At lower density the 4D devolves back to 3D

 Low densitities, the normal planets.  The distance betweenearh and sun is r1^2 + r2& squared.  But this is two mass bodies, kinetic energy way below capacity.  So we ues r1^2 + r^2 = r&2, go back to 3d.

Look at the 4 tuples, the lowest complexity is 1,1,1,3.  That does no increase the continued fraction ratio and drops to 1,2,3 +2 taken from vacuum.  This is the breaking symmetry thing.    A 4D at low energy is not sustainable.    But you can always simulate the 4D with a sequence of three different 3Ds.

 Notice mercury looks very circular, a good Pi, but that is looking via the 3D, in 4D it is a bit oval. Mercury has a slight spiral. 

The total orbital accuracy is conserved, to some bound out to some enclosed surface. That condition always leave a conflict in some center point.   How many time can we play relativity in a rpow?

I think they do it once per each initial description of mass.   But why not do a 5D version is energy levels that high can be observed.  

But, anyway, the two curved system is maintained by very large transition changes,the the system is not quite closed.  These black holes erradiate each time they take in more mass.  They emit along the long diameter.   The effect is unobservable, there is no angle of view toward the short center that captures the long diameter.  So the short center always look circular to us. On that axis we think all black holes are perfect spheres.