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Question about HDE.

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Let's imagine that we have a character with 4D HDE, with multiple evidence and all that, but the character lives in (or travels to) a 3D dimension. Would that be enough to disprove the HDE or do we simply assume that the authors do not know much about dimensions and forget that a higher dimensional object cannot exist in a lower dimension? (In the same way that a 3D cube does not fit on a (2D) piece of paper due to lack of depth, a 4-dimensional object would not fit in the third dimension due to the lack of that extra dimension)
 
If the evidence outweighs a single contradiction. Then the evidence would be more probable and the contradiction can be argued as fiction being fiction (that is assuming they really got into detail)

Though one need to be aware that if a 4D being travels to a 3D world it could be possible that it is simply using a 3D splice of itself. Unless they fully established that the 4D being indeed entered the world in it's full ness.

Take for example a paper and a rubix cube.
If I put the rubix cube on top of the paper it shadow could project to the part that the rubix cube covers. They could project their 3D splice as small as they want it to be or as big as they want it to be.

There are many ways to argue it. One also a hypercube that is still 4D but it's length or width are not larger than a universe thus it can exist inside the universe even with extra depth. This wouldn't reflect it in terms of potency so a full 4D being with an AP limited to what it can do in reality etc. though they will still have that extra axis which makes it so it is hard to completely affect it with abilities limited to 3D objects

In a way case by case evaluation would be the best option here.
 
We don't consider this an anti-feat feat or anything, four-dimensional beings can partially exist in three-dimensional spaces with just a cross-section of their being. So we usually just assume that is what is going on.
 
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