Oddly enough, the Abfield cannot be considered the negation of the Schemafield, since the process of negating an object's contents is something entirely constructible within the Schemafield. It also cannot count entirely as an abstraction of any operation the Schemafield applies to Prism Gates and other functions within, of course, because that is simply one step higher in the Schemafield. Rather, the best analogy one can make between the two objects - at risk of invoking the Schemafield's "comparison" containment - is that it is the Deep Imaginarium to the Schemafield's Shallow. The Abfield is no longer permeable to abstraction or degeneration, or to any organizational concepts established in the cosmological domains below.
This means that it innately has a level of indescribability, perhaps not as great as that of Nothing - though, on the other hand, it is misguided to attempt to compare the two in the first place - but sufficient to disallow entry through any sort of ontological manipulation or organized informational attack.
Contents and Exploitation
It is easiest to say what the contents of the Abfield are not: they do not form a set, or any construct under mathematical or logical systems of any kind. They do exist, in some sense, but there can be no axioms formalizing which things exist or do not exist in the abfield, no axioms that establish why no axioms for determining this exist, and so on repeatedly.
It could be said that the Abfield is an ultimatum in that it is entirely detached from all structures below, and "supersedes" the Schemafield, which strictly contains everything consistently or inconsistently expressible. Identifying a single object within the Abfield is impossible, however. While unboundedly complex structures, lifeforms, civilizations, and cosmic entities may exist within it, and can even be described in great detail, any means of expressing them will bring them into the Schemafield.
This particular property - retroactive ejection of information - makes the Abfield a popular target for concept mining, similar to that in the Imaginarium. Naturally, it is both more random and infinitely more dangerous; as the Schemafield does not necessarily connect all ideas in all ways, and the Abfield's nature allows for the existence of objects with far more discrepancies than any system can enumerate, bringing in something totally unconnected to one's own base construction of reality causes total reality collapses or worse. Accessing the Abfield in the first place, of course, is only possible from certain points in the Schemafield or -fields within, points that specifically allow for the transfer of information out of a realm where information breaks down.
Nonetheless, there is the infinitesimal "chance" - disconnected from proper probability, of course - of retrieving an unschemed artifact, be that an entity, item, or -verse, that could be unbound by logic and higher metasystems. Such a procedure is speculated to allow omnipotence far beyond that of the conventional hierarchy, ultimatum-surpassing events and structures, and unthinkably more mind-bending things, if one's local set theory is not demolished in the process in the way a hydrogen bomb would break open a porcelain pot from inside.
Rationally, it is infeasible to compare the Abfield to any other cosmological or hypercosmological structure, even an ultimatum, due to its rejection of comparability. While it is not necessarily strictly false to claim that its contents can surpass any other structures, this statement has no meaning until concepts are brought into a Schemafield, frequently destroying it in the process and rendering further comparative analysis therefore useless.
Weighing the Abfield in comparison to other concepts such as the Box or Nothing are therefore counterproductive and perhaps detrimental to any concepts involved.