One difference between this and ordinary vectors is that here the geodesics are joined at their end, rather than intersecting in the middle.
In a causal invariant system, all geodesics eventually meet in the future
Possible version: there is no string rewriting system that gives you a certain sequence of strings and nothing but those strings. Does there exist a finite local rule that gives you a particular sequence?
Consider all simple multiway systems
For what sequences can one have a rule with a finite number of cases, and limited size strings?
Given that you observe a sequence, what substitution systems are consistent with that sequence?
For what observed sequences does there exist a rule that doesn’t lead to branching?
Single threadedness is possible when:
There is no overlap between strings except for last element
For ST (= Single threadedness) you must have no duplicates unless the tail of the sequence is periodic.