The equations of spiral, sphere size and the science of sphere packing

 Its all about the counter posing spirals into the packed nulls that keeps them stable. If phase  spirals in too fast, the phase gets crowded, and phase is not balanced throughout the sphere. Or too slow; the spiral has to be just right to hold the sphere at minimum phase. This is the great realization. This is why we have the finite sphere, and  why we all want to read Vitaly Efimov.

The sphere size, the difference between the phase bubbles.  That is the one half, work it out, I think that nails the three sphere size issue.  There will always be a sphere size set that expand the set of solutions. So, write the f'' in a separate sphere size, relative to the other sphere size. The f^3 and f can be straightened with the proper definition of a line of symmetry. Using the same quant numbers. Then compute the range of solutions, that is your band width, and that is the way to get at the sphere packing science.

Fibonacci experts need to look for a whole set of problems like these, the sequence is very good. Look at two, or three sequences, with a scale difference about which you get a line of symmetry. A whole range of solutions will appear.

At the Higgs frequency, there is no solution.  There has to be just the right amount of spread between wave numbers before this equation holds, there are not an infinite variety of quantum triplets that meet the speck. This may not be the end of the story, but its a very good start. Spiral is the reason we write Maxwell with two components, a M and an E.  Maxwell will be redone.

Spin, these are the equations of spin, the great fermion mystery solved. I am actually getting pretty good at this stuff.  I will go into this a bit later, we will look at null packing with spiral as a band width issue. It  is this kind of realization that causes the banana prize.

Higgs cannot spiral because it is up against light. It is the first wave number down from light, it is bandwidth efficient to give up a line of symmetry, so Higgs, the first real wave number, simply becomes the baud rate,