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".