Minimum redundancy vs minimum variance vs sphere packing

Why does matter coagulate? Coagulation causes quantum integers, but simply minimizing phase can be done by making nothing but wave motion up to the band limit, but we end up with redundant wave motion.  How is it that the vacuum figured out that maximizing entropy up to a given temperature (sample rate) works better?

It is a spectral optimization problem, and the spectral modes are set by the vacuum having the radial axis of symmetry. So the wave number 7*13 = 91 would not be a surprise, it is the closest the number line can get to two Nyquist rates in a radial axis of symmetry. Those two numbers should be derivable from simple analysis of sphere packing with discrete units.

Just playing the numbers game here, 13-7 = 6, another fundamental measurment.  But the volume to area of a sphere is r/3, and the null quant is:
 3 * 6*6, so the best quants to pack sphere are 6 * 6.  So we get a match between the requirement of separability, sphere packing and Nyquist, (which minimizes phase imbalance). All of this is based on the radial axis of symmetry, the sample rate naturally adapts to the irrational base.  Can this be proved?

I think it is easy to show 3 and 2 are the most orthogonal groups. Then show the sample rate must be maximally irrational, and close to Nyquist; and you have it. There is no better number line for sphere packing.

So the process is simple, the vacuum hits the Higgs limit at 107. Then agglomerates the nulls until they are maximally separated from  Heisenberg at 127, which becomes 108. Then its irrational base adjusts to avoid interference and the 7,13 result as that is the maximum Nyquist set over the available error range which minimizes interference. Thus the sample rate of light, a constant defined by Higgs and its relationship to maximizing the separation of packed nulls from Heisenberg.The old wave vs particle debate, played out for real in the bubbles of space. From there we show a 1/6 phase shift in the bubbles lead to a fractional improvement, and we get the mixing angle and the quark machine.

The necessity of maximum entropy and quantization results from  the necessity of an axis of symmetry, which is an integer definition of separable groups.

Powers of powers:

I always assume the bubble can simulate  the hyperbolic, or the form:
(e^x+1/e^x), so when 7*13 appears in the exponent, I assume it looks like:

(e^x + 1/e^x)^n   Cosh taken to the power n
(e^2x + 2 + 1/e^2x)^n-1
(e^3x+2e^x +3/e^x+2/e^2x +1/e^3x)^(n-1)

Which becomes a power series in e generating all the intermediate wave modes made of x and n, including fractions. So, first, I like to ignore sample rate altogether and just work with quantization, then forget about whether I have frequency or wavelength in the exponent. Not that I am lazy (I am) but that I am incompetent with regard to remembering all this stuff, just like a bubble.

Anyway, the multiple: 7*13, as a power of a power series, generates all the intermediate wave modes. So it is reasonable to think of it as a near Nyquist-Shannon sampling system.  So, I am not just willy nilly applying sampling theory to exponents, though I often do that, so watch out!

However, why not just redefine the Hyperbolics in terms of the most irrational number, computed to a finite value equal to the precision generated by the proton.