System
This article is about the story term System. For a basic run-down of the game mechanics, go to Getting Started.
A System is a conceptual mechanism that enables any enclosed space to enact a certain "truth" upon reality within itself through constant replenishment of faith from the people that reside within it, otherwise known as the Master Rule. An alternative and simpler way of describing a System is a code of law that can overwrite reality within its area, but only as long as the majority of the people that reside within this space believe in it.
The requirements for what an 'enclosed space' entails is treated very loosely. An enclosed space can be as straightforward as the walls created within an App Battle and a building, or can be as loose as a whole World surrounded by a wall (such as the entire city of Tokyo) or the inside of a person's body.
While the term "System" is commonly used to describe the different societal mechanisms each World has in order to function, it is a broad term used to describe any rules and mechanisms placed within an enclosed space. The term has been used to describe how the Walls of Tokyo prevent people from leaving, as well as to describe smaller instances such as the rules of a Virtual World.
Master Rule
The Master Rule, also commonly referred to as majority rule, is the powering force behind all Systems. It works under a very simple function: What the majority of people within an enclosed space believe becomes reality. There are seemingly no limits to what this system can do, from enabling the use of Sacred Artifacts outside of the App once the majority of Tokyo residents are App users, or reversing time once enough people wish for a reset.
The simplicity of the Master Rule also makes it very susceptible to being taken advantage of by those cunning enough to use it to their advantage. 
Nodens was able to shift the masses' belief of an outer space invasion from 'impossible' to 'possible' by broadcasting his own invasion memories via media manipulation, and 
∀Isaac attempted to assimilate the whole population of Tokyo into 
Ramu by only absorbing the majority of the population.
App System
The area inside The Walls, or Tokyo, is unique in that there, 24 different Systems of 24 different Worlds meet and clash including Tokyo's own original System. Thus a framework and protocol to deal with entities foreign to the it is needed. This would include how the world permits Rules to override its own laws of physics. A new System is set in place by the App.
Protocols of the App System
In Tokyo, Rules with similar powers cannot be applied at the same time and place. Examples include the following:
Horkeu Kamui could not freeze the ice that 
Chernobog cast on the 
Protagonist during the events of Black Snow on the Hot Spring Mountains
Benten could not redirect the waves of the sea with her Rule to interfere with the attempt of the 
Mermaids to steer a ship during the events of Embark! Summer Ocean Adventure
Outside of the System
Anything that fails to be covered by the App System's protocol is said to be outside of the System. For example, in Tokyo, while Rules are permitted to overwrite its own laws of physics, no protocol is in place for conflicting Rules, which would cause an Exception.
Not all things outside of the System are necessarily Exceptions. For example, 
Black Storm may or may not be considered an Exception. Black Storm fell out of the System because the System had no protocol for foreign individuals of similar mythologies coexisting in Tokyo. As a result, it was not able to stably maintain its memories, presumably because it could only maintain the memories of Typhon in the world.
World Systems
To see specific examples of how a World's System works, see individual pages of Worlds
Each of the different Worlds are run by its own unique System. These Systems are made to help the World last for eternity and achieve a utopian state by holding different priorities between each other. The world of Takamagahara looks to discard anything that it deems as unnecessary and publicly displays every shameful action committed for all to see in order to encourage its people to no longer commit any more mistakes or sins. The world of Kamui Kotan attempts to achieve eternity through eternal stagnation; by never letting its inhabitants grow far enough to develop any new skills, or to live long enough to pass down new discoveries to future generations, it hopes to snuff out any risk of growth and change.
The Worlds are split into majority and minority; the majority believes that the current System is perfect and should continue, while the minority believes that it is flawed in some way. In all the Worlds, the Exile would represent the minority and would be subsequently banished in order to keep the current world order. This banishment is necessary in order to establish the majority/minority split as existing in the first place and to place the majority on the top, keeping the System functioning.
Subsystems
World Systems are flawed on principle, and so may need a secondary subsystem to support itself. In Takamagahara, the Virtual Reality Dragon Palace operated by 
Otohime was created in order to remove any strong memories of pain and sadness from its visitors.
If a World System Fails
If the majority of inhabitants within a World believe that the way their World works is inherently flawed and doubt its effectiveness, the World will be destroyed. It is up to the World Representative to make sure that the people never discover this truth and always believe in the System.
Virtual Reality Systems
Due to being artificially manufactured, Systems within virtual worlds can be custom made. For example, 
Boogeyman's virtual world within his Sacred Artifact operated under a Fairy Tale System. Children who misbehave and run away from home are sent into Boogeyman's virtual world, where they will go through a process of rehabilitation in order to learn what they had done wrong via fairy tale-esque scare tactics and later chocolate making in Candyland.
Notes
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