Quant Arithmetic in twos binary

The quantizer is building a, typically, 4096 bit twos bonary number.  If each quant order was quantized once, the number would look like:

1000010001000001000100....... down to 4096 bits

The 0 spots are the fractional quants held by the quantize, the numbers we need to do computation on output. But the quantizer need only look at one part of that number at a time, as it marches up the order chain quantizing the applied force. So the quantizer table maintains the number of zeros in the form of 1/(2**n), where n are the number of zeros between the current index and the previous. Then it maintains the value 0 or 1 depending on whether it has been quantized, and keeps the order index if it has to construct the real number to compare to current force.

The fractional quant and its precision are important variables in determining grouping.  So the local value looks like:
{0,1} + (1/(2**n) * k, k being the fractional component, and n is typically between 1 and 6.

The global value looks like:
2^Index + 2^(Index - n) *[{0,1} + (1/2**n) * k}]
2^(Index-n) * (1 +  {0,1} + (1/2**n) * k}
2^(Index-n) * [{1,2} + (k/2**n) ]

Mostly the quantizer is doing very small integer arithmetic.
The other change I made is I decided that recursion should happen as we march down the longest sequence, and not be done at each sample of the sequence. Mainly because that is what we are looking for, changes in the structure along the sequence.

Them, the first rule of physics I add is that force moves up the quant chain, so the system can pre-compute the starting point for large force and we won't have to march through the whole order.

Where do the fractions come from?

Good question, and one I am learning about myself.  But waves quantize more phase than they need to pack a quant of Null, the excess phase become charge, or motion if it cannot be distributed elsewhere. Can we call that Quantization noise? The software assumes Null and phase are equal, but they are random noise up to the Plank bandwidth. It makes no distinction under the assumption that fractional balances that remain will fix the problem and leave mass and wave quantized properly. But that is what why I have the quantizer so simple, I want it as dumb as it can be.

When two mass quants adjoin
I assume a principle which may not be true, the vacuum would degenerate if it quantized the second mass, so I just skip that.  That is kind of cheating and needs to be verified. But my logic is that the vacuum can either pack the second mass with a wave quant too low or two high, there is no match.

I can scale my applied force with a scale factor to move it up to the higher orders.

On the proton and neutron I am looking for a pattern of the neutron, at the (3/2)**100 order, to look like: 010001011101 then I add a small force and it flips to the proton which would be 0100010001000, in which I would see right away that the Shannon condition for the three bits has gone up on the order of (3/2)**98, or so. making it an extremely separated group, and not prone to degenerate.

What physicists call forces are generally extremely separated groups.  So I am very interested in seeing what the conditions were, or are, that make the magnetic order so widely separated. I also want to 'install' the neutron and generally apply large forces and see how the electron forms along with the proton.  These are games this system can conduct.

So, great simplification all around.