When the radius is three

For any sphere, using whatever units, the area and volume are equal at r = 3.  In the proton, the match is when N = 91 in phi^N, and one third of that is N=30.333, and that is a match with (3/2)^36, and 36 * 3 = 108. So, if this theory is correct, then indeed the key variable is sphere area to volume. That is the point of maximum packing. The reason is that the surface area is as equally dense as the volume so space is least wasted. This is true with Phi and only a radial degree of freedom. Add spin and then add charge and the point can be shifted because the units of counting change, and the change is permanent with no redundancy.