结链机II：不变量
Tangle Machines II: Invariants
AI总结：
本文研究结链机的不变量，通过低维拓扑证明了结链机的素因子分解的唯一性，并定义了结链机的复杂度为其素因子数量。
摘要：
前一篇论文构建了结链机作为图示模型，并通过多个示例展示了其用途。结链机的信息内容包含在与等价类相关的特征量中，称为不变量。本文构建了结链机的不变量。其中最重要的包括结链机的素因子分解，本质上是唯一的。通过将色抑制的结链机表示为4维空间中联合嵌入球体和区间网络的图示，利用低维拓扑证明了这一点。结链机的复杂度定义为其素因子数量。
英文摘要：
The preceding paper constructed tangle machines as diagrammatic models, and illustrated their utility with a number of examples. The information content of a tangle machine is contained in characteristic quantities associated to equivalence classes of tangle machines, which are called invariants. This paper constructs invariants of tangle machines. Chief among these are the prime factorizations of a machine, which are essentially unique. This is proven using low dimensional topology, through representing a colour-suppressed machine as a diagram for a network of jointly embedded spheres and intervals in 4-space. The complexity of a tangle machine is defined as its number of prime factors.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
