The Box is the cosmological object that contains everything. Regardless of internal properties, it is in the Box, for any value of "it".
This means that the Box is the largest imaginable, unimaginable, theoretical, nontheoretical, unphysical, metaphysical, pataphysical, useful or useless set. The Box is, and the Box is not, if you will.
The Box contains anything beyond space, time, reality, logic, and everything else that could ever be thought of or not thought of. The Box contains the Omniverse, as well as the infinite variations of said verse, to the point where it is not even a "verse".
The Box not only contains all of existence, but infinite variations of an infinite set of 'concepts' completely different from existence. The Box contains everything outside the box, whilst still being contained by The Box. Additionally, the Box contains all properties and anything that can be elaborated or not elaborated upon; effectively, all statements include the tag "is inside the Box" by definition.
The Box also follows all types of physical realm using all properties, including the metaphysical realm and the pataphysical realm.
No entity, concept, possibility, or impossibility exists outside the Box. Any attempts at explaining how something exists beyond the Box are retroactively nullified; by placing something "beyond" or "outside" it, the very fact that the object/verse/being holds properties at all places it inside the Box. All permutations of logic are in the Box, and it also contains an infinite number of copies of itself. One version of this would be Altarca.
Rulers of the Box
Because the Box contains all entities with all powers and utility functions, there can be no single ruler of the Box from inside of the Box; any single entity that attempts to rule the Box would have all possible versions of itself, including those with exactly opposite motivations, also attempt to rule the Box, elsewhere.
However, if an entity has equal capacity to rule over existence as the Box has to contain it, this entity may be able to rule over the entire Box. Only one entity is known to possibly be capable of doing this: The True God.
Furthermore, omniscient entities like The Aspect Lords have learned to work in unison with each other and are aware of their parallel existences, so they can rule over The Box, but not every single little part of it since there are definable parts where the aspect lords do not hold power.
Lesser Versions of the Box
Contained inside the Box are numerous lesser (but equal) versions of the Box. Their absolute containment is weaker than that of the Box itself, which means that in theory it is possible for sufficiently omnipotent beings to transcend the Box; however, this is done only on a lesser version of the Box, with the true version of the Box being beyond most levels of omnipotence, with only true omnipotence (if it exists) being able to exceed the Box.
The placement of the least version of the Box is up for debate, since how far the Box can be reduced whilst still maintaining its essential Boxlike quality depends exactly on how sufficiently Boxlike is defined. Some interpretations of the least version of the Box put it as low as merely the Omniverse, containing all of reality; other interpretations still put it infinitely higher than the Omniverse containing a vast range of paradoxes but still infinitely lesser than the Box.
Any version of the Box that is partially thinkable, including, arguably, anything described by a complex enough human conception of the Box, is also a lesser version of the Box rather than the actual Box itself. This is because the actual greatest version of the Box is both beyond unthinkable and contains everything else that is beyond unthinkable.
Equal Versions of the Box
Numerous structures are equivalent to the Box and contain everything that the Box contains. These structures are contained also inside of the Box; the Box has no requirements for well-foundedness and therefore can easily contain structures that are equal to itself. These Box-equivalent structures are called top-level containers.
An example of one such structure is the Box itself. Another example of a structure is the Omniumverse, which through the Imaginarium contains the Box and everything in the Box, since all of the contents in the Box can be simply imagined through the description of the contents of the Box. Another such structure is Paradox Space, which contains the Box due to the paradoxical properties of the Box, as well as all of the contents of the Box due to any contradictions that may be present inside it (each entity within the Box has a corresponding contradictory entity).
All equal versions of the Box are beyond unthinkable, since they are obviously equally unthinkable to the main Box itself.
Exterior of the Box
One natural view of the Box is to see it as some kind of structure embedded in an even larger space, which lends itself to fallacies such as the possibility of escaping the Box or a container that encloses the Box. This view is flawed because of the exterior of the Box, as a thing that can be defined, is itself contained within the Box. Anything with a high level of omnipotence (except true omnipotence, which may not be possible) that attempts to escape the box will find itself in an exterior of the Box which is itself contained within the Box.
Position on Scales
One way to compare the size of any cosmological structure to other things is to place them on a scale and assign numerical values to them. The Box is also ranked on these scales, typically at high levels near or at the top due to the nature of the Box as the top-level structure.
Holomanga's Surreal Verse Levels
On Holomanga's Surreal Verse Levels, the Box is positioned at ∞, the projective infinity on the extended surreal line greater than any other surreal number. Whilst not strictly a surreal number, the Box is positioned here in order to ensure that it is larger than any other -verse defined regardless of how complex and all-encompassing its structure is.
Holomanga's Unreality Scale
On Holomanga's Unreality Scale, the Box is positioned at ∞, representing the projective infinity on an extended surreal line greater than any other surreal number. The reason for considering the Box as the most unreal thing, being infinitely unreal, is justified by the Reality/Unreality view of the Box.
There are various ways to view the Box and sort them on existing hierarchies, many of them involving having the Box be in two dichotomous ends of an infinite scale.
One perspective of the box is that it is the hypercosmological structure that requires the least information to specify. As one travels higher up any verse hierarchy, less information is needed at each level. A universe requires physics and initial conditions, but an archverse requires no initial conditions to be specified (and possibly physics with more free parameters, represented in different universes), because all timelines are present somewhere, and an omniverse requires no physics to be specified, because every possible universe is present somewhere.
At the level of the Box, absolutely no information is needed. The Box, containing literally everything, has no free parameters to modify; at most, it would require one bit, to represent whether it is either the Box or Unthinkable Reality, but even this is controversial with many models requiring zero bits to specify the Box.
Another perspective, along the same lines, is that it is the supercosmological structure that requires the most information to specify. The complete state of an elementary particle requires around five bits to specify. The complete state of a universe requires around 1090 bits. Larger structures need even more information to describe fully. The Box, containing everything, requires all possible information to specify, an unsetly infinite amount of bits vastly beyond anything else.
Along these lines is the symmetry view of the Box. This holds that the Box is uniquely the most symmetrical possible of any entity. This is because, regardless of what transformations are applied to the Box, it remains identical. Mirroring every part of the Box, for example, would leave the Box unchanged because it already contains the mirrored versions of all -verses and they would simply switch places without altering the Box itself.
This can follow naturally from the simplicity view, and is categorized within it, because transformations can be seen as altering the information that defines an object. The Box, without any free parameters, has any transformation applying to an empty set, which clearly leaves it unchanged.
Another perspective places the Box as the most extant thing. Going from the absence of something to more of something makes it more existent, in a sense; a lone quark is not very existent, because most of everything possible and impossible is well outside of the quark and the information is simply not contained or derivable. The Box, as containing the most of anything, is consequently the most extant of anything.
Alternate lines place the Box as, in fact, being the least extant thing. This sorts objects on a scale from reality to unreality, with the most real things (objects connected by space-like worldlines) being located at one end, then the Omniverse as the threshold between reality and unreality, with paradoxes and other impossible things occupying the Paradox Space less real than everything contained within the Omniverse. The Box, containing all paradoxes simultaneously, including mutually contradictory ones, is less real than any of them.
Relationship between Nothing and the Box
The relationship of the Box with Nothing is very ambiguous, as far as anything can be said about nothing at all. Generally, as nothing holds all properties that are not held by another thing, Nothing can be considered to be beyond the Box (since there exist no -verses/structures larger than the Box), and more powerful than anything contained inside the Box. Since Nothing can not be categorized, defined, or fit into any framework with meaningful properties, further commentary on the relationship between the Box and Nothing is difficult to determine the true purpose of, seeing as there is enough evidence to keep the debate going on for quite a while.
Universe Classifications of the Box
When classified by communality, the Box has both no and all possible interactions with other hypercosmological structures of the same tier. There are an infinite number of arbitrary lesser variants of the Box, which interact with each other in all possible different ways, which are all (by the symmetry argument) identical to the full Box and contained within the full Box, which stands alone at the top level.
Most other classifications on the universe classifications list are meaningless. The Box has areas that follow anywhere from simplistic Euclidean spaces to having no notions of geometry at all, as well as areas ranging from having consistent and predictable physics to having no notions of logic or meta-logic whatsoever.
In terms of fiction
No matter how ridiculously powerful any entity or being in a story is, they are confined within The Box, as well as infinite variations of said being. In essence, the entirety of fiction is not even a Planck size microbe within The Box. This can all be explained in greater detail through the Imaginarium.