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Is it possible to be a 6D Character/Construct in a verse which is limited to a 4D Cosmology?

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Given that the cosmology of a verse has been elucidated and deducted to be objectively 4D at best, is it possible for a character or construct to scale to 6D within said verse?
 
Depending on the situation, if this character is simply a 3-D/4-D being and possesses a 6-D stats, then it could be a few ways. If it is a 6-D being, then it could not, because 6-D is too large for a 4-D cosmology to contain, in which case this 6-D character could exist outside of the 4-D cosmology. However, this could be a contradiction because in order for this character to exist, the place that he exists would also have to be 6-D and of course it would be counted as part of the cosmological whole (the void that encompasses the universes, etc...)
 
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