My spreadsheet particle collider:
I cheated a bit. I counted by fives,trees and two separately to match a power of Phi that includes the whole sphere (the tree populated up to the maximum surface. I get a maximum, yes. I am not ready to call it the number but I can tell that the exponents are looking like a series of small primes multiplied. The implied Avagadro is huge, by the way, and my spreadsheet (Gnumeric) would not find the 5D system.
Hence, the existence of a 4D system will imply about ten orders of magnitude then the 3D. We have to wonder how we might pass from the one to the other in a black hole. It may not be possible to acquire the material needed without collapsing back to 3D.
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