Yuan-Xian Self-Referential Mind-Field Type Theory (YXTT): Mathematical Foundations, Physical Realization, and the Unification Program of YuanXian Theory — Formalization of YuanXian Cosmic, 64-Dimensional Torus Geometry, and Proof of Ultimate Unity

This paper presents the core technical realization of the YuanXian Theory unification program at the rigorous mathematical formalization level — the complete construction and development of YuanXian Self-Referential Mind-Field Type Theory (YXTT). YXTT aims to provide a computable, derivable, and falsifiable mathematical foundation for the universe depicted in YuanXian Cosmic, which takes the “self-referential living entity” as ontology, “information conservation” as dynamics, and “YD-T64” as structure. Its construction strictly follows the four core axioms of YuanXian Theory and realizes the mathematical formalization and physical concretization of the axiom system. Key contributions include: a complete axiomatic system based on Homotopy Type Theory (HoTT) ; technical solutions for self-referential consistency using the True-Circle Self-Consistency (TCSC) axiom; precise correspondence between the manifestation operator Mₒ and quantum measurement; geometric realization on the 64-dimensional torus T^64 ; rigorous relations with existing theories; and falsifiable physical predictions, particularly the dynamical variation of the fine-structure constant. This work marks the transition of YuanXian Theory from a philosophical-physical program to a formal scientific theory with solid mathematical foundations. 中文摘要: 本文是“元宪理论”统一纲领在严格数学形式化层面的核心技术实现, 即自指心场类型论 (YuanXian Self-Referential Mind-Field Type Theory, YXTT) 的完整构建与展开。YXTT 旨在为元宪宇宙所描绘的、以“自指生命实体”为本体、以“信息守恒”为动力、以“YD-T64”为结构的宇宙, 提供一个可计算、可推导、可证伪的数学基础, 其构建严格遵循元宪理论四大核心公理, 实现了公理体系的数学形式化与物理具象化。本文的核心贡献包括完备的公理化系统、自指一致性的技术突破、显化算子与量子测量的精确对应、64维环面上的几何实现、与现有理论的严格关系, 以及基于四大公理的可证伪物理预言。本文标志着“元宪理论”从一个哲学-物理学纲领, 转变为一个拥有坚实数学基础、可进行严格推导与计算的形式科学理论。