Yuanxian Theory · Global Logical Self-Consistency Proof: Self-Referential Topology, Meta-Language Hierarchy and the Topological Origin of Physical Laws
Year: 2026
Type: preprint
Abstract: This paper establishes the global logical self-consistency of Yuanxian Theory on the 64-dimensional compact torus \(\mathcal{T}^{64}=(\mathbb{R}/2\pi\mathbb{Z})^{64}\). Starting from the self-referential operator \(\delta_{\mathrm{SR}}\) that satisfies the stratified quadratic equation \(\delta_{\mathrm{SR}}^{2}+\delta_{\mathrm{SR}}-\mathrm{id}=0\), we derive its spectral structure \(\{1,\delta_{\mathrm{YXT}}\}\) with \(\delta_{\mathrm{YXT}}=(\sqrt{5}-1)/2\), the complete stratified trace formula, the manifestation functor \(\mathcal{M}\), and the fidelity bound \(\phi(\mathcal{M})\le\delta_{\mathrm{YXT}}^{3}\). 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 \(\Delta F_{\mathrm{step}}\ge\ln\phi\approx0.4812\), and that free will is the residual higher-cohomology freedom \(H^{i}\) (\(i\ge1\)) that cannot be locked by local axioms. Dark matter and dark energy are identified as the structural adhesives of \(H^{1},H^{2}\) 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 \(\tau(P)\) 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 \(\mathcal{T}^{64}=(\mathbb{R}/2\pi\mathbb{Z})^{64}\) 上建立元宪理论的全域逻辑自洽性。从满足分层二次方程 \(\delta_{\mathrm{SR}}^{2}+\delta_{\mathrm{SR}}-\mathrm{id}=0\) 的自指算子 \(\delta_{\mathrm{SR}}\) 出发,导出其谱结构 \(\{1,\delta_{\mathrm{YXT}}\}\)(其中 \(\delta_{\mathrm{YXT}}=(\sqrt{5}-1)/2\))、完整的分层迹公式、显影函子 \(\mathcal{M}\) 以及保真度上界 \(\phi(\mathcal{M})\le\delta_{\mathrm{YXT}}^{3}\)。 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 \(\Delta F_{\mathrm{step}}\ge\ln\phi\approx0.4812\),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 \(H^{i}\)(\(i\ge1\))。暗物质与暗能量分别被识别为 \(H^{1},H^{2}\) 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 \(\tau(P)\) 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。
Author: Acharya, Zhenyuan
Language: English
Subfield: Statistical and Nonlinear Physics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7225809148
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