Complete accounting of developmental replication pathways for c2 in the Outlier cellular automaton

Determine the complete set of distinct developmental cluster-lineage pathways—defined as sequences of cluster instances in the causal ancestry graph—that lead to self-replication of the cluster c2 under the Outlier cellular automaton rule, rather than only categorizing events by replication duration.

Background

The paper analyzes self-replication in the Outlier cellular automaton by constructing a causal ancestry graph of cluster instances and identifying self-replicating clusters. Focusing on the cluster c2, the authors find robust replication with many descendants and generations.

When examining all replication events derived from the initial c2 replicator, the authors report 18 distinct replication durations and infer that the number of unique developmental pathways—distinct sequences of clusters leading to replication—must exceed the count of observed durations. They explicitly state that producing a complete accounting of these pathways remains open.