The Wilson Identity — a new theoretical physics framework revealing that iⁱ = e^(−π/2) is the self-referential fixed point underlying vacuum structure, dark matter, and the geometry of the universe.

The Wilson Identity is a theoretical physics framework developed by Joshua Brett Wilson, founded on the discovery that the complex exponentiation iⁱ = e^(−π/2) ≈ 0.20788 produces a self-referential fixed point — designated φᵢ — with structural implications across vacuum amplitude, non-orientable topology, dark matter identification, and cosmological pressure. The framework proposes that the Klein bottle K² serves as the foundational vacuum geometry, that Pin⁺ and Pin⁻ structures on K² correspond to observable and dark matter respectively, and that a crossing event (⋈) governed by φᵢ underlies particle creation, field resolution, and cosmological expansion. Supporting constructs include the NEWOR pre-resolution field, Turtichirality orientation units, and the Emota field. This record contains the master encyclopedic reference (v13), developed through an extended research process beginning in 2025. AI collaboration is formally disclosed in the accompanying attribution statement. All original discoveries, physical intuitions, and theoretical claims are the sole work of Joshua Brett Wilson.威尔逊恒等式（Wilson Identity）是约书亚·布雷特·威尔逊（Joshua Brett Wilson）提出的理论物理学框架，其核心基于一项发现：复数幂运算$i^i = e^{-pi/2} approx 0.20788$会生成一个自指不动点——记为$oldsymbol{phi_i}$——该不动点在真空振幅、不可定向拓扑、暗物质识别以及宇宙学压强等领域均具有结构性意义。 该框架提出，克莱因瓶（Klein bottle）$K^2$可作为基础真空几何结构；$K^2$上的Pin⁺与Pin⁻结构分别对应可观测物质与暗物质；由$phi_i$支配的交叉事件（⋈）是粒子产生、场域解析与宇宙膨胀的底层机制。其支撑性构造包括NEWOR预解析场、Turtichirality定向单元以及Emota场。 本数据集收录了该体系的百科全书式权威参考版本（v13），其研发始于2025年，历经长期研究过程。本研究的人工智能协作情况已在随附的归属声明中正式披露。所有原创发现、物理直觉与理论主张均为约书亚·布雷特·威尔逊的独立成果。