Beato-zeroed (symbol O0o0O) is a Bloxin Hyper-zero purportedly larger than De-zeroed but smaller than 0, first appearing in The Bloxin Channel video (SNEAK PEAK) Between -0 and 0. However it can at least be said that Beato-zeroed is strictly larger than hegirondo, and is strictly smaller than or the same size as 0.
Definition[]
Beato-zeroed is defined as equal to 0^15. It is implied to be smaller in magnitude than either -0 or 0 (placing it "between" them), and it is implied to be larger than branoro, tutanoro, gihenoro, jiwanoro, kodanoro, arrunoro, hegirondo, and de-zeroed. This can be presumed because it occurs after all of these numbers yet before 0 (where we can assume the numbers are in strictly increasing size).
Contradictions[]
Firstly 0^15, as some commentors have already pointed out, would be equal to 0. Proof. Anything times 0 is 0. 0^15 = 0^14 * 0 = 0 (by first assumption), therefore 0^15 = 0. QED. What if we assume the existence of things such that Anything times 0 is not always 0? In this case we can say that in mathematics it is none the less true that 0 * 0 = 0. We can say 0^2 = 0 * 0 = 0 therefore. By induction we can say if we have shown for some k, 0^k = 0, then it necessarily follows that 0^(k+1) = 0^k * 0 = 0 * 0 = 0. Thus again even if we do not make this initial assumption, since 0^15 does not itself propose any new kinds of numbers, it is still only 0. From this it follows that since 0^15 = 0 that |0^15| = |0|. Therefore 0^15 could not be smaller than 0, it would have to be the same "size", that is, neither smaller nor larger. This however contradicts the implicit assumption that the video is ordered in strictly increasing order of size after -0.
A second contradiction requires us to make some non-standard assumptions. Namely that De-zeroed as 0^12, and Beato-zeroed as 0^15, are not standard mathematical expressions, but rather abuses of notation to describe sizes. This may be justified by defining 0^2 not as the operation of 0 raised to the power of 2, but as a single symbol representing a new mathematical object. We make the following observation, that for reals, x, which are elements of the interval (0,1), that it holds that:
|x| > |x^2| > |x^3| > ...
We can call these numbers "small numbers". We know take the limit as x goes to 0, and assume it holds at 0 as well, in the sense that there is some set of objects of strictly decreasing size (not powers of 0 in the ordinary sense), thus:
|0| > |0^2| > |0^3| > ...
We may define this not as, powers of 0 in the usual sense, but as limited powers of 0, with a strict size order relation applied to them by generalization. This is the same as the way we can define infinitesimals as limits of a sequence such as 1/2,1/4.1/8,... yet still strictly larger than 0. That is, treating the limit as retaining the same property as any member of the sequence (thus the limit as being treated greater than 0). In the same way we can hold that the sequence of propositions |1/2| > |(1/2)^2| , |1/4| > |(1/4)^2| , |1/8| > |(1/8)^2| , ... has a limiting statement that retains the same property of any member of the sequence, this time not held to be an infinitesimal, but 0 itself, and that there is some object than we may denote by 0^2 that is of strictly smaller magnitude.
This implies however that |0^15| < |0^12| --> |Beato-zeroed| < |De-zeroed| while the video implies |De-zeroed| < |Beato-zeroed|. There is no standard resolution for either of these contradictions.