Q: How do temporal dimensions impact tiering?
A: The relationship between the spatial dimensions of a universe and the additional temporal dimension(s) may be visualized as something akin to the frames of a movie placed side-by-side. Basically, the time-like direction may be thought of as a line comprised of uncountably infinitely many points, each of which is a static "snapshot" of the whole universe at any given moment, with the set of all such events comprising the totality of spacetime. But, a cosmological structure can contain two or more perpendicular time axis, rather than just a singular time axis. By having two perpendicular axis the cosmology must have a "higher" level of time that can fit the crossing time axis, for the same reason why a geometric "X" line and a geometric "Y" line would require a two-dimensional plane to catalogue their interaction properly. Instead of a direction of movement, however, a temporal axis is the temporal element of the cosmology, which is the "snapshots" along the line that captures all the states in which the cosmology can exist in. By having two axis, there must be an even higher-dimensional container, as every axis would add an uncountable infinite element to the cosmology, as there must be an uncountable infinite number of snapshots to an already uncountable infinite number of snapshots.
So, for a typical universe, it is a 3-A or three-dimensional structure of significant size collected as an uncountable infinite number of static snapshots through its time axis, making the space-time of the cosmology Low 2-C to fit all the possible universe iterations (3D+1). By having a second axis going in a perpendicular direction, this requires the space-time of the cosmology to have a fifth-dimensional axis to capture the "snapshots" that generate a fourth-dimensional axis (3D+2). More time axis would add an additional total axis with the overall cosmology. Additionally, while a three-dimensional structure is used as an example, this can also work with higher-dimensional structures. So a sixth-dimensional structure with three temporal axis (6D+3) would require a nine-dimensional space of infinite size to contain all the snapshots generated by the space-time continuum.
Outside of explanations which state that multiple time dimensions exist, it is difficult to show that a work of fiction has more than one. The key point that has to be established is that there is a kind of time that flows in a different direction than the past or the future or any of the spatial directions.
Things like timelines having time that passes at different rates would not qualify, as even the theory of general relativity already establishes that with just one regular time dimension time can flow at different rates in different places. Time flowing backwards in another universe would also not qualify it to have an additional time dimension, as it would still use the same directions of past and future as regular time, just with events playing out in reverse. For the same reasons, statements about independent time streams or of separate kinds of time, which could flow parallel to the original time, would not qualify.
Dimensions that are timeless voids or are described as beyond spacetime in general would also not qualify. Unless they contradict themselves, these realms should not have a time dimension at all, with change in them happening according to other principles. If they, on the other hand, do contradict themselves, the statement of them not having regular time would inherently not be reliable, making the idea equally unusable.
Of particular consideration are instances in which timelines as a whole are changed, such that there is a timeline (or multiple timelines) before they were changed and after they were changed or created/destroyed. As the timelines as a whole are changed, the before and after in this context can't be the past and future the timelines usually use, but should be a separate direction.
However, caution is necessary. As explained above, we require that the additional time dimension is "a line comprised of uncountably infinitely many points." If new versions of timelines are only created if they are changed through singular action, such as time travel for example, then the number of "snapshots" of the timeline would be far more limited. The amount of snapshots would be one more than the number of times the timeline was changed. So, for example, if the timeline is rewritten 2 times, there would be 3 snapshots of the timeline: the original, the timeline after the first rewrite, and the timeline after the second rewrite. Which is far less than the required uncountably infinitely many that a higher temporal axis requires.
Aside from direct statements, the easiest way to confirm that the line is comprised of uncountably infinitely many points/"snapshots" is to show that the development of the timelines is time-like. I.e. typically one would want a statement indicating that the alteration of the timelines is subject to its own flow of time, or that timelines are separated from each other by an additional temporal dimension through which a special form of time travel may be used to reach other versions of that timeline. The most important part is that the timelines are separated from each other by an additional temporal axis, as this implies that the initial version of the timeline is merely one "snapshot" out of a continuous, uncountably infinite flow of "snapshots."
Note that cases in which the timelines are separated by a spatial axis, are merely branching timelines, or otherwise cannot be demonstrated to have an additional temporal axis separating them would not qualify, and that such statements can be considered contradicted if the fiction specifies that new versions of the timeline, i.e. additional snapshots, are only created when the timeline is altered or similar.
One other pitfall to consider is the case of branching timelines, where one can return to a past with fewer timelines by just going back to a point in the regular past that was before the split happened. In such cases one has to decide based on context if that is meant or if a prior version where the splits also didn't exist in the regular future is meant. The former case doesn't qualify for an additional time dimension, while the latter might if it meets the other outlined criteria.
