So how many units of 'Disorder' in the atom?

The Lucas system is circular, but it would accumulate the 1-tanh^2 as it spirals through the orbit. That gets Pi/2. But it is scaled and so may actually be getting Pi or 2* Pi, who knows? Anyway, that accumulation is a volume as the hyperbolics are circular. So the fine structure residue is a volume, and I am not sure where physicists have the 3/2 in their formula.

To get the total number of those, take (Pi/Fs) or (pi/2*Fs) and so one; you numbers like 215, 430 etc. Call these the total volume of the sphere in units of Fs, and you have it, I think.

Do I have units upside down? Could be.  Previously in that spectral chart, I could count up or down, it wasn't hyperbolic.  Now I have to be careful.  But Tanh is linear around the small angles, and that is where most most measurements of Pi will take place.  So we may have to count from the center out. The system will always try and operate along the linear portion.

Atomic Orbitals:

This makes sense regarding the atomic orbitals because the first two Lucas polynomials have no zero, so the shell is spherical,  Add another Lucas number and we get that inner and outer shell. How does the Lucas system handle the higher s orbitals with no angular or magnetic moment? Most likely the Lucas polynomials that have congruent zeros are used in series, as if it can skip intermediate polynomials.  

Magnetic moment:

  But you can see the set of Lucas polynomials can satisfy the n,l,m system in standard use. Magnetic moment probably happens then the center no longer is a point source. So the Lucas numbers no longer count by 2,4,8 etc.  They will snap too on the odd numbers.  When the incongruent polynomial appear, it is mismatched with the s orbital and has to curve the shell to realign them along the tanh linear, and that means splitting the outer shell into separate regions, each region having the same odd curvature.

The thing seems to be driven by surface distortion on the surface of the unit spehere, wherever that is, near the center. So the orbitals compensate for asymmetry in the nucleus, I would think. It likely make Pi by making the zeros as symmetrically out from the some center as possible. The vacuum does not have direct access to both sinh, and cosh. It basically adds, and even then can only add maybe three numbers at a time. So the vacuum simply redistributes the interts and imbalances to make a 3 bit adder work at any one time.  In other words, it does not do sophisticated math to meet some human regular complex plane, it just warps the local vacuum to do simple straight line adds.


I hate to spoil the party, be we are dealing with  something having an IQ of 1.5.