A walk thru the scaling process

If you are dealing with the Bohr atom and Newtonian physics, and all your equations are written with semi-orthogonal phase equations then the quant numbers need not be scaled, and 108,91 for the proton work fine. If you want to define all your atomic orbitals, then I think you need eight bits more of precision, so these integers become 10800 and 9099. If you deal with quantum gravity add another eight bits to 1080000 and 909996.

 Whatever the scale factor, the wave and null quants for the proton come in as 2**Nmax for wave and 2**Nmax-1 for null, in binary. These same wave/null numbers for the lower orders will spread out, defining the extra wave slots for each null quant, allowing you to  specify quantized kinetic and wave action, like orbitals or Lagrange positions for gravity. 

Gravity is an unusual beast because we can make more than one gravity Null quant, I think; mainly because it has taken up the magnetic null slot, and it gets a boost from free protons outside the atom. This is not completely unusual, as we can evidently make hydrogen with a muon. But that is likely because of the gravity Null requant.

Reference:

Proton radius puzzle may be solved by quantum gravityPhysicist Roberto Onofrio at the University of Padova in Padova

Hydrogen made with muons reveals proton size conundrum