Its about 'one' and 'zero' being equidisant everywhere

This condition sinh^2 + 1 = cosh^2, and the Shannon condition are all the same theory.  That 'one' is a computed quantity, maintained by the motion of matter, the 'one'.  If matter hits close to the 'zero' it degenerates. I have a few drawings almost ready to show how the 'zeros' are moved about so the 'one' has equidistant paths through the linear portion of tanh.  It is all about making the optimum 'yardstick' where the F and 1/F are chosen to keep the zeros at the proper mid-points.  This is the minimum redundancy condition. The system is ultimately limited because the relative ratio of the largest F to 1/F becomes close to the residual irrational error in Pi.

Weinberg knows this, I was listening to one of his lectures, and he got the problem, and knew this was measure theory and warping of Riemann space. So this is real stuff.

Stay tuned, I am going to put up some rough schematics and show how these tear dropped orbitals have the effect of making the zeros equidistributed.  So, the Lattice Chromodynamics folks are on the right track, the idea of a continuous coupling constant is off base a little. The coupling is still quantized, but wave, or the imaginary part of the lattice between grid 'notches'. Things are getting much simpler in physics, its a new world. The folks who did quantum conductance nailed it.  The multiple paths through the linear  tanh is the key link between combinatorics and quantum mechanics.

This graph is the plot of Lucas polynomial L(5,r)+L(6,r)-L(6,r), over the unit circle from 0 to Pi.  The boundary conditions are met, the resultant is zero at angle 0 and Pi. But along the unit circle is a double wave at Pi/2. The vacuum wants to disperse that variation over the whole circumference, so it make an oval, it literally changes the shape scaling of the unit circle x,y axis (still a little fuzzy);  but this distributes entropy. We get the tear drop thing.  What unit sphere is warped? The shell and the 'one' both have complementary distortions. Doesn't that distort the value of Pi? No because of -iLog(i).  In the sum the power series sum remains the same, because the probability of a 'digit' counting is adjusted for the remapping of the grid.

Finite element computations use the concept, matching grid size to the variation  in the function being computed. In Shannon theory this condition makes the baud size, the distance between signals, consistent. In measure theory this condition makes the estimation of 'one' consistent. In physics it makes the total system, in the sum, nearly spherical. In statistics it means you have square matrices and a diagonal identity. In number theory it means you are counting with maximum accuracy using the minimum number of digits. And in network theory it means you have a minimal spanning tree.

How does the vacuum stretch the grid?
It redistributes the Nulls, the little inert elements of the vacuum can be shifted around.  Packing the Nulls makes matter by keep contained light trapped in the limit of the curvature, the Fine Structure limit.. That is the Higgs mechanism. So when stretching the grid, the relative change in curvature, or Tanh'(L(n) + L(n+1), must total Pi in its variation.  That is the total variation in Pi matches Pi, the finite log condition, the Shannon condition, the equal queue lengths condition, etc. Kinetic energy becomes adiabatic.

Note:
I figured that the Fine Structure Constant was a variation in volume.  I may be wrong, and physicists should clarify. But, it really should be computed as the variation in the value 'one', for spherical systems. It  itself is a 'constant' with the same proportional variation. Given the constant, the laws of physics should fall out from the equal distribution of entropy.  What if one built a system with a different number? Hmmm.... It may not be possible, the set of combinations may always be open. This was Shannon's world where cables were infinitely long. Recursive sequences tend toward Phi in their ratios, though I cannot prove this always that case. Making the variance in the value 'one' larger just causes the system to scale up and work with an nth root of 'one',