Ontological Extension Based on ZFC: Formal Foundations of the Self-Referential Mind Field and Reconstruction of YuanXian Axioms

This paper constructs a rigorous ontological extension for YuanXian Theory (YXT) within the axiomatic framework of Zermelo-Fraenkel set theory (ZFC). We explicitly introduce three core ontological symbols: SelfReferentialMindField as a basic type representing the meta-cognitive entity of the universe; T^64 as a concrete, computable 64-dimensional toroidal topological space equipped with a complete Riemannian metric, connection, and fiber bundle structure; and UniverseFactor as a conserved, global constant function corresponding to the fine-structure constant = 1/137. 035999084. Based on these constructions, we reconstruct the four core axioms of YuanXian Theory — True Circle Self-Consistency (TCSC), Conservation of the Universal Factor (FSC), Unique Spacetime Manifold (STM), and Self-Referential Mind Field Generation (SRM) — transforming philosophical concepts such as “the universe is an absolutely isolated, self-referential closed system” into formally precise theorems within ZFC. Main contributions include providing a solid set-theoretic foundation for YuanXian Theory, achieving full computability of the T^64 structure, formalizing the notion of self-reference in classical mathematics, and implementing and partially verifying all definitions and theorems in Lean 4 and Coq. This work lays a key formal foundation for advancing YuanXian Theory from philosophical speculation toward a computable and machine-verifiable mathematical-physical theory. 本文在 Zermelo-Fraenkel 集合论 (ZFC) 的公理化框架下, 为元宪理论 (YuanXian Theory, YXT) 构建了一个严格的本体论扩展。我们明确引入了三个核心本体论符号: 自指心场 (SelfReferentialMindField) 作为基本类型, 表示宇宙的元认知实体;64维环面 (T^64) 作为一个具体的、可计算的拓扑空间, 配备完整的黎曼度量、联络和纤维丛结构;宇宙因子 (UniverseFactor) 作为一个守恒的全局常函数, 对应精细结构常数 = 1/137. 035999084 的数学抽象。 基于这些构造, 我们重建了元宪理论的四大公理——真圆自洽性 (TCSC) 、宇宙因素守恒 (FSC) 、时空流形唯一性 (STM) 、自指心场生成 (SRM), 将“宇宙是绝对孤立、自指闭合系统”等哲学概念转化为 ZFC 内具有精确语义的形式化定理。 主要贡献包括: 为元宪理论提供坚实的集合论基础, 实现 T^64 的完全可计算性, 在经典数学框架内形式化“自指性”概念, 并已在 Lean 4 和 Coq 中实现与部分验证所有定义和公理。本研究为元宪理论从哲学思辨走向可计算、可机器验证的数学物理理论奠定了关键的形式化基石。