The Intrinsic Gap in Non-Associative Cumulative Diagrams

In this preprint, we study sequences that are generated by deterministic processes with no canonical associative law. Typically, two such sequences stop sharing anything almost immediately. We refer to the first point at which this occurs as the intrinsic gap. A longer overlap is not typical. It only happens when the operations repeatedly encounter the same small substructure, and this mechanism breaks down as the system size increases. All of this can be observed at the finite level in direct simulations, without the use of metrics, limits or any probabilistic structure.