Fibonacci sequences and group theory

Fibonacci sequences and group theory Yes, I knew something was up, this PHD thesis by AM Brunner worked the issue a bit.
String theory is a group theory.

An entire book on the subject: Fibonacci Numbers and Groups

What I do is not new, I just wonder why the idea was not extended all that down to the original generators. It would seem natural that the vacuum can do nothing else but generate the group, it has no global knowledge.

Shannon vs Hamiltonian

Right, So the Shannon system, taken as its inverse, is simply that mapping of a stochastic group into an integer set.  The integer set defined by Shannon is the boundary point, and between boundaries kinetic energy is supported. The Hamitonian is valid between boundary points. We have boundary points in physics because the vacuum needs kinetic energy to maintain the sample rate. Do my little operators D1 = 1/2(m-f) and D2 = 1/2(m+f), which astute readers notice is the form of the hyperbolic, are generators of the boundaries. (D1+D2) * (D1-D2) define the Compton condition, e^x * e^-1 = 1.

Energy

The total energy of the universe is allocated for one reason, to maintain enough stochastic activity that the phase exchange rate with nulls is stable. It is all about maintaining the speed of light.  Or, alternatively, it is about maintaining the Nyquist sampling rate within stochastic groups.  When the exact maximum entropy point is achieved, we get explosions because sample rates on either side of the packed nulls diverge.

What about Higgs?

Professor Higgs says the system was top down, a big thing was created, and that resulted in the necessity of maintaining Nyquist, that is the Big Bang. The opposite is the steady state, the vacuum started and built from the bottom up.  So, spacetime inflation is all about establishing the speed of light.

Why the Fibonacci rate?

Phase did not cause that. Phase is stable when it can combine any two groups, but all the groups look like they have size 1 and 2, because of the three types of vacuum. So the {-1,0,1} cause the Fibonacci rate, not the other way around. Any Shanon barrier is marked by (3/2)^n and (3/2)^(n-1). Phase, just trying to make nulls add up can only find and integer set very close to 1 + 2 = 3.  If not for the Shannon bariers, it would find all sorts of groups like: 2+3=5, 2+5 = 7, etc.  So, if everything is scaled to the Shannon barriers, the rate looks Fibonacci, relative to the 3/2; but that's just us humans scaling numbers so every thing goes by powers.

So a critic would say, hey, those spots where two null quants have no Fibonacci quant is simply a math trick.  Not quite, it is a math trick that tells us how significantly different a wave quant would be to fit between those spots. And that match trick says, too significantly different, the packed nulls would not be stable.