Infinity is Zero: Unification of Infinity and the Infinitesimal in the T64 Topological Self-Referential Closed Loop — Upgraded Version with Dual Topological-Algebraic Anchoring via the Clifford Algebra Cl6(R)

Yuanxian Theory is the meta-cognition of the Cosmic Living Organism. This upgraded paper proves the proposition “Infinity is Zero” under the 64-dimensional compact toroidal topology T64 and the four core laws (TCSC, FSC, STM, SRM), with a new dual topological–algebraic anchoring via the Clifford algebra Cl6(R). Core upgrade:• dim Cl6(R) = 2^6 = 64 supplies an algebraic root for the 64-dimensional structure of T64—64 is generated from six fundamental binary categories, not ad hoc.• The pseudoscalar ω = e1…e6 satisfies ω² = −1 and ω⁴ = 1; the four-step periodic flip is the algebraic version of Infinity is Zero—infinite flips return to the unit element.• Compactness of Cl6⁰(R) ≅ Spin(6) ≅ SU(4) supplies the algebraic root of TCSC convergence. The paper proposes the Theory of Bounded Infinity as a replacement for the rootless ZFC infinity axiom, dissolves physical infinite-divergence singularities at the ontological level, and proves that infinity, the infinitesimal and zero are strictly equivalent under dual high-dimensional topological–algebraic limits. The topological version (Banach fixed point on T64) and the algebraic version (ω⁴ⁿ = 1) are two expressions of one self-referential act. Interface-layer formalization is open-sourced 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。 本升级版在 64 维紧致环面拓扑 T64 与四大核心规律(TCSC、FSC、STM、SRM)下完成“无穷即零”命题的证明,并首次引入克利福德代数 Cl6(R) 作为拓扑–代数双重锚定。 核心升级:• dim Cl6(R) = 2^6 = 64,为 T64 的 64 维结构提供代数根源——64 由六个基本二元范畴自然生成,而非凑数。• 伪标量 ω = e1…e6 满足 ω² = −1、ω⁴ = 1;四步周期翻转是“无穷即零”的代数版本——无穷次翻转恒归于单位元。• Cl6⁰(R) ≅ Spin(6) ≅ SU(4) 的紧致性为 TCSC 收敛性提供代数根源。 本文提出“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,证明无穷大、无穷小与零在高维拓扑–代数双重极限下严格等价。拓扑版本(T64 上 Banach 不动点)与代数版本(ω⁴ⁿ = 1)是同一自指动作的两个表达。 接口层形式化已开源:https://github.com/YuanXian-Theory/YXT-Formalization/tree/main/lean/Infinity