Finite smooth digraphs, that is, finite directed graphs without sources and sinks, can be partially ordered via pp-constructability. We give a complete description of this poset and, in particular, we prove that it is a distributive lattice. Moreover, we show that in order to separate two smooth digraphs in our poset it suffices to show that the polymorphism clone of one of the digraphs satisfies a prime cyclic loop condition that is not satisfied by the polymorphism clone of the other. Furthermore, we prove that the poset of cyclic loop conditions ordered by their strength for clones is a distributive lattice, too.

中文翻译：

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平滑有向图模原始正可构造性和循环循环条件

有限光滑有向图，即没有源和汇的有限有向图，可以通过 pp-constructability 进行部分排序。我们给出了这个偏序的完整描述，特别是我们证明了它是一个分布格。此外，我们表明，为了在我们的设置中分离两个光滑的有向图，只需证明其中一个有向图的多态性克隆满足另一个多态性克隆不满足的素循环条件即可。此外，我们证明了按克隆强度排序的循环循环条件的集合也是一个分布格。