tanh * tanh' + 1/2 tanh'' = 0
This is the Hamiltonion for the TOE.
The curve is tanh'', composed of tanh * tanh'. It is the environment that is imposed on the system when adapted.
This curve goes down to the uncertainty of the system and is in balance with the environment. That peak is where all the transcendentals are most accurate, their rational approximations get settles at 1.5 on this chart. But 1.5 is not a solution, mainly because the system need to play the Wythoff game at that point where the combinations of events are maximum. Tanh is the amount of 'charge' the system support for any integer point along the curve. tanh' is eqwuivalent to momentum.
To the left of that peak, the bubbles are crowded, and want migrate to tanh = 0, to the right, tanh goes to one and there is no gain from an exchange, sinh and cosh are about the same. The effective quant of the electron is 1.5, mainly because the quarks bounce it between 1 and 2.
Where is that peak relative to the nucleus? I am not sure, actually. But I am pretty sure angle count from the center of compaction, starting at zero. But I have gotten mixed up on that many times, beware.
I think the environment to the right of the peak is actually decompresses relative to the nominal vacuum, it is the positive charge region from the proton. To ghe left of the peak, the tanh function is very linear with the angle and tanh' is maximum. So the gluons, as you see, have a lot of room between zero and one to set the environment, always near the vacuum uncertainty. This collection is an avogadro of bubble, and the electron is about 10e14 bubbles, so a lot of Whythoff moves going on, but they all obey Wicks theorem.
Posotrons can slip over the peak going from left to right. But they are quant on stuck in a quant two environment, they need to decompress, so their tanh' flips sign, they appear positive. They are do not meet the constraint equation above.
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