A Complete Characterization of the Electron within the SRE Framework: A Unified Account of Axiomatization, the Fine-Structure Constant, Molecular Computation, and Orbital Assignment

This manuscript provides a unified and complete characterization of the electron within the framework of Status–Relational Entropy (SRE) dynamics: the electron is the unique, stable, noise-robust emergent fixed point of the sparse operator `R` over the coherent core of a binary self-organizing network, whose basal structure is the three-dimensional cube Q₃ (vertex count 8, edge count 12, first Betti number 5, i.e., 12 × 5 = 60). The manuscript unfolds along a reproducible logical chain: (1) three independent topological derivation paths for the fine-structure constant α ≈ 1/137.036 are given (the Laplacian spectral-gap of the Möbius ring graph, the four-state eigen-spectrum frequency formula, and the Möbius-parameterized arc-length perturbation), and the Tier 0 independent computational review confirms that λ₀ is not an independent primitive and that the n = 60 hit is a discretization coincidence; (2) through the Fork A axiomatization (A1–A4 + R1), the double-cover four-state complex (8, 12, 5, 60) is derived independently from the four axioms, an observable dictionary α = λ₂/λ_max = v/c is established, and the residual is promoted to the A5 bare coupling δ = 4.347×10⁻⁵; (3) the sparse operator `R` is shown to be unique, convergent, and robust over the coherent core of the binary network (P0/R2/R3, with a 10/10 validation suite); (4) the account is transferred to molecular computation, providing the MCI spectral fingerprint, Q₃ basal recognition, and MDS relational-inversion geometry; (5) the laws of electron orbital assignment are derived from the 16-cell state space (Pauli as cell-uniqueness, capacity laws C_ℓ = 4ℓ+2 and C_n = 2n², Hund's rule as tension minimization, and the numerical coincidence of 60 with the capacity of the first four shells). This work does not prove that the SRE axioms hold objectively; all conclusions are internally self-consistent constructions within the SRE model, and real physical and chemical inferences must be independently verified by external means. 本文在状态‑关系熵(SRE)动力学框架下,对电子给出统一的完整刻画:电子是二元自组织网络相干核上稀疏算子 `R` 的唯一、稳定、抗噪涌现不动点,其本体结构为三维立方体 Q₃(顶点数 8、棱数 12、第一贝蒂数 5,即 12×5 = 60)。全文沿一条可复现的逻辑链展开:(1) 给出精细结构常数 α ≈ 1/137.036 的三条独立拓扑推导路径(Möbius 环图拉普拉斯谱间隙、四态本征谱频率公式、Möbius 参数化弧长微扰),经 Tier 0 独立计算审查确认 λ₀ 非独立原语、n=60 命中为离散化巧合;(2) 以 Fork A 公理化(A1–A4 + R1)从四条公理独立推出双覆盖四态复形 (8,12,5,60),建立可观测字典 α = λ₂/λ_max = v/c,并将残差升格为 A5 裸耦合δ = 4.347×10⁻⁵;(3) 证明稀疏算子 `R` 在二元网络相干核上唯一、收敛且鲁棒(P0/R2/R3,验证套件 10/10 通过);(4) 迁移至分子计算,给出 MCI 谱指纹、Q₃ 本体识别与 MDS 关系反演几何;(5) 由 16 单胞态空间推演电子轨道分配规律(泡利=单元唯一性、容量定则 C_ℓ=4ℓ+2、C_n=2n²、洪特=张力最小化、60 与前四壳层容量的数字重合)。本工作不证明 SRE 公理客观成立; 全部结论均为 SRE 模型内部的自洽性构造,现实物理与化学推论须经外部手段独立核验。