If the samples were Nyquist, they would overlap by one half. But, they optimally pack by the golden ratio, that determines their relative shape ratios. They simply push into a shape the makes space as densely vacuum as possible. Then phase imbalance is pushed to the optimum congestion ratio, the ratio in which unpacked and packed nulls are most stable, and make symmetric groups. That gives us three curvatures, the unused Nyquist, the golden and the Pauli. The latter is apparent, the middle is real, the Nyquist is a relative basis.
How does the vacuum do this? The relaxation ratio is the ratio by which on sample changes shape relative to another. That always maintains balance, within the precision of vacuum density. Free Nulls do not exchange. So we get this ratio of obliqueness; the Null, and two anti symmetrical shapes. They are in balance at maximum packing to the extent vacuum density is measured to the golden ratio, which would be the density distance over which mis shaped vacuum samples squeeze each other.
The optimum congestion rate is simply the rate where arithmetic works, determined by symmetrical group formations. That number should be related to Nyquist and the golden, a natural outcome, though I am a bit over my head, but lets look:
Nyquist .5, Golden .618, Pauli .6666; .5 + .118 + .048 See any pattern? Neither do I, call the pattern expert. But the Pauli rate should be fixed to Nyquist, and the golden rate fixed by the measurable density ratio within that. If the vacuum shaped itself past the range that Pauli is untrue, then we get constant shape distortion as as gaps appear now and then. Pauli is the first stable group integer, determined by the the density of space, in units of vacuum. And when tat ratio computes to the first integer, we have Pauli. The shape ratio adjusted to make the first integer a workable 'counter', and it becomes a close approximation to golden. The first integer is the denisty/vacuum size, computed in Nyquist 2s, without remainder. Where's my calculator?
So anywhere and everywhere, the vacuum equalizes phase up to the first integer, and Pauil is set to handle the remainder. The numbers scaled to make Pauli the first integer.
That makes a universal constant. free Nulls go at the Golden rate, the speed of light, packed Nulls go at the Pauli rate. E = Mc squared is off a bit because packing of free Nulls is less than golden.
So now we have it. As matter is packed, it leaves more excess free Nulls relative to vacuum density. Phase alignment is always a bit less than can supprt free Nulls. But free Nulls travel at Golden, so scientist think there is more energy hidden up there, and there is. The free Nulls get pushed down in order, (make smaller mass), and that excess eventually becomes Black Holetrons, the teeny weeny things the farthest out. But Black Holetron are measuring the common mode of the Universe, in terms of excess free Nulls, they make phase alignment, and thus we will eventually go Black Hole, and blow up.
The ratio, Golden curvature and Pauli curvature is constant at each quantization level. waves as Golden, mass at Pauli. Matter is stable, within a level, because phase alignment which contains matter adjusts slightly faster (Golden) than mass can disintegrate (Pauli). Because the ratio is constant, I can define the right angle and use complex quantization levels. The ratio between the two is .928. So energu is Emin * sqrt(1+.928**2) or Emin* k = k*1.36 Emin. At each level I break up phase and mass into sin(k*1.36) and cos(1.36). The easier was to do this is to pack all mass at Pauli, then go back and pack all the wave at Golden.
That means the Universe is closer than we think, we measure light at mass speed, according to E=MC**2. It also means that Null gets a bit more space than the phases when the vacuum adjusts to the Golden rate. These ratios should show up when an expert in topology works the problem. The universe defined by the, yet unproven theory, of how two antisymmetric shapes pack relative to their symmetric counterpart. Race me to that theory, you topologists everywhere!
That would be physics counting system defined.
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