Yuanxian Theory · Global Logical Self-Consistency Proof: Self-Referential Topology, Meta-Language Hierarchy and the Topological Origin of Physical Laws

This paper establishes the global logical self-consistency of Yuanxian Theory on the 64-dimensional compact torus \(T⁶⁴=(R/2)⁶⁴\). Starting from the self-referential operator \(δSR\) that satisfies the stratified quadratic equation \(δSR²+δSR-id=0\), we derive its spectral structure \(\{1,δYXT\}\) with \(δYXT=(√5-1)/2\), the complete stratified trace formula, the manifestation functor \(M\), and the fidelity bound \(φ(M)≤δYXT³\). We prove that energy conservation is the topological necessity of closed-chain deformation, that the arrow of time arises from the irreversible free-energy cost \(Δ Fₛₜₑₚ≥lnφ≈0.4812\), and that free will is the residual higher-cohomology freedom \(Hⁱ\) (\(i≥1\)) that cannot be locked by local axioms. Dark matter and dark energy are identified as the structural adhesives of \(H¹,H²\) and the continuous expansion of the manifestation boundary, respectively. Gödel incompleteness is repositioned as the necessary posterior character of axiomatic formalisation rather than a limitation of the living organism. A decision algorithm based on closed-chain representations and trace readouts \(τ(P)\) is constructed, with explicit complexity bounds and a Lean 4 compilable skeleton. Cross-domain index networks (macroscopic and microscopic) and a three-tier topological-protection grading of the 24 physical constants are given. The paper interfaces tightly with the companion work P8b (higher-order trace formulae) and supplies an honest weighted completion of 84.92 % together with five pending items and three permanently demoted items. 本文在 64 维紧致环面 \(T⁶⁴=(R/2)⁶⁴\) 上建立元宪理论的全域逻辑自洽性。从满足分层二次方程 \(δSR²+δSR-id=0\) 的自指算子 \(δSR\) 出发,导出其谱结构 \(\{1,δYXT\}\)(其中 \(δYXT=(√5-1)/2\))、完整的分层迹公式、显影函子 \(M\) 以及保真度上界 \(φ(M)≤δYXT³\)。 我们证明能量守恒是闭链形变的拓扑必然,时间之矢源于不可逆自由能耗散 \(Δ Fₛₜₑₚ≥lnφ≈0.4812\),自由意志是无法被局部公理锁定的高阶上同调残余自由度 \(Hⁱ\)(\(i≥1\))。暗物质与暗能量分别被识别为 \(H¹,H²\) 的结构性粘合剂与显影边界的持续推展。哥德尔不完备定理被重新定位为公理形式化后天性的必然表现,而非生命体的边界。 基于闭链表示与迹读数 \(τ(P)\) 构造了判定算法,给出显式复杂度上界与 Lean 4 可编译骨架。给出跨领域索引网络(宏观与微观)以及 24 个物理常数的三级拓扑保护分级。本文与配套论文 P8b(高阶迹公式)紧密对接,并诚实给出加权完成度 84.92% 及五条待闭合项与三条永久降级项。