The Hyperthetical
In the Solitary Universe, the Hyperthetical is the conceptual state of time itself, an equilibrium where all past, present, and potential future events occur simultaneously.
It is represented symbolically as a tree, the base embodying the ongoing present, or "true timeline" of the story's events; the roots standing for the past, what has already happened and cannot be changed; and the branches representing the infinite possibilities of the future.
Probabilities
In Vast Error, the future can only be perceived through the lens of probability, of potential hypothetical futures that branch off from alternate choices that could have been made in the story but never did because the hyperthetical demands it - this effectively makes their existence entirely fictional, or "non-canon", but they still play out as if they were real to sate the curiosity of whatever audience happens to be watchin at the time.
Probabilities are solely predicated on what wasn't done, only taking into account what has been done up until the point from which they split off from the true timeline. Because of this, there comes a point for every probability where they stop making sense and fall apart, at which point logic begins to rupture and anything goes, which can allow for otherwise impossible things to occur such as a probability influencing the true timeline.
Once a probability has played out to the extent of its perceivable interest, gaiaeon picks up the slack and erases them, ensuring that every probability ends in a blank slate and that none can have any influence on the true timeline 
.