Determination of the Proton Radius from Closed Surface Conditions

This paper derives the proton’s geometric radius directly from three universal relations in Closed Surface Theory:(1) moment constancy mr=const,(2) energy–frequency equivalence mC²=hν, and(3) tangential velocity condition rω=C.Solving these simultaneously yields a unique radius r=ℏ/(mC), equivalent to the reduced Compton wavelength (~2×10⁻¹⁶ m).The result shows that the proton’s scale is not empirical but a geometric inevitability defined by Planck’s constant and the speed of light.The relation mr=ℏ/C reveals that the first moment of mass is a universal invariant linking energy, curvature, and frequency.