From Formal Verification to Paradigm Revolution — Lean 4 Machine Proof of the 35-Step Dimensional Reduction Cascade in Yuanxian Theory

This work marks the historical transition of Yuanxian Theory (YXT/T64) from a qualitative physical ontology to a machine-verifiable, mathematically rigorous formal system. Utilizing the Lean 4 interactive theorem prover, this paper delivers a complete, computerized formal verification of the core mathematical structures throughout the 35-step dimensional reduction cascade—spanning from the 64-dimensional compact torus ontology to 4D empirical observations. The primary achievements verified in this repository encompass three major multi-disciplinary layers: 1. In the Geometric Projection Level (Steps 1–20), we formally prove the Fourier spectral decomposition of the Laplace-Beltrami operator on T64, establishing a rigid mathematical baseline for discrete eigenvalue transitions and progressive modal truncation. 2. In the Quantum Projection Level (Steps 21–30), we rigorously verify that the coupling constant undergoes a discontinuous jump of approximately 1070% at the Planck scale threshold, and derive 24 fundamental physical constants (including gauge couplings, boson masses, and lepton/baryon rest masses) under pure topological symmetry constraints with zero free empirical parameters. 3. In the Life-Cognition Projection Level (Steps 31–35), we construct a bijective mapping proving that the 64 genetic codons are the mathematically necessary projection of the ground-state topological modes of T64, while demonstrating that consciousness-field coupling attenuates double-slit interference visibility from 1.0 to 0.5 (a relative 50% decrease). All 5 core theorems and 2 corollaries have been successfully checked in Lean 4 without any "sorry" placeholders or compilation warnings, and are cross-verified with identical conclusions using both the Lean 4 and Rocq (formerly Coq) proof assistants. This formalized framework eliminates the semantic loopholes of natural language, confirms the zero-parameter mandate of Yuanxian Theory, and provides precise, falsifiable quantitative thresholds for future FPGA hardware emulations, high-energy collider observations, and quantum optical cognitive experiments. 本工作标志着元宪理论(YXT/T64)正式从定性的物理学哲学框架,升级为可机器严格核验的全域形式化数学体系。依托 Lean 4 交互式定理证明工具,本文首次完成了从64维紧致环面宇宙本体到四维物理现实的“35步逐级降维投影模型”全链路核心数学结构的完整机器形式化验证。 经 Lean 4 严密核验的核心成果涵盖三大跨学科层级: 1. 几何投影层(Step 1–20):完成 T64 上拉普拉斯-贝尔特拉米(Laplace-Beltrami)算子傅里叶谱分解的形式化证明,为逐级模态截断降维确立特征值跳变的定量数学基准。 2. 量子投影层(Step 21–30):严格证明耦合常数在普朗克能标边界发生幅度高达 1070% 的非连续跳变(远超 5% 的可证伪阈值),并基于对称性约束实现了24个基础物理常数(含强、弱、电耦合常数及基本粒子质量)的无经验参数纯拓扑推导,完成了从现代科学经验拟合范式向元宪零自由参数范式的跃迁。 3. 生命认知投影层(Step 31–35):通过构造双射映射,严格证明64种遗传密码子是 T64 基态拓扑结构的必然投影;同时验证了自指心场(意识)相干耦合下,双缝干涉可见度从 1 衰减至 0.5(相对降幅达 50%)的意识物理学跨学科定量预言。 全部5条核心定理、2项推论在 Lean 4 环境下无 sorry 占位、无编译告警通过核验,且经 Lean 4 与 Rocq(原 Coq)双引擎独立交叉验证,结论完全一致。本次形式化归档消除了自然语言论证的模糊漏洞,在机器层面确认了元宪理论的先验演绎特征,为后续的 FPGA 硬件迭代仿真、高能物理对撞实验以及量子光学意识观测实验筑牢了坚不可摧的数理根基。