Dimensional Similarity Theory

The Dimensional Similarity Theory is a theory confirmed to exist within the dimensional cycle most of the events transpire in.

Logic
The Dimensional Similarity Theory governs all similarities in dimensional cycles like the one Pink and friends exist in.

Each event in each individual dimension must have some relevance to another in the same cycle, no matter what it is, or who it is that must be repeated. Events must happen similarly as well, and if something affects one dimension, it must affect all.

For example, the Star World looks very much like the Mushroom Kingdom world due to the influence of the Dimensional Similarity Theory. The levels are the same in structure, and the same amount of inhabitants exist in both worlds, counterparts of each other.

Mario, Stario, and Quario are all counterparts, created by the laws of the Dimensional Similarity Theory, that there must be a Mario in each dimension. Sometimes these rules fluctuate and allow a specific person more than one counterpart in a specific dimension (Bowser as such has 3 counterparts in the Star World in the form of Mastar, Cosmicalitaurus and Zythurvion).

In Super Mario 64: The Curse of the Invincibility Frames the Dimensional Similarity Theory also was revealed to govern the surrounding radius of a given person in relation to their counterparts, as well as the knowledge one has. When Pinkolol16 travelled to the Star World, Vindimka's actions had created a dimensional loop where knowledge wasn't being transferred properly as she was in the Star World, and thus her 4D counterpart and her Star World counterpart lacked the knowledge to know what was going on. Her 4D counterpart assumed it was a dimensional problem due to what the DST tried repairing, but only came to the amount it could do. When the heroes felt the energy, the DST spread this warning energy around to each counterpart, warning of the dire circumstances. This energy would track down the ones in danger and would fade away once order was restored. When characters go to other dimensions as well, the DST assures both sides they know they're talking to each other.

The DST is also known to control emotions of characters as well to a certain degree. Characters don't exactly act the same way, but are expected to have similar personalities, and there must be a special exception if there must be one. For example, the 4D counterparts are slightly more mature compared to their next dimensional counterparts, and know mostly about dimensions just as the next dimensioners know about color codes. Some characters have emotions swapped in this case but still a similar personality type. Powers follow this same basic guideline. (Enzo is known to be quite jolly and initiates mock-fear in some situations, Enzour is quite playful and instills mock-anger in situations where he feels like it. Both have an instance where they imitate an emotion, this is due to the DST).

Sometimes the DST may be delayed but still allows events to happen. In the case of CoIF, Rainboo wanted to follow Enzour to see his misery when he was trapped. Troll Boo later wanted to follow Enzo when he was getting chased by Enzour to see how he was doing. The DST governed his likeness for a situation. Sometimes, if events happen that change canon, events can be wiped entirely. Such as in the case of Into the Fourth Dimension, Mario meeting Quario and co. sealed the fate of Quario meeting Mario, and there is no point to his second meeting.

Characters meeting in one dimension could lead to a character going to a similar place for a predetermined reason in another dimension. Getting hurt also applies to all dimensional cycle inhabitants. A good example is the events of Into the Fourth Dimension, when Mario and MM54321 were captured, each of their counterparts in both the Fourth Dimension and the Star World had just fainted.

However, to the eyes of inhabitants, they see their decisions as normal and they only know of this to understand their lives better.

Trivia

 * It has been mainly pointed out in MM54321's series to highlight similar characters meeting, or specific characters going to locations or getting hurt by things. The DST governs these things too, but is however a very simplistic display of events.
 * Sometimes when the DST messes up the results can be quite confusing. Enzo and Enzour's color codes are a good example here.