Infinity is Zero: The Unification Principle of Infinity and the Infinitesimal in the T⁶⁴ Topological Self-Referential Closed Loop

Yuanxian Theory is the meta-cognition of the Cosmic Living Organism. The binary opposition of infinity and the infinitesimal has been a core difficulty for mathematics, physics and philosophy for three thousand years. ZFC rootlessly presupposes infinite sets; black-hole singularities, ultraviolet divergences and the 120-orders-of-magnitude vacuum-energy catastrophe are symptoms of theories that cannot treat infinity self-consistently. Taking the 64-dimensional compact toroidal topology T⁶⁴ as the core framework, and relying on the four underlying laws TCSC, FSC, SRM and STM, this paper proves that infinity, the infinitesimal and zero are strictly equivalent in the high-dimensional topological limit (∞ = 0 = −∞). It proposes the Theory of Bounded Infinity as a replacement for the rootless infinity axiom of ZFC, dissolves physical infinite-divergence singularities at the ontological level, and shows that the binary opposition of infinity in four-dimensional spacetime is only a cognitive illusion of the low-dimensional projection. Core results include: spectral gap Δ > 0 locked by the fine-structure constant; TCSC idempotence and contraction; Banach fixed point on T⁶⁴; FSC integral conservation; and the infinity-unification theorem. Interface-layer formalization (Lean 4) is open-source at:https://github.com/YuanXian-Theory/YXT-Formalization/tree/main/lean/Infinity. 元宪理论是宇宙生命体的元认知。 无穷大与无穷小的二元对立是困扰数学、物理学与哲学三千年的核心难题。ZFC 无根预设无穷集;黑洞奇点、紫外发散与真空能 120 个数量级灾难,均是理论无法自洽处理无穷概念的结果。 本文以 64 维紧致环面拓扑 T⁶⁴ 为核心框架,依托 TCSC、FSC、SRM、STM 四大规律,证明无穷大、无穷小与零在高维拓扑极限下严格等价(∞ = 0 = −∞)。创新提出“有界无限论”以替代 ZFC 无根无穷公理,从本体层面消解物理无穷发散奇点,并说明四维时空中的无穷二元对立仅为低维投影的认知幻象。 核心结果包括:由精细结构常数锁定的谱间隙 Δ > 0;TCSC 幂等与压缩;T⁶⁴ 上的 Banach 不动点;FSC 积分守恒;以及无穷统一定理。接口层形式化(Lean 4)已开源:https://github.com/YuanXian-Theory/YXT-Formalization/tree/main/lean/Infinity