莫比乌斯电子与三叶结重子的T3原生代数拓扑自旋轨道与核心定理完整推导T3‑Native Algebra, Topological‑Spin Orbits and Full Proof of Core Theorems for Möbius Electron and Trefoil Baryon

Abstract Within the native algebraic system T3‑v2.1 (), this paper presents rigorous algebraic derivation and complete proof for topological‑spin orbits of the Möbius electron and trefoil baryon. Main achievements: A unified algebraic language in super‑Euler form is proposed. The Möbius spinor operator and trefoil braiding operator are defined; topological periods are encapsulated inside exponential functions. The Möbius vortex orbit for electron is constructed. Spinor topological properties: sign‑flip at and recovery at , are derived rigorously. It is proved that the whole Möbius‑electron orbit lies entirely on the null‑factor cone (). The algebraic origin of its topological irreversibility is revealed. Baryon orbit is constructed. It closes periodically with period without spinor sign‑flip. It traverses the null‑factor cone intermittently, corresponding to topological cross‑coupling of three vortex filaments. Four core theorems for electron and three core theorems for baryon are proved. They supply the underlying algebraic skeleton for Dirac‑equation derivation and factor computation in quantum sequel. Keywords: T3‑algebra; Möbius electron; trefoil baryon; super‑Euler form; topological spin; null‑factor cone; spinor 摘要 本报告在T3‑v2.1原生代数体系()下,完成了莫比乌斯电子与三叶结重子拓扑自旋轨道的严格代数推导与核心定理的完整证明。 核心成果包括: 提出了超欧拉形式的统一代数语言,定义了莫比乌斯旋量算子与三叶结编织算子,将拓扑周期封装进指数函数。 建立了电子莫比乌斯涡旋轨道 ,严格导出了旋量拓扑的 反号、 复原特性。 证明了莫比乌斯电子轨道恒居于零因子锥 之上(),揭示了其拓扑不可逆的代数本质。 构建了重子轨道 ,实现 周期闭合,无旋量反号,并证明其间断穿越零因子锥,对应三根涡丝拓扑交叉耦合。 完成四大核心定理与三大核心定理的严格证明,为量子篇的狄拉克方程、 因子提供底层骨架。 关键词:T3代数;莫比乌斯电子;三叶结重子;超欧拉形式;拓扑自旋;零因子锥;旋量