Like this

OK, I say to myself, if mathematicians are so smart, then a search of sphere packing on Riemann surfaces should turn something up. And it comes right up!  Mathematicians are really that smart!

But this is a binary packing, two bubble sizes. Not what I thought, now these smart mathematicians have confused me, darn. Then:

A compact binary circle packing with the most similarly sized circles possible.^[4] It is also the densest possible packing of discs with this size ratio.^[5]

OK, great, I bet when we make this a sphere, we get three sphere packing is most efficient. So, I drill further down the link chain. I further suspect that four sphere packing is best in an ellipsoidal world. Stay tuned...

And this:

 The expression on the left is the definition of the finite log taken to infinity on a Reimann number lined curved at s. Einstein used this to find that the finite log for a 3/2 curved number line has a maximum, 2.6124... That is, there is a point where the finite log and the most irrational number match.  The thing on the right is the product of those denominators. Each denominator is the precision by which a separable group has an inverse, how close are its smallest fraction to an inverse.  So we have log measures entropy.

Combine the two ideas, sphere packing has a maximum accuracy, and that maximum is right at the proton peak in my spectral chart. So, depending on what you are doing with your number line, there is a best finite size; the point at which multiply is best matched to the entropy your process creates.

The individual components on the left are simply the measuring error each of your quants created when your units are maximum entropy (minimum redundancy). These are the measuring units, exponents,  when the integer set is converted to the power series used by the process. That power series measures signal when redundancy is minimized.  They make the Planck's curve for your governing process when using the most optimum group separation.

All this stuff fits, all we need to do is follow up and find the group generating function for three sphere packing, which defines the Reimann curve. Then we have our line of symmetry generator, and we have the theory of everything.  Those darn mathematicians are going to get a banana real soon.