Angular Momentum Invariant of Closed Surfaces: A Unified Explanation for Electron and Nuclear Size

This paper formulates a universal angular momentum invariant for closed surfaces. By enforcing the tangential closure condition ω=c/r, the rotational momentum becomes p=mrc. Combined with the invariant moment mr=ℏ/c, the result is p=κℏ. The electron at its Compton scale corresponds to κ=1, the Bohr orbital shell corresponds to κ=, and the helium nucleus corresponds to κ≈32. These findings explain why electron and nuclear sizes are not arbitrary but fixed by closed-surface equilibrium, with interaction constants providing scaling factors.