Linear vs Curves, the compromise is a waste of thought and serves no purpose in AuT.
Pi is so clearly a non-event, that the only issue is why pay any attention to it as some sort of pre-AuT museum piece and how best to explain its complete elimination. Not partial elimination, complete elimination. I am done with pi, you should be also. If you bake me a pie it should be square.
A curve works better for a big bang type result. The linear F-series works better to define the period of overlap and the resulting amount of compression/capacitance and decompression/discharge. The gradual change between multiple universe yields an illusory curve so the combination of the two provides a mechanism to suit giving linear solutions a curved appearance, but only to the point where pi is no longer solved.
In this way the total information solution to pi is preserved based on averaging the results of linear spirals together to even out the answers. All change is quantum and the expression of the solutions can be solved as intersecting F-series spirals which intersect at points of compression and a certain levels of compression, where the “majority” of points for a given state are compressed, afterwards there is a state of decompression (as little as 51% (or 50.00001%, etc) afterwards which we interpret as a big bang but is merely the change from 51% compressed to 51% decompressed where compression refers to alignment of state and/or alignment of overlap for a given solution of x. The 90 degree turn can also be defined in terms of numeric position. That would be “overlap occurs at every 2nd F-series solution. This eliminates the dimensional model and is the key to solving pi based on the total amount of information. That is, instead of solving for some stupid pi infinite series as is done in pre-AuT math, the solution is based on the total amount of information and the number of “averaged turns” or “averaged overlaps defined by every other F-series” where there is a very large, but finite number of turns. Or overlaps. Pi becomes nothing more than an approximation of this average or 90 degree quantum terms which appears curved due to averaging. There is no curve or pi in the AuT universe and if there was, you'd throw it at my face.
https://www.youtube.com/watch?v=GFW-WfuX2Dk
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