A cladist is an identity that is embodied in one or more instances. While each of these instances remains their own complete individual with their own mind, they share the same memories and identity. Cladists are members of a clade (even if they are the only member of that clade) and those who have forked from a cladist are instances of that cladist, with the originating instance being described as the down-tree instance.
At the point when a cladist forks into a new instance, the two instances are identical in terms of their history, though their memories from that point immediately begin to diverge, if only by virtue of them having two different physical viewpoints. In most cases, the new instance will retain the same identity as their down-tree instance at first, though over time this may drift. The point at which an instance becomes a new cladist, adopting their own identity (and, often, name) unique from their down-tree, is called individuation. This is a matter of intent — even if only subconscious or half-sensed — on behalf of the instance, rather than simply a mechanical process.
While every cladist (indeed, every instance of every cladist) works differently, there are some general patterns that have been observed over time.
Two instances of the same cladist
In "Assignment", Ioan Bălan#Tracker forks Ioan Bălan#5f39bccd7 to write an article on a flashcult. Although this instance remains separate from eir down-tree instance for some time, ey retains the identity of Ioan Bălan. Not only does ey not diverge very long, but it was always eir intent to merge back down.
An instance unintentionally diverging to the point of individuation
In Qoheleth, the instance of Ioan Bălan#Tracker assigned to work on the project with Dear finds that ey has changed enough in the process as to have individuated. When #Tracker requests that ey merge down, there is a sense of rankling against identity, a sense of jealousy surrounding the hard-won experiences of the project. While ey does merge down, ey first forks in order to remain eir own individual, adopting the name Codrin Bălan, becoming the second member in the Bălan clade.
An instance intentionally diverging and adopting a new identity
In Nevi'im, Codrin Bălan#Castor decides to send an instance to Artemis to continue living there. Ey forks and, over the course of a few minutes, the new instance continues to change both physically and in terms of identity, adopting the name Sorina Bălan. In this sense, given the intent begun before the point of forking, Sorina exists as a unique cladist at the moment of forking, before even changing her name.