Talking of symmetries: The Gm product of the proton mass multiplied by the quantum adjustor, 3.62994678, is equal to the Planck radius times Gmc/2, 4.050599332x10^-37. If we substitute 2/c for G then:
(2/c)x(1.672623x10^-27)x(3.62994678)=4.05049049x10^-35m, the Planck radius.
multiply 4.05049049x10-35 by (c^2)/2 and you have 1.801996x10^-18 which is the Gm product of the Planck mass. Divide this by Gc/2 and you have 1.82015x10^-16m which is half the proton Compton wavelength, (1.32141x10^-15m)/2, multiplied by 3.62994678=1.82015x10^-16m. Nature will have it no other way.