Hurwitz and hyperbolics

This looks to me like the hyperbolic flow equation. Change it to:


Add another p/q and get: p/q * (1-(p/q^2) = 1/L * (1/2) * p/q^3, where we approximate the value one as 1/a * (p/q).  Then everything works out. The infinite of solutions merely states that tanh goes to 1 for ever. So given some level of  variation, there exists a sequential sequence that spans up to the maximum value of one. Its all about estimating one, or zero, on the other side. For each angle, I think, this just allocates combinations between for point on the X axis and for its inverse, maximizing the allocation of combinations.  In fact, the House of Cards, 21 (with Kevin Spacey) movie TV series,  had a bit of dialogue about this.

What are these?

A Diophantine equation is an equation in which only integer solutions are allowed.

They are simply solutions which map to a finite spanning trees , which will have an integer number of links.

Here is one of them that generates the Markov numbers. Use ergodic theory and describe x,y,z as constructs from unit vectors that our gaussian distributed. take the E[xyz], in their unit vectors. Cancel the terms for orthogonal vectors.  Then show that any finite spanning tree with gaussian variations is stable, and group forming. Connect the minimum phase property of Gauss to minimum spanning trees, that gets you minimum redundancy Shannon encoding. Then you get Markov numbers as the number of branches in a mixed log computation tree.

Stuff like that is the way to go.   Come on mathematicians, make this a complete theory of aggregate statistics and teach the fundamental theorems for economics and physics. I want to see this stuff everywhere, hyperbolics and Lagrange, the calculus of combinatorics. Its a new world, Newton is gone. I am not trying to pester the mathematicians, but they know this stuff; a lot of this approach has been done before by them, I stole most of it.
Like   Greenhall's proof of  Isserlis' theorem. He assume gaussian distribution of random variables, then orthogonalizes them.  Show that this assumption implies a stable adaptive process, and that the spanning tree must be minimal and unique.  Stuff like that, build the complete theory of combinatoric calculus, come on, what's stopping you? You can have the full Swedish banana, I don't care. Feynman diagrams are halfway there, they are a partition function.  The algorithms of finite arithmetic are just group generators, with the Lagrange as basis functions. It's all here, go ahead, redo math, create a revolution. Dump Newton, he was Episcopalian anyway.