Force

This is the force from a phase imbalance.  What our the units of force? The change in the density of bubble relative to the standard bubble, along an axis of symmetry.  It is a measure of the amount of kinetic energy needed such that the bubbles are contained in a sphere. So, put the radius in this equation on the other side, and get  (r/3) the signal to noise radius.  F becomes the sample rate on the other side, q1q2 become the quant. The q1q2 is just the vacuum making a digits of q1 from digits of q2, a power series of a power series. The ke thing will just be the greatest common multiple of the two digit systems. What you get is:

At the sample rate of F, what is the Shannon orthogonal quant and digit number that optimally counts the radius of the standing wave motion which makes a symmetry with a multiplicative identity of almost one. I include the almost to account for a the randomness of finite things.

But what we really get is:
(2^N + 2^-N)/2, which are the whole digits and fractional digits, up to, but not including N. But you really want two versions, one at the light quant and one at the Null quant.

We are exceeding my expertise, and at some point, a generous group theory person will explain this.  But, the system has two quant rates, so it can pack a sphere in small and large layers, getting better efficiency. In this arrangement, the wave counts fractions between layers, the Nulls count whole numbers.  There exponents match at the boundary (Compton).  There is more to the story which I am just beginning to learn.

But it seems the sample rate of light is adjusted so that the system gains the maximum number of groups in total, and the efficiency gain is from maximizing group density.  The sample rate of light adjusts to the necessity of sphere packing so that most of your integers land on that prime number hump, to the left.

I'd like to see a system which maximizes ellipsoid packing, and see what the sample rate of light comes out as.