Q: What is "qualitative superiority"?
A: To put it simply: It is superiority over lesser things that involves no element of quantity, or amount, in any manner whatsoever. It, instead, hinges entirely on the nature of the character's existence and ontology. In general, all characters with such superiority over lesser things are
1-A.
To better understand the concept, consider the fact that all tiers from
11-C to
Low 1-A can ultimately be bridged together by summing up smaller things, and can likewise be decomposed down into these smaller constituents. For example, a mathematical space with an inaccessible cardinal's worth of dimensions (Well into
High 1-B+) is reducible to the individual elements comprising it, each of which is a 0-dimensional point.
An example of the same principle can be seen in the
Tychonoff cube: Given the unit interval [0,1] (A 1-dimensional object) and an arbitrary cardinal number κ, one can represent by [0,1]^κ the generalization of the unit interval to κ-many dimensions. In English: If we had a line segment of length 1, and multiplied it by itself, an inaccessible cardinal's worth of times, the result would be a Tychonoff cube of inaccessibly-many dimensions. A
11-B object can be multiplied by itself in order to net a
High 1-B+ object. This continuity between the two, where a larger object can be expressed as a composition of many smaller objects, is what makes the gap between these tiers quantitative.
A character that holds a qualitative superiority over lesser things, however, represents a full discrete jump from everything that came before. They reside in a greater mode of existence entirely, being irreducible to anything that lies in the lower state of existence.
This inaccessibility possessed by qualitatively superior characters and realms can also be expressed in terms of sheer ontology, generally speaking. That is to say: They are fundamentally different from the nature of the lower reality, and this different nature is precisely the source of their superiority over it. Since their "otherness" is identical to their transcendence, no expansion or extension of the lower reality and anything in it can possibly attain to them, as long as it maintains its particular nature. Put it simply: They are as powerful as they are alien.
Q: Are there any disqualifiers for qualitative superiority?
A: The potential disqualifiers largely revolve around the aforementioned aspect of inaccessibility: A qualitative superiority is completely irreducible to anything lesser than itself, and conversely, it cannot be reached by any additive process whatsoever.
The first practical effect of this fact is that the power of a
1-A character cannot be dispersed so much that it reaches into a lower tier. Since there is no conceivable extension of any lower tier that can yield equality to a
1-A structure, neither can there be any subdivision (Even an
infinite subdivision) of
1-A that reduces down into such tiers. Unless, of course, this division is somehow non-quantitative in nature (i.e. The results of the division are not actually numerical "chunks" of the character's power); however, this should be made reasonably clear by statements or through background context.
Secondly, a
1-A level cannot be attained by a process in which the lower level quantitatively "adds up" to itself to break through into the higher one, due to the total lack of structural continuity between the two; the higher level cannot be attained, nor expressed by, any expansions of the lower one, and therefore things from the latter cannot interfere with the former by means of their own lower existences. Put simply: A non-
1-A cannot reach the level of
1-A by appealing to another non-
1-A
However, there are ways to bypass this barrier. For example, a non-
1-A can be empowered by a higher entity into being able to influence things on a qualitatively superior level. This can happen either by a straightforward power boost, or by means of some innate metaphysical potential rooted in something from a higher reality (This can include both characters who are converted into natives of higher planes and characters who are physically lower-dimensional but have
1-A statistics). In neither case is the capability to reach into the higher level something emergent from the structure of the lower level, and therefore they are acceptable ways to get around the above hurdles.
Furthermore, since the "lack of continuity" that exists between the higher level and the lower one is structural, and not causal, there can potentially be more unorthodox ways of bypassing the 1-A barrier. For example: Things that don't have anything to do with raw power, but just a general transfer/exposure of information between one level and another. Another example could be cosmologies where a higher level originates from the thoughts/beliefs/etc of inhabitants of a lower level; while these thoughts literally originating within the lower reality and then somehow "floating away" to form a higher one would be a disqualifier, no anti-feat is present if the verse has it so these operations simply already exist in a higher reality.
On the matter of power sources: That would depend on the nature of the power source itself. For example, a common trope in fiction is power sources that, so to speak, are "for the taking," meaning they are naturally self-diffusive and don't offer any resistance whatsoever to being tapped into, as being utilized in such a way is in their nature. Drawing power from such sources is obviously not actually an anti-feat for them being
1-A, especially so if they are depicted as naturally connected to, and united with, the beings that tap into them.
However, if the "power source" in question consists in a lower character literally overwhelming a would-be
1-A object with their own abilities and forcibly absorbing it into themselves, then that constitutes an anti-feat, unless the occasion falls under the stipulations above.
Note, also, the pertinence of
Plot-Induced Stupidity and similar factors when weighing out whether certain showings are valid disqualifiers. Overall, it depends entirely on a combination of the nature of the showings themselves, their importance, and the verse's general insistence on the transcendence of the realm being interacted with. Individual analysis is to be employed for each particular case.