An even simpler prrof of Shannon entropy theory

In any channel, running at maximum information transfer, the residual entropy in the channel must be zero. Hence the power retained in  the channel must always be normalized to one.  Thus:
Power_in - Power_out = 1, but power is a square. So this is the hyperbolic flow constraint.

That does bring up a point. The adapted system is not a stable Shannon, it keeps entropy in the channel above zero, it transfers the map via connectivity, so we have:

Power_in-Power_out = Phi, I do believe. I think that adds asymmetry because:

phi^(1/2+n) + phi^(1/2 - n -1) is the hyperbolic form, but if the powers of Phi come from a sequence then the sequence is shifted by one to compose the hyperbolic:


Exp X     1/2    |  1/2+2  | 1/2+3
Exp 1/X  1/2-1 |  1/2 - 3  | 1/2 -4

So there is a charge shift.  Now the result is still the hyperbolic flow model, but the connected network is offset. I think there is a Wythoff row that does this, let me check.