Dimension estimation from generalized interval-size distributions

Determine whether the distribution of generalized interval sizes provides a better estimate of causal-set dimension than the distribution of ordinary interval sizes.

Background

The paper explains that ordinary interval-size distributions can encode the Minkowski dimension of a causal set, but that convergence of the associated limiting values is slow. The generalized interval polynomial introduced in the paper records richer information involving upsets, downsets, and their intersections.

The authors explicitly leave unresolved whether this additional generalized-interval information improves dimension estimation. The question is motivated by the limitations of existing interval-size methods in causal set theory.

References

One shortcoming of estimating dimension through the distribution of interval sizes is that the convergence of the values $s_kd$ is slow . This led us to the following question: can the extra information from the distribution of generalized interval sizes offer a better estimate for causal set dimension?

— The Generalized Interval Polynomial of a Poset  (2511.14924 - George et al., 18 Nov 2025) in Section 7.2, “Estimating Dimension”