T3拓扑弹性场论的离散接力模型: 基于非结合代数的动力学演化报告Discrete Relay Model for T3 Topological Elastic Field Theory: Dynamical Evolution Report Based on Non‑Associative Algebra

Abstract Based on the T3 non‑associative algebra (v2.1), this report proposes the T3 Relay Model, which reformulates the continuous T3 field theory into a computable discrete‑cell evolutionary system. The state of each spatial cell is described by a T3 number . The algebraic norm serves as the criterion of topological stability. Relay transfer is triggered once the state falls below the critical threshold . This report rigorously derives the rules for one‑dimensional single‑chain relay and multi‑component bifurcated relay, and proves the mathematical necessity of the energy‑fidelity constraint . Explicit evolution formulae for elliptic and hyperbolic spirals are presented, and the mechanism of emergent arrow‑of‑time originating from non‑associativity is clarified. This model provides a solid mathematical foundation for numerical simulation of T3 theory and its interface with discrete quantum field theory. Keywords: T3 non‑associative algebra; relay‑motion model; topological stability; discrete cellular automaton; arrow of time 摘要 本报告基于T3非结合代数(v2.1),提出离散接力运动模型(T3 Relay Model),将T3连续场论转化为可计算的离散元胞演化系统。每个空间单元的状态由T3数 描述,以代数范数 作为拓扑稳定性判据。当状态跌破临界阈值 时,触发接力传递。报告严格推导了单链一维接力与多分量分岔接力规则,证明能量保真约束 的数学必然性;同时给出椭圆、双曲螺旋显式内部演化公式,并阐释由非结合性所产生的时间箭头机制。本模型为T3理论的数值模拟以及对接离散量子场论提供坚实数学基础。 关键词:T3非结合代数;接力运动模型;拓扑稳定性;离散元胞自动机;时间箭头