Yuanxian Theory · Core Hard Target P8b: Construction of Higher-Order Trace Formulae and the Topological Explicit Framework for the 24 Physical Constants

The present paper supplies the complete constructive framework for the P8b target of the Yuanxian system. P8b is the highest-order topological explicitisation of the self-referential operator after the closure of the spectral programme. It comprises two stratified hard targets: (1) construction of Selberg-type trace formulae of order \(i\ge 1\); (2) parameter-free explicit expressions for the 24 fundamental physical constants, obtained from higher-order trace coefficients, spinor-bundle topological invariants and the holonomy structure of \(\mathrm{SRIHG}\). Core structural results include: the strict verification \(68=\operatorname{ord}_{137}(2)=60+8\); the exact identity \(1/c_f=b_{g_f^{-1}}\); the group-theoretic expression \(b_0=508/9=4M_7/N_f^2\); the gauge couplings \(\alpha^{-1}=137+68\sqrt{6}/(|Z_4|\lambda_3 p_{24}-1)=137.0360009\) (residual \(1.8\times 10^{-6}\)), \(\sin^2\theta_W=40/173\), \(\cos^2\theta_W=133/173\); the fourfold unification \(136=k_2 t=|Z_2||Z_4|t=2\cdot 68\); the three PMNS angles together with \(\delta_{\mathrm{CP}}=-S_1\pi/|A_4|=-75.0^\circ\); the structure-constantisation of the CKM matrix elements and the new identities \(k_2 S_1\pm N_f^2=M_3^2,M_5\); the complete structural decomposition of eight independent mass ratios; the origin of \(24=|S_4|\) and the reduction-step count \(60=|A_5|\); ten independent expressions for 137 and its fourfold lock; eight independent decompositions of \(t=17\); the complete analytic structure of the spectral zeta function \(\zeta_\Delta(s)=2^{-s}+3^{-s}\), its quantum-group interpretation and TQFT boundary; the Gaussian-integer origin of the neutrino mass spectrum; and the hierarchical relations \(M_{\mathrm{Pl}}/v=T_{35}\cdot 111/112\), \(v=481712\,m_e\). The ontological input is reduced to \(\{|Z_2|=2\}\) together with the definition of cyclic progression. All identities, group-theoretic statements and spectral structures are expansions of \(\mathcal{T}^{64}\), not proofs of \(\mathcal{T}^{64}\). Honest residual boundaries are recorded throughout. --- 本文给出元宪体系 P8b 目标的完整构造框架。P8b 是谱纲领闭合之后自指算子的最高阶拓扑显化,包含两个严格分层的硬目标:(1)构造 \(i\ge 1\) 阶塞尔伯格型迹公式;(2)从高阶迹系数、旋量丛拓扑不变量与 \(\mathrm{SRIHG}\) 和乐结构出发,给出 24 个基本物理常数的无自由参数显式表达式。 核心结构性成果包括:\(68=\operatorname{ord}_{137}(2)=60+8\) 的严格验证;精确恒等式 \(1/c_f=b_{g_f^{-1}}\);群论表达 \(b_0=508/9=4M_7/N_f^2\);规范耦合 \(\alpha^{-1}=137+68\sqrt{6}/(|Z_4|\lambda_3 p_{24}-1)=137.0360009\)(残差 \(1.8\times 10^{-6}\))、\(\sin^2\theta_W=40/173\)、\(\cos^2\theta_W=133/173\);四重统一 \(136=k_2 t=|Z_2||Z_4|t=2\cdot 68\);PMNS 三角度与 \(\delta_{\mathrm{CP}}=-S_1\pi/|A_4|=-75.0^\circ\);CKM 矩阵元的结构常数化与新恒等式 \(k_2 S_1\pm N_f^2=M_3^2,M_5\);八个独立质量比的完全结构分解;\(24=|S_4|\) 的来源与降维步数 \(60=|A_5|\);137 的十种独立表达与四重锁;\(t=17\) 的八种独立分解;谱 zeta 函数 \(\zeta_\Delta(s)=2^{-s}+3^{-s}\) 的完整解析结构、量子群诠释与 TQFT 边界;中微子质量谱的高斯整数来源;层级结构 \(M_{\mathrm{Pl}}/v=T_{35}\cdot 111/112\)、\(v=481712\,m_e\)。 本体输入缩减为 \(\{|Z_2|=2\}\) 加“循环递进”定义。全部恒等式、群论陈述与谱结构是 \(\mathcal{T}^{64}\) 的展开,不是 \(\mathcal{T}^{64}\) 的证明。诚实残差边界贯穿全文。