标题： 通过辛拟群的因果关系检测 显示英文标题

标题： Causality Detection via Symplectic Quandles

摘要： 我们研究辛拟群着色是否能够揭示由“天空链接”编码的因果结构——即由时空中所有通过两点的光束组成的链接。 在已知亚历山大-康韦多项式局限性的基础上，我们将两个Hopf链接的连接和（代表所有因果无关的情况）与前两个Allen-Swenberg链接（当该多项式不起作用时仅有的已知例子）进行比较。 对于每个图示，我们报告了拟群计数不变量（着色总数）以及一个增强版本，该版本记录了每种着色中出现的不同颜色数量。 在我们对小有限域的测试中，普通计数在不同例子中通常一致，但增强不变量始终能将Hopf情况与Allen-Swenberg族区分开，并且随着域的增长变得更加具有区分性。 一个简单的转移步骤表明，这种效果在整个序列中持续存在。 这些结果表明，增强的辛拟群着色作为一种实际且可计算的因果性指示，可能比单独的经典多项式更能捕捉到因果性；此类例子的首次发现是由Jain完成的。 显示英文摘要

摘要： We study whether symplectic quandle colorings can reveal causal structure encoded by "sky links" - i.e. links consisting of spheres of all light rays through two points in the space of all light rays of a spacetime. Building on the known limitations of the Alexander-Conway polynomial, we compare the connected sum of two Hopf links (which represents all causally unrelated situations) with the first two Allen-Swenberg links (that are the only known examples when this polynomial does not work). For each diagram we report both the quandle counting invariant (total number of colorings) and an enhanced version that records how many distinct colors appear in each coloring. In our tests over small finite fields, plain counts often agree across examples, but the enhanced invariant consistently separates the Hopf case from the Allen-Swenberg family, and becomes more discriminating as the field grows. A simple transfer step suggests that this effect persists along the whole sequence. These results point to enhanced symplectic quandle colorings as a practical, computable indication of causality that classical polynomials alone may miss; the first examples of this kind were discovered by Jain.