I can't understand that. The source of the weak force is quark-quark flavour-swapping interactions mediated by virtual intermediate vector bosons. Quark diameter is not known but has been determined experimentally to be less than 0.43E-16m.

THHuxleynew
: From the old Physics viewpoint you can't understand Mills logic. But keep in mind that the standard model failed and that there exist proofs (according to Geneste) that the math is flawed. If you measure a quark radius (what is just a guess because you can't separate most quarks and only measure there excitation fields), then the underlaying math, used to gauge the experiment, also determines the outcome of the measurement. In fact, according to Mills Maxwell calculations, there are no basic "particles" like W,Z, Higgs etc. bosons.

Particles, in classical understanding, do have a rest mass and can be separated from each other. In basic Maxwell physics most particles are "resonances = basic particle plus captured photon". Mills still assumes that quarks are basic particles. But if you expand his thinking, then even quarks could be viewed as a special feature of the underlaying energy flow. At the very end only the Proton and electron remain as classical standard particles, which of course, depending on the type of measurements can show sub-particles with particle like nature. The rest are photons and resonances.

F would appear to be a function domain I X S1 (the set of all points on all great circles) and range S2 (the surface of a sphere embedded in R3). I think you need the arrow in the opposite direction so that with F you are mapping a point on S2 to the set of all great circles that go through that point? I don't understand how this constrains G because it will exist (though may be trivial) for all G. I also expect that you actually require the existence of the Euclidean metric on R3 which induces a manifold on the embedded S2 - because you assume differential structure below.

The simplest approximation for a great circle density can be made as following. Orthogonal great circles have two crossing points. Each point is cut by a infinite number of circles, where the number of circles/point is given by the length x 2 x point-density on a circle -2 (the corssing points count once..). You have to prove, that you only walk once over a point (generating to circles) and that all finite walks lead to a symmetric distribution of the circles. All patterns following geodesics rules are regular. If you take the midpoint of a "spheric quadrant", then divide the quadrant by 2/2 and apply the rule again, you never will meet the same point again and you will cover the whole surface of the sphere.

The line density will always be identical for all decreasing (total an subs) areas in S2. (Border rule e.g. is north/west. You only need to cover/show it for half the sphere)

( If you throw away all n-1 circles/points and look at the n^{th} generation it will be even simpler.)