Does the fine structure constant scale up?

Isn't that the theoretical question in physics, can we make the larger sphere from protons and keep the spherical maximum entropy constant?

This is like the compound interest question in finance, why does the YoY interest rate increase with longer terms. The Schwarzschild radius assumes all spheres are perfect, made of infinitely divisible elements. Light is constant, hence has infinite degrees of freedom.

The fine structure may not scale up. The sun makes a great sphere but it is not in equilibrium and is making helium and emitting light. Planetary orbits seem to be limited in degrees of freedom and Lagrange points have limited stability.

The current standard  physics has gravity as limitless, meaning it knows Pi exactly.  But we still make adjustments based on relativity, so that cannot be the complete answer.

This is why I think free protons play a larger role and are much more prevalent than we think. Proton make the relativity adjustment where needed  They add another term to the equations of the larger sphere at the boundaries.I do not buy into the concept of empty space. The vacuum cannot know the value of Pi since it must be computed as a power series, and that is a finitely quantized, sum.

How badly does the Sun compute Pi? 

All by itself with no energy release, one can look at the orbital plane, its about 3 degrees. The proton is good up to 90 degrees, I think, using the Lucas number scale, and that seems to agree with the orbitals.  Stable orbits are hard to create without tidal action breaking up the planets. If goes back to the degrees of freedom needed to compute a good sphere, and planets do not have that in their masses. The sun has to  fine tune, like the quarks can, spreading protons out.  Looking at the hyperbolic equation of the sphere, the sun does not match volume with radius. If gravity is to be accurate up to the fine structure, then protons have to be spread around until the radius and volume match at the boundary. Is that a shift left by an exponent of 17 in the Lucas numbers?  Dunno, haven't thought this through. But I would be looking at Wythoff arrays if I were a sphere packer trying to scale up.