J_{\mathrm{eff}}\) 第10步、第15步相位锚点的定性对接。