Formal Foundation and Machine Verification of YuanXian Theory: ZFC Compatibility, Relative Consistency Proof, and Lean 4 Implementation

YuanXian Theory (YXT / YD-T^64) proposes that the universe's spacetime is a 64-dimensional compact torus T^64, with physical constants originating from the fixed point of the Self-Referential Mind Field Ψ. This paper establishes the formal legitimacy of the theory by proving its relative consistency with Zermelo-Fraenkel set theory with Choice (ZFC). We construct an inner model in a sufficiently large V_κ and verify all core YXT axioms. We also provide a complete open-source Lean 4 formalization, distinguishing operator self-reference (validated by the Banach Fixed Point Theorem) from forbidden set self-reference. All core modules are machine-verifiable. This work completes the transition of YuanXian Theory from a philosophical framework to a rigorous, computer-verifiable formal scientific system. 元宪理论 (YXT / YD-T^64) 提出宇宙时空为 64 维紧致环面 T^64, 物理常数源于自指心场 Ψ 的不动点。本文通过证明该理论与 ZFC 集合论的相对一致性, 确立了其形式合法性。 我们在足够大的 V_κ 中构造内模型, 并验证了所有核心公理。同时提供了完整的 Lean 4 开源形式化实现, 严格区分了基于 Banach 不动点定理的合法算子自指与违反正则公理的集合自指。所有核心模块均可被机器验证。 本文标志着元宪理论从哲学纲领走向严格可机器验证的形式科学体系。