T3 Topological Elastic Field Theory: A Unified Analysis Report from Non-Associative Algebra and Topological Phase Transitions to Gravitation and Cosmology T3拓扑弹性场论: 从非结合代数、拓扑相变到引力与宇宙学的统一分析报告

Abstract This report presents a unified field-theory framework based on T3 non-associative algebra and topological elastic dynamics. Abandoning the traditional “action-at-a-distance force” and “point-particle” models, T3 theory defines the underlying substrate of the universe as a continuous medium with intrinsic topological elasticity (the T3 vacuum field). The maximum elastic velocity limit of this medium along a single dimension is the speed of light c. This report rigorously proves that the stable topological structures of elementary particles are governed by the orthogonal-capacity limit of three-dimensional space: the single-branch Möbius strip (lepton, N=1) reaches an intrinsic full-power velocity of 2c through parallel elastic superposition, while the three-orthogonal-branch trefoil knot (baryon, N=3) reaches 2√3·c through three-dimensional spatial synthesis. Higher-order knots with N ≥ 4 disintegrate because non-orthogonal interference drives their velocity below the √2·c survival threshold. Building on this dynamical foundation, the report derives the gravitational equation g = V⁴/(GM), revealing the vortex-inflow nature of gravitation. It further establishes an electron-photon phase-transition equation through the T3-Euler complex-rotation structure, explaining the topological origin of quantum discreteness (Planck’s constant h). Finally, the report proposes a “gear-topology model” and a “compound-gear arrangement mechanism” to unify the Pauli exclusion principle, electromagnetic interaction, nuclear binding energy, and chemical bonds within the T3 vacuum topological dynamics framework. It also proposes a topological origin of electric charge: charge is not an intrinsic label of the particle core but a dynamical effect of a surrounding √2·c metastable vortex shell. By introducing the Frenet-Serret frame, the report rigorously proves that the superposition coefficient S is determined by the ratio of curvature κ to torsion τ, providing a solid mathematical proof for… [line truncated, original length=2039] 摘要 本报告提出一套基于T3非结合代数与拓扑弹性动力学的统一场论框架。T3理论摒弃了传统的”超距力”与”点粒子”模型,将宇宙底层定义为一种具有内禀拓扑弹性的连续介质(T3真空场)。该介质在单一维度上的最大弹性速度极限为光速 c。本报告严格证明:基本粒子的稳定拓扑结构受制于三维空间的正交容量极限——单分支莫比乌斯环(轻子,N=1)通过平行弹性叠加达到 2c 的本体满功率;三正交分支的三叶结(重子,N=3)通过三维立体合成达到 2√3·c。N ≥ 4 的高阶纽结因非正交干涉导致速度跌破 √2·c 生存门槛而解体。基于此动力学基础,本报告推导出引力方程 g = V⁴/(GM),揭示了引力的旋流向心本质。报告进一步通过T3-Euler复旋结构,建立了电子-光子相变方程,解释了量子离散性(普朗克常数 h)的拓扑起源。最后,报告提出”齿轮拓扑模型”与”复合齿轮排列机制”,将泡利不相容原理、电磁相互作用、原子核结合能及化学键统一在T3真空拓扑动力学框架下。报告还提出了电荷的拓扑起源机制:电荷并非内核本体内禀标签,而是外围 √2·c 亚稳态涡旋壳层的动力学效应。通过引入Frenet-Serret标架,本报告严格证明了叠加效应系数 S 由曲率 κ 与挠率 τ 的比值决定,这为自旋拓扑的动力学起源提供了坚实的数学证明。