The mechanics of overlapping bubbles in physics

Let's consider the idea of the vacuum being composed of overlapping bubbles, but we impose two conditions.One condition says they can only overlap to some limt, call that the finstructure limit.  That is, there is some limit to the retains motion that insures no bubble is complete swallowed, bubbles do not go to zero.

Let's impose the second condition that bubbles must be locally additive.  That is, and number of bubbles i a compressed environment must be pushed into that environment via their neighbors, hence the concentration of some bubbles with overlap n must have originated from an additive combination of their neighbors.

The condition 0f local additivity generates our Fibonacci base, any sequence of the form: a,b,a+b,b+a+b, etc.  Then we ask, what is the rate of change in neighboring bubbles with respect to the exponent? Our formula below gives us the answer.

 We end up with a multiple of ln(c), or in our case the ln(phi).  But that logarithm is accurate when the rate of change is equal to the density.  If the bubbles are limited to retaining a fine structure of motion, they are dimensions, and the value ln(c) will become stable at the point of maximum dimension. What is that computation?

  Here it is.  Let N be the total number of bubbles, Phi^n, compressible according to spherical compression.  That number is near 91, or 13*7.  When m = 13*7, then to a an approximation up to the fine structure, 13 will calculate the logarithm of Ph^7 from Ph^91.  If 13, in this case, is the dimensionality, we find a limit in which the maximum amount of overlap between bubble and their concentration match, we get a Brownian motion equilibrium and the system will no longer compress. The arrangement of spectral motions, the overlap modes, and the local concentrations will match, spectrum and quantity are set to maximum compression.

How that happens, and how we evolve from Fibonacci to Lucas and beyond is a subject for the mathematicians.  But it is clear we get a balance between our three transcendentals, they all match in precision. There has to be a pattern by which the finite system moves about the Wythroff array, each time mapping three rational approximations to the three transcendentals and maintaining maximum dimensionality and conservation of bubble. Those matches have to create a Poincare group, including the Higgs mechanism for the bubble that cannot find a better spectral mode. That has got to be the theory of everything, there is no other way.

The spectral modes distribute making the Schramm Loewner index. The Brownian motion equation can them be written entirely in the rational approximation of Phi, over a set of spectral modes.  Time is simply the over all spectral density, finite and having some integer set of modal points. The Ito calculus is simple the path over which the Poincare group makes adjustments for motion, the group itself defines multiplication tree for the system, and that should be finite log additive, composed of multiple 'primes'.