From that alone, it may already appear as if there is not a single object, concept or anything else (including literal nothing) not contained within the Itfield, making it completely identical to The Box. But this is not the case. The entire rest of the Box's article could be placed into this one with the word 'Box' replaced with the word 'Itfield' and the Itfield would still not contain even a fraction of what the Box contains. This is all because it is missing just four words in the first sentence of its definition.
The Itfield is identical to the Box in every way except for one: The Itfield does not ignore the internal properties of an object or any paradoxes that occur due to this. Because of this, the amount it contains is substantially less. But why is the Itfield so much smaller just because of a seemingly insignificant detail?
Despite being tiny compared to the Box, the Itfield is a truly colossal structure. Any object or concept you can or can't think of is within the Itfield. Any object or concepts that you neither can nor can't think of or any variations there-upon are within the Itfield. Anything that is not an object nor concept, or anything that is not any of the above options or any extension of such is within the Itfield. All n-aryfields and other fields (including the Schemafield and Abfield) along with everything they contain are within the Itfield.
Anything, whether it is or isn't a thing (or any other possibility) is within the Itfield. Well, almost anything. There is a very specific group of objects that the Itfield does not, and cannot, contain, despite its definition confirming it can and does contain anything and everything.
Naturally, in Hypercosmology it is assumed everything exists. If there was so much as one object, concept or otherwise that did not exist, it could not be contained by the Box, and therefore the Box does not contain everything. This means we can confirm that since the Box contains everything, it would contain an object that cannot be contained because it contains everything. And this is using the word 'cannot' in its most absolute sense. There is no trick or technicality that the Itfield can abuse to contain it, it simply cannot be contained in any way. So the Itfield would not contain this object as it simply cannot be contained by any structure. The fact that the Itfield contains everything, and that object is part of 'everything', is meaningless. It simply cannot be contained, regardless of the Itfield's properties.
The Box, however, is immune to this as the Box ignores the internal properties of the object and any paradoxes that arise from this. An inability to be contained is an internal property and containing an object that can't be contained is a paradox. As such, both are ignored allowing the Box to contain this uncontainable object. It is for this reason that the Box still contains everything while the Itfield does not.
The Extent of This Weakness
The extent of just how much the Ifield does not contain may not be initially clear. After all, "things that absolutely cannot be contained" is a very specific and (presumably) small group of objects and/or concepts. However, it should be noted that there are far fewer restrictions on these objects than the ones within the Itfield. While objects within the Itfield are not required to operate within the boundaries of any form of logic, be expressed as information or not operate within the realm of paradoxicality, they still must be contained, which is a limitation. Objects beyond the Itfield, however, are truly free. They do not have to hold any property. They can, but do not have to. They are contained by nothing, and as such must abide by nothing. They even are debatably free of Nothing itself.
This allows them to be or do truly impossible things that objects within the Itfield cannot be or do. (Such as, for example, not be contained by a structure that contains anything.) Among their many abilities would be to exist in far greater numbers than the objects in the Itfield, and ignore anything that may allow any objects within the Itfield to reach remotely similar quantities.
Because of this, there are far more objects outside of the Itfield than within it, and the vast majority of objects within the Box are truly impossible. Despite the Itfield containing almost all objects and/or concepts that will ever be discussed, it does not, in fact, contain even a fraction of all objects and/or concepts that actually exist. This is a very common theme within Hypercosmology, where structures contain the majority of concepts discussed but the minority of concepts that exists. Examples include the Schemafield and Binaryfield.
Beyond the Itfield
The Itfields marks a serious turning point in terms of all Cosmology. At a universal level, all concepts can be easily comprehended by human minds. As -verses increase in size, however, the number of concepts that humans can understand decreases while the number of concepts that require models to understand increases. The Multiverse, as a low level -verse, contains mostly fully comprehensible concepts, but some which require models. Higher-level -verses, such as the Omniverse, contain more concepts that require models to comprehend than ones that do not. Once The Barrelplex is reached, all concepts beyond it require models, as they're no longer any concepts that can be comprehended without them.
Then, as we progress into Hypercosmological concepts, the amount of concepts that cannot be understood even with models increases while the amount that can decreases. Lower level Hypercosmological -verses such as Selfverses can largely be comprehended via models with a few aspects that cannot, while mid-range -verses like the Trinaryfield largely cannot be comprehended via models with only a few aspects that can.
Finally, when going beyond Itfield into high-level Hypercosmology, models become completely useless. Things beyond the Itfield cannot be properly modeled whatsoever and as such attempting to examine such concepts becomes useless and only the relationships between objects become worth examining. (Usually represented by Parafields.)
-Verses can still exist which contain things beyond the Itfield, the Box being the most notable example. To do so, they must simply hold the Box's property of ignoring all internal properties of objects it contains as well as all paradoxes that result from this. The two most basic -verses beyond the Itfield are the Nonfield and Antifield.