Classification of causally complete spaces on 3 events with binary inputs
Abstract
We present an exhaustive classification of the 2644 causally complete spaces of input histories on 3 events with binary inputs, together with the algorithm used to find them. This paper forms the supplementary material for a trilogy of works: spaces of input histories, our dynamical generalisation of causal orders, are introduced in "The Combinatorics of Causality"; the sheaf-theoretic treatment of causal distributions is detailed in "The Topology of Causality"; the polytopes formed by the associated empirical models are studied in "The Geometry of Causality".
Cite
@article{arxiv.2303.09925,
title = {Classification of causally complete spaces on 3 events with binary inputs},
author = {Stefano Gogioso and Nicola Pinzani},
journal= {arXiv preprint arXiv:2303.09925},
year = {2023}
}
Comments
Originally the appendix of arXiv:2206.08911v2, now extended and published as a stand-alone paper. Some material is shared with the main three papers in the trilogy: "The Combinatorics of Causality" [arXiv:2206.08911], "The Topology of Causality" [arXiv:2303.07148] and "The Geometry of Causality" [arXiv:2303.09017]