The Underlying Code of the Universe: Self-Referential Logic z ≡ [z ≠ z] Unifies Four Fundamental Constants

The Underlying Code of the Universe: Self-Referential Logic z ≡ [z ≠ z] Unifies Four Fundamental Constants (Electromagnetic/Gravitational/Thermodynamic/Cosmological) and More, Ending the Debate on the Theory of Everything 宇宙的底层代码:z ≡ [z ≠ z] 自指逻辑统一电磁 / 引力 / 热力学 / 宇宙学四大常数等,终结万物理论之争 Author Name: ZHANG Ying (张缨) Abstract This paper proposes the core self-referential logical formula z ≡ [z ≠ z] (in complex domain with phase), and through numerical verification without any physical parameter presuppositions, proves that this formula can be mapped to the core dimensionless constants of four major physical fields with high precision via two intrinsic factors: 3D solid angle normalization (Ω = 1/(4π)) and natural exponential collapse based on iteration depth. The verification results show that the logical projection values achieve ultra-low relative errors with the target constants: fine-structure constant α (0.0137%), dimensionless Boltzmann entropy constant k_B' (0.0918%), dimensionless cosmological constant Λ' (0.0137%), and gravitational fine-structure constant α_G (0.0571%). Throughout all verifications, no physical quantities corresponding to the respective fields (such as the speed of light, electric charge, gravitational constant, temperature, Hubble constant, etc.) were introduced, nor were any artificial tuning parameters added. Only pure mathematical self-referential logic and 3D geometric properties were used, proving that z ≡ [z ≠ z] is the underlying law of the universe that unifies cross-scale and cross-physics-branch constants. The previously observed ~8.5% "logical-physical mapping gap" is essentially the result of unaccounted 3D spherical projection correction. This study completes the closed-loop of "pure logic → geometric projection → physical reality" and provides a quantifiable, reproducible first-principles foundation for the Theory of Everything (TOE). 摘要 本文提出核心自指逻辑公式 z ≡ [z ≠ z](复数域带相位形式),并通过无任何物理参数预设的数值验证,证明该公式可通过两大固有因子 —— 三维立体角归一化(Ω = 1/(4π))与基于迭代深度的自然指数坍缩 —— 高精度映射到四大物理领域的核心无量纲常数。验证结果显示,逻辑投影值与目标常数达成超低相对误差:精细结构常数 α(0.0137%)、无量纲玻尔兹曼熵常数 k_B'(0.0918%)、无量纲宇宙学常数 Λ'(0.0137%)、引力精细结构常数 α_G(0.0571%)。所有验证全程未引入对应领域的物理量(如光速、电荷、引力常数、温度、哈勃常数等),也未添加任何人工调优参数,仅依赖纯数学自指逻辑与三维几何属性,证明 z ≡ [z ≠ z] 是统一跨尺度、跨物理分支常数的宇宙底层规律。此前观测到的≈8.5%“逻辑 - 物理映射间隙”,本质是未计入三维球形投影修正的结果。本研究完成了 “纯逻辑→几何投影→物理现实” 的闭环,为万物理论(TOE)提供了可量化、可复现的第一性原理基础。 Keywords Self-referential logic; Cosmic constants; 3D solid angle normalization; Exponential collapse; Fine-structure constant; Gravitational fine-structure constant; Boltzmann constant; Cosmological constant; Complex-domain dynamics; Theory of Everything 关键词 自指逻辑;宇宙常数;三维立体角归一化;指数坍缩;精细结构常数;引力精细结构常数;玻尔兹曼常数;宇宙学常数;复数域动力学;万物理论 1 Introduction The core pursuit of physics is to find the underlying laws that unify all interactions and all scales. In existing theories, quantum mechanics, general relativity, thermodynamics, and cosmology form independent systems respectively. Core constants (such as α, α_G, k_B', Λ') are regarded as "empirical values" or "initial cosmic parameters", lacking a unified logical origin. The self-referential logical formula z ≡ [z ≠ z] proposed in this paper is essentially the "statistical stability of logical inconsistency"—without any physical presuppositions or artificial tuning, this logic can spontaneously converge to a stable raw residual through the modulus-phase dual dimensions of the complex domain and three-dimensional neighborhood coupling. Previous studies observed a consistent ~8.5% relative error between this raw residual and physical constants, which was defined as the "logical-physical mapping gap". However, this study reveals that the gap is not an inherent defect but a result of omitting geometric projection correction. By introducing two intrinsic factors derived from pure logic and geometry: 3D solid angle normalization factor Ω = 1/(4π) (reflecting the geometric properties of 3D observational space); Natural exponential collapse based on iteration depth (simulating the scale degradation of logic from microscopic to cosmic scales); the raw logical residual can be accurately projected to physical constants with ultra-low errors (