Constructive Realization of the Arithmetic-Physical Correspondence: A Proof of the Riemann Hypothesis Based on the YuanXian Axiom System

In view of the long-standing limitation of the “arithmetic-physical correspondence” to heuristic analogies, this paper takes the four core axioms of Yuan-Xian Theory (YXT) as the first principles and deeply integrates the YXTT global action S ₘₗₓₓ from “Global Cosmic Dynamics”. It constructively realizes a strictly categorical functor of the arithmetic-physical correspondence. This functor maps the linear vibration spectrum of the self-referential mind-field ₒₑ on the 64-dimensional torus T^64 (the real eigenvalues of the self-adjoint operator O) one-to-one onto the non-trivial zeros of the Riemann function. Through the True-Circle Self-Consistency axiom (TCSC), this paper rigorously proves that all non-trivial zeros must be rigidly locked on the critical line Re (s) =1/2. If any zero deviates from this line, it will directly cause non-physical disturbances in the energy density of ₒₑ, thereby rendering the energy-momentum tensor T_ anomalous and ultimately destroying the steady state of the macroscopic spacetime curvature. At the same time, the distribution of zeros acts as the “gear mechanism” that regulates the fine-structure constant to remain constant, forming a closed feedback loop with Axiom I. The Riemann complex plane is essentially the holographic projection plane of two specific dimensions (momentum-phase dimensions) of T^64. The full text presents the closed derivation from the global action S ₘₗₓₓ to the Riemann hypothesis, including explicit equations of motion, linearized operators, kernel functions, and commutative diagrams. It also provides a machine-verifiable Lean 4 formal proof and a directly runnable Python numerical simulation code. This paper marks the complete unification of “Global Cosmic Dynamics” with the core problems of number theory. 针对“算术-物理对应”长期局限于启发式类比的瓶颈, 本文以元宪理论 (YXT) 四大核心公理为第一原理, 深度融合《全域动力学》中的 YXTT 全局作用量 S ₘₗₓₓ, 构造性地实现了严格范畴论意义上的算术-物理对应函子 。该函子将 64 维环面 T^64 上自指心场 ₒₑ 的线性振动谱 (自伴算子 O 的实本征值) 一一映射到黎曼 函数的非平凡零点。 通过真圆自洽性公理 (TCSC), 本文严格证明所有非平凡零点必须刚性锁定在临界线 Re (s) =1/2。若任一零点偏离该线, 将直接导致 ₒₑ 能量密度产生非物理扰动, 从而使能量-动量张量 T_ 异常, 最终破坏宏观时空曲率的稳态。同时, 零点分布作为调节精细结构常数 保持恒定的“齿轮机制”, 与公理 I 形成闭合反馈回路。黎曼复平面本质上是 T^64 特定两个维度 (动量-相位维度) 的全息投影平面。 全文给出从全局作用量 S ₘₗₓₓ 到黎曼猜想的闭合推导, 包括显式运动方程、线性化算子、核函数及交换图, 并提供机器可验证的 Lean 4 形式化证明代码及可直接运行的 Python 数值模拟代码。本文标志着《全域动力学》与数论核心难题的完全统一。