It is a numbering system with two different fractional precision. One counts fractions, the other whole numbers, but they have to be compact, operating within a certain range until the fractional part exceeds it limit, then a new group forms.

Pauli counts whole numbers, and light counts fractions. But the match must remain within the group, or order.
Fractions can have trailing zeros (Nulls) until the trailing Nulls make a whole.
Pauli can have leading phase until the leading phase makes the first fraction.

Remeber, waves are packed at the Fibonacci quantization, the two binary system is an approximation that Fibonacci uses, and the packed Nulls are quantized at the Pauli level. Its a mess to sort out, and is going to take some time. But here is a better start, and the numbers I get are all within range of the 96,48 levels, or small multiple of them.

Pauli of ordern M can count r digits such that:

P**M > [p**(M-1)+P**(M-2)...+P**(M-r)] which must be greater than light in the same group having
order N with k digits such that

P**(M-e) > [L**(1-N + L**(2-N)+...L**(k-N))}

Two quant ratios, counting whole numbers and fractions in the same group, then we go up one group.
My mistake last time was 1) Math errors, but I always make them, and 2) I just wanted to get the relative ordering right, and leave the digit sequence till later. That was why I wasn't worried about partials results.
But I glommed onto those original numbers, (98,49) they are close.

The entire atom should count down, Higgs as the significant bits, then the other groups hanging within as less significant bits, without interference. Groups contained with groups. This works because the light is faster then the pauli and contains the current group, literally acts as a border region.
Going down in the groups, contained within groups, the quantum numbers are the digit count.
It should result in the quark transformation matrix, that is where I am headed. And I am closing in.

So, we can fill in the entire 'bit sequence':

starting with the maximum mass, which is unsatble, I presume:

P**Nmax ..|.. P**QaurkMax.... P**QaerkMax-r......P*8QuarkMax-p....

And between each Qark Group, should fit the qluons, at the R rate. Then there is room thee for the leptons, each group separated, and meeting maximum entropy to an integer with fraction.

The general arrangement of quantization levels down the the magnetic is estimated, and the atom should be contained with a range of:

P**100 ... P*60 or somewhere like that. Going down in quantization powers of P.

Light quantizes larger, and should fit within these range, matching group for group. Light need not count at the same rate as Pauli, it just needs to match the range and be separable between groups. There will be peer groups in Pauli and peer groups in light, each subdividing into match sub groups and so on.

Light packs the atom as a Fibonacci, I am pretty sure, or close enough to start. It can be modelled as a binary digit sequence with three huge gaps:

01000000000000000000000001000000000000000000000000010000000000000000

The leading zero is the unsustainable Higgs. The sequence should be about 48 bits long, or there abouts. And the spans contain a matching Pauli sequence counting in smaller quant ratios.

We know from the mass ratio of proton to electron that each of those gaps is about P**14 or P**16, in that range. And the P ranges are matched in pairs. 16 is 1/3 of 48, sop these types of number get me excited.

So we want to find the binary number, in 2**N, and match it to sets of Pauli numbers at (3/2)**M, and meet the Shannon in each set and subset.

So 2**N, N near 48 will be Shannon close to 1/2 of P**M, the P counting in (3/2), over the whole atom. Now there is likely a third rate, the kinetic rate, but I ignore that four now, but it will count up to Pauli groups and sub groups. But the ratios seem to be going:

1/2, Nyquist, 3/2 mass, 5/3 kinetic, and all packed at the light rate, Fibonacci.

So 2**Nmax < (3/2)**Pmax = (3**Pmax) * (2**-Pmax)

2**[Nmax +PMax} = 3**Pmax

or Nmax+Pmax = log2(3) * Pmax each Pmax and Nmax to the nearest integer.

Nmax = Pmax * [log2(3)-1] or Nmax/Pmax = .585

and closer to zero than an other combination.

I keep getting numbers near the range of Pmax = 106 to 62 as being in the range, but I have to double check the maximum order I expect, going back to Plank and doing the number right. Tp=5.39106(32) × 10

^{−44} s should be the second per sample, or close to it, about 2**143. But Planks are units of packed Nulls, aren't they? A plank is P**(-Pmax).

If so, a plank is a quantizatiopn at the 3/2 rate, giving me 246= 123 * 2 = Pmax and Nmax = 144 = 48 *3. The number are in the right range, if I can make up my mind on the right matching ratio. The Pmax is the largest prime * 2, in the range. This is likely not a coincidence.

But wave are packed at the Fibonacci ratio, and if that is the case then the Plank is F**-207 or F**-208 if we add one.

I am picking the Pmax and Nmax that most closely match integers. 48 and 96 and now 123, keep coming up as common multiples. I am trying to sort this out. There are three quantities here. The binary quantization Fibonacci uses to pack waves, the Pauli quantization that measures packed Nulls, and the 2s binary system that Fibonacci assume when packing waves.

Gluons and Quarks make the color white. In the binary approximation, white is a large (high order) 7 bit number made by adding up three 10 bit numbers, a good startin range. The gluons are likely exchanging free Null with the quarks, they 'superconduct' mass. But the color white is close to the Higgs mass.

Pmax is our quantization of binary Higgs at Pauli (3/2) levels. So a binary 7 bits of that quantized at Pauli to make a proton, is composed of three wave/quark combinations, quantized as Pauli occupying 11 bits, each. And each of these come out as 6 bits in binary approximation, they are the quark/gluon combinations. Each of these, in binary approximation, have about 3 in Pauli and 2 in wave, to a rough approximation.

Remember, the Higgs order is only about 40 bits, out to the electron, in a universe with is like 300 bits, just to give scale ranges. But it is the highest order, it is counting huge numbers. I am working from binary approximating that with (3/2) then get that into (1/2+root(5)), where the Pauli mass are the most significant digits, in (3/2), of the (1/2+root(5)/2), the wave counting up to the nearest half of each Pauli mass. The wave is packed, meaning it will carry free Null without quantizing them, and can still bind the packed Nulls. The digit system must be able to divide out the groups and sub groups with ease, we are after all simulating dumb vacuum.

The question, now, is how to make the bit system uniform so I can minimize the back and forth, something I am not really qualified to do.

The vacuum can pnly do addition within its quant levels, s0, addition becomes:

q**n + q**m = q**n + remainder. where n nearest integer . Which means we can use fibonacci as the unified basis, as long as were are careful with rounding and remainders.

Start with the disorganized set of free nulls and phase in balanced pairs. The vacuum, everywhere, quantizes these in units of 2 (one unit a null and two phase), then sets of 3/2, then set of 5/3 and so on until there is no more balancing. Whenever a set is quantized at order n, and the next order would reduce entropy, it has to skip the order. It will find these points because there is no exchange that balances phase any better. The phase and Nulls are bound in the region. But there is a remainder that keeps on balancing. at the edges, surrounding existing set that have grouped.

If the vacuum can measure fractional phase to infinity, and keep swapping, then it will to the largest value in 14 digits, the largest value being 1.82e43, the Plank speed.

OK, now I need to model density, the idea that quantization stops at a small bits because there is too much phase imbalance to solve at light speed. I will use sensitivity to get that, the more sensitive the measure of phase imbalance the more dense. This is the Shannon condition, phase imbalance is noise, it lowers the quantization rate. As the vacuum packs nulls and balances wave, the SNR increases. Quantization level steps up.

Noise is horrific, the vaccume just barely separates itself into negative, Null, positive positons. The SNR then is:

Q/2= log2(1+SNR) signal is Plank energy organized, noise is density, we start with the number of Planks, in phase, which is 2/3, and that is squared. Then each time some phase separates itself, the Signal in the system goes up by .the Shannon condition and the noise drops.

We should find noise drops fastest when wave and null quantize at nearly the same level. Lets put all the noise on loose nulls having kinetic energy. The more they are packed, the less noise. The vacuum stop when everything is quantized up to light quantization. At that point, the 1/2+root(5)/2 value does no better than packing by the integer ratio in steps. Since Nyquist is causal, it can work, by definition. When it has reduced noise sufficiently, the higher quantization kicks in until it can no longer work, and it drops back to Nyquist.

The sampling rates should go as: Nyquist, Pauli, Kinetic then light. Looking at quantizing the largest thing, Pauli stops at about an 11 bit integer, that is way too compact and I do not account for noise yet. Noise comes from original energy plus quantization variance, the amount one quantization rate overlaps as the system settles. We end up with balanced packed nulls, kinetic energy and wave, co quantized. I am not really sure about kinetic energy, and I assume it stays at Nyquist, that is, unpacked.

So I start with enough noise to step the thing, but not stop it. There should be an energy level that makes a proton, or quarks.