Details and corrections on the sphere packing curve

Correction, Quantum number N counts a sphere of area P^(N+1), so I have the X axis shifted still correct, I think, because I inverted the SNR.

I want to convert the quantizer from what it tried to do, block off the sphere into equal area layers, into what it did after Hitting the Higgs boundary and packing the Nulls.

I used the basic maximum entropy encoding of a noise channel:

Q/C = log2(1+S/N)

Where C was a multiple of the Wave number n, Q is the quant measured, a unit less number. S is area, N volume.

Signal to Noise came to:

3/(phi^(n/2), n being the wave number and  phi the most irrational number. This is area to volume because phi^n is counting area and area to volume is 3/radius.

Why not just plot the Noise by wave number?
Because I want the noise relative to the maximum entropy packing function, not the minimum phase wave number. Hence Shannon converts from one norm to the other. Think of the shoe store manager. He measures noise in the mall, people walking around.  Then he sets up his shoe store, and measures the noise  people entering his store. He wants to know how much tennis shoes radiate noise in his register, and I want to know how much noise is radiated from the quarks. How does the spectrum look after Higgs did the maximum entropy encoding, not before.

Anyway, I put this in the form. I have the exponent and the irrational phi because I want to remove signal, and just look at noise.  That is, how congested are my checkout counters, not how much per sale; using my shoe store analogy.

   j*(phi^(n/2))
----------------------------- = Noise
[2^(Q/ (k*n) -1]

I am treating the function as a two bit number in which each quant is counted at a declining multiple of the Higgs rate.  Longer wavelength, lower frequency counting, lower order bits; make for lower signal to noise and lower Q.

The j is there to scale my y axis into nice looking fractions. The k in the exponent serves the same thing as the Boltzmann's, it changes the base from what nature uses to what I use, and it scales temperature (rate) from some historical standard.  k also has a factor of two in in because I need to sample each bit at twice the quant rate.

So this tells me which parts (frequencies) of the atom will radiate when I shake the thing.