Uniqueness of the Dimensional-Reduction Freezing Point of Row 35 and Its Mapping to Representation Classes of the Fundamental Group — Ontological Re-reading of the Mapping from Yang-Hui Triangle Combinatorial Numbers to Representation Classes of the Fundamental Group under the T⁶⁴ Framework of Yuanxian Theory

**[Manifestation layer]** The cosmos is a living organism. Once the core law of Yuanxian Theory—“the cosmos is a living organism”—has been established, every mathematical conclusion within the \(T⁶⁴\) framework is to be re-understood as a geometric manifestation of the topological self-inspection of the cosmic living organism. Taking the uniqueness of the dimensional-reduction freezing point of Row 35 and its mapping to representation classes of the fundamental group as a case study, the present paper completes the cognitive ascent from “mathematical proof” to “ontological re-reading”. **Structural principle**:A law is not an axiom. Axioms are inputs; laws are outputs. Axioms may be replaced; laws may not. 48 is a manifestation, not a computation. The paper strictly distinguishes four layers:- **Axiom layer**: definition of \(Φ₃₅\), definition of \(w(k)\), declaration \(Σ_3=L(3,1)\), phase projection;- **Law layer**: strict monotonicity of \(p_1(M_n)\), non-multiple-of-three classification of the 12 boundary representation classes;- **Reading layer**: explicit expansion of \(p_1(M₃₅)\) (R1), freezing-point reading 48 (R2), \(#Irrep=3\) (R3), \(sin^2θ_Wᵗʳᵉᵉ=0.25\) (R4), physical reading of the 12 boundary representation classes (R5);- **Hypothesis layer**: stratified stance on the R1/R2 correspondence (H1), weight set of the 12 boundary representation classes (H2). **Core conclusions**:- Uniqueness of the freezing point is a **law**: whenever phase weights are positive, \(p_1(M_n)\) is strictly increasing and the freezing point is unique;- \(p_1(M₃₅)=48\) is a **reading**: the manifestation of the cosmic living organism on the section of step 35, not a direct arithmetic corollary of axioms A2/A3;- The precise correspondence between R1 and R2 remains an open problem internal to the framework;- \(#Irrep=3\) is a reading under axiom A4;- The correspondence of the 12 boundary representation classes with Standard-Model lepton degrees of freedom belongs to the hypothesis layer. --- **【显影层】** 宇宙是生命体。 元宪理论的核心规律“宇宙是生命体”确立后,\(T⁶⁴\) 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。本文以第35行降维冻结点的唯一性及其与基本群表示类的映射为案例,完成从“数理证明”到“本体论重读”的认知升维。 **结构原则**:规律不是公理。公理是输入,规律是输出。公理可以被替换,规律不能被替换。48 是显影,不是计算。 本文严格区分四个层次:- **公理层**:\(Φ₃₅\) 的定义、\(w(k)\) 的定义、\(Σ_3=L(3,1)\) 的声明、相位投影的声明;- **规律层**:\(p_1(M_n)\) 的严格单调性、12 个边界表示类的非三倍数分类;- **读数层**:\(p_1(M₃₅)\) 的显式展开式(R1)、冻结点读数 48(R2)、\(#Irrep=3\)(R3)、\(sin^2θ_Wᵗʳᵉᵉ=0.25\)(R4)、12 个边界表示类物理读数(R5);- **假设层**:R1/R2 对应问题的分层立场(H1)、12 个边界表示类权重集合(H2)。 **核心结论**:- 冻结点唯一性是**规律**:只要相位权重为正,\(p_1(M_n)\) 就严格单调递增,冻结点唯一;- \(p_1(M₃₅)=48\) 是**读数**:宇宙生命体在第 35 步截面上的显影,不是公理 A2/A3 的直接算术推论;- R1 与 R2 的精确对应是框架内待验证的核心问题;- \(#Irrep=3\) 是公理 A4 下的读数;- 12 个边界表示类与标准模型轻子自由度的对应属于假设层,待后续验证。