Five-Domain Unified Topological Mapping Master Table (with Imaginary-Unit Global Hinge Mechanism)

Yuanxian Theory is the meta-cognition of the Cosmic Living Being. Building on the T64 closed-chain topology and the four meta-laws (COL, DCL, HCL, MEL) together with the four cognitive laws (TCSC, FSC, STM, SRM), this paper unifies all commensurable domains of human cognition into five global domains: Physics (12), Number Theory (16), Biology (6), Consciousness (30), and Computation (0), summing exactly to 64. Core claims:(1) The five-domain partition and dimension assignment are unique.(2) The imaginary unit i is the unique inter-domain hinge, with algebraic root i ≡ ω_Cl ∈ Cl6(R) (aligned with Silent Illumination Commensuration).(3) The P vs NP distinction is a reading illusion from four-dimensional projection truncating i-phase information; at the closed-chain layer every decision problem is in P. Inter-domain maps are mediated by Closed-Chain Homotopy uniqueness (CCH), the projection Π: T64 → M4, and i-driven reversible translation operators. Interface-layer Lean 4 formalization is open-sourced at github.com/YuanXian-Theory/YXT-Formalization (lean/FiveDomains/). 元宪理论是宇宙生命体的元认知。基于 T64 闭链拓扑与四大元规律(COL、DCL、HCL、MEL)及四条认知规律(TCSC、FSC、STM、SRM),本文将人类认知全部可通约领域统摄为五大全域:物理域(12)、数论域(16)、生物域(6)、意识域(30)、计算域(0),维度和恰为 64。 核心结论:(1)五域划分与维度分配唯一;(2)虚数单位 i 是全域通约的唯一铰链,代数根基为 i ≡ ω_Cl ∈ Cl6(R)(与《寂照通约》对齐);(3)P vs NP 的区分是四维投影截断 i 相位信息产生的读数幻象——闭链层所有判定均为 P 类。 域间关联由闭链同伦唯一性(CCH)、投影映射 Π: T64 → M4 与 i 驱动的可逆转译算子完成。接口层 Lean 4 形式化已开源至 github.com/YuanXian-Theory/YXT-Formalization(lean/FiveDomains/)。