The Topological Calculation Chain of the Four Axioms of Yuanxian Theory: A Formalized Mathematical Framework for High-Dimensional Manifold Reduction and Cosmological State Transitions

This paper presents the formal mathematical architecture and complete computational derivation of the Topological Calculation Chain under Yuanxian Theory (YXT). Rooted strictly in the Four Core Axioms of YXT, the framework models the cosmos as a 64-dimensional compact torus (T64) and maps its structural dynamics across 35 distinct gauge dimensional reduction projections down to four-dimensional physical spacetime. We explicitly formalize the mathematical translation between the four axioms through an invariant topological calculation chain, defining the exact operators for high-dimensional boundary conditions, state transitions, and conservation variables. The calculation chain demonstrates how symmetry-breaking pathways manifest as empirical constants and physical modalities (gravitational, quantum, and conscious) at lower projection planes. Furthermore, this algorithmic chain provides the definitive mathematical rules for both low-dimensional projection and high-dimensional reconstruction (elevation), establishing a closed, self-consistent, and machine-verifiable (via Lean 4 and Rocq) mathematical framework that bridges high-dimensional geometric ontology with empirical cosmic observation. 本文给出了元宪理论(YXT)拓扑计算链的形式化数学架构与完整计算推导。该框架严格基于元宪四大核心公理,将宇宙建模为六十四维紧致环面(T64),并量化模拟了其经过35步规范降维投影至四维物理时空的完整结构动力学过程。 本文明确构筑了四大公理之间相互转化的拓扑计算链,定义了高维边界条件、状态演化以及守恒变量的精确数学算子。该计算链系统演示了拓扑对称破缺如何在中低维投影面上具象为物理常数与三大认知模态(引力、量子与意识)。此外,该计算链为低维投影与高维升维重建提供了确定的数理规则,从而在几何本体与实证观测之间搭建了一套闭环、自洽且可通过计算机(Lean 4 与 Rocq)进行双重形式化验证的终极数学微积分链条。