The the Markov Diophantine equation equation imposes an algebra on the surface of a volume, using index space. It says the indexing on the surface has a three fold symmetry relative to the volume, indices are duplicated, there is compression of indices. The three fold symmetry yields the Markov graph where one solution rotates back into itself with the same stepping algorithm.
But does a three colored central banking pit follow these rules? If so, then those numbers are raw data window sizes and we see how index space is allocated when we interleave three sequences. They are very much spread, with most of the index space managing one of the inputs. Why is that?
It is a n outcome of Lagrange spectral theory which is all about approximating irrational sequences. And I think that is about primes becoming sparse as one proceeds to become increasingly accurate by umping up the Markov tree.
The claim, and possible proof, is that the Markov equation is the equation of arccosh, with f(t) = arcosh(3t/2), with a round off error, 4/9.
arc is a transformation that takes us from function space to index space. It works for sets of functions that are linear combinations of exponentials. The exponentials can be finite, but the implied assumption is that, in the limit, we can show index space maintains normative measures, in this case, to 4/9.
If you have symmetry, you have a log system, one can index the jumps through symmetry.
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