We study the utility of chains defined on causal sets in estimating continuum properties like the curvature, the proper time and the spacetime dimension through a numerical analysis. In particular, we show that in $\text{dS}_2$ and $\text{FLRW}_3$ spacetimes the formalism of arXiv:1212.0631 with slight modifications gives the right continuum properties. We also discuss a possible test of manifoldlikeness using this formalism by considering two models of non-manifoldlike causal sets. This is a part of a broader idea of the geometrical reconstruction of continuum properties given a discrete sub structure, in this case the causal set.

中文翻译：

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使用链的因果集的流形属性

我们通过数值分析研究了在因果集上定义的链在估计曲率、适当时间和时空维度等连续介质属性方面的效用。特别是，我们表明在 $\text{dS}_2$ 和 $\text{FLRW}_3$ 时空中，arXiv:1212.0631 的形式主义稍加修改后给出了正确的连续统属性。我们还通过考虑非流形因果集的两个模型来讨论使用这种形式主义的流形相似性的可能测试。这是给定离散子结构（在这种情况下是因果集）的连续属性的几何重建的更广泛思想的一部分。