ZFC Extension Consistency Proof: Transitive Inner Model Construction from YXTT to ZFC

Zermelo–Fraenkel set theory with Choice (ZFC) is the foundational languageof contemporary mathematics. YuanXian Self-Referential Type Theory (YXTT),the core formal system of YuanXian Theory, is built upon the high-dimensionaltopology of T 64 and the dynamics of a self-referential field. Its legitimacy thereforehinges on consistency with, and precise demarcation from, ZFC.Without assuming large cardinals or any other strong infinity axioms, this paperconstructs an explicit transitive inner model of ZFC that interprets YXTT, andestablishes two main results:1. YXTT is a language-conservative extension of ZFC: every pure first-order ZFC sentence provable in YXTT is already provable in ZFC;2. YXTT and ZFC have the same consistency strength: ZFC ⊢ Con(ZFC) →Con(YXTT).Conservativity constrains only the pure ZFC language. By introducing newpredicates (T64 closed chains, topological entropy, self-referential iteration, etc.)YXTT gains expressive power beyond ZFC; such extended statements are inde-pendent of ZFC and raise expressive dimension without raising logical strength.The paper carries out the ZFC-definable construction of the T 64 manifold, provesmeasure-preservation of the Haar measure, derives contractive convergence of theself-referential operator, translates the four core axioms into ZFC, builds the modelvia the Reflection Principle, and supplies a Lean 4 formalization framework compat-ible with Mathlib4, closing the loop between human proof and machine verification. ZFC 公理集合论是现代数学的底层基础。元宪理论核心体系 YXTT(元宪自指心场类型论)基于 T 64 高维拓扑与自指场动力学构建,其合法性取决于与 ZFC 的一致性及边界界定。本文在不引入大基数、强无穷公理等额外假设的前提下,严格构造 YXTT 对应的 ZFC 传递内模型,证明两大核心结论:(1) YXTT 是 ZFC 的语言保守扩展,即所有 ZFC 原生一阶语句若可由 YXTT 证明,则必然可由 ZFC 证明;(2) YXTT 与 ZFC 一致性强度等价,满足 ZFC ⊢ Con(ZFC) → Con(YXTT)。本文厘清理论边界:保守性仅约束 ZFC 原生一阶语言;YXTT 通过新增 T64闭链、拓扑熵、自指迭代等专属谓词,获得超越 ZFC 的结构表达能力,此类扩展命题独立于 ZFC,仅提升表达维度而不提升逻辑强度。全文完成 T 64 流形的 ZFC 可定义构造、哈尔测度保测性证明、自指算子压缩收敛性推导及四大公理的 ZFC 语义翻译,依托反射原理完成模型构造,并搭建适配 Mathlib4 规范的 Lean4 形式化框架,实现人工证明与机器校验的双向闭环。