Yuanxian Theory · Core Hard Target P8b: Construction of Higher-Order Trace Formulae and the Topological Explicit Framework for the 24 Physical Constants
Year: 2026
Type: preprint
Abstract: 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。
Author: Acharya, Zhenyuan
Language: English
Subfield: Statistical and Nonlinear Physics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7225610538
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