The author appears to be struggling with the infinite problems caused by treating the particles as point particles(maybe). Maybe, this infinity problem can be solved through chapter 2-5(The minimal size of existence) of my paper.
The equation above means that if masses are uniformly distributed within the radius , the size of negative binding energy becomes equal to that of mass energy. This can be the same that the rest mass, which used to be free for the mass defect effect caused by binding energy, has all disappeared. This means the total energy value representing "some existence" coming to 0 and "extinction of the existence". Therefore, is considered to act as “the minimal radius(size)” or “a bottom line” of existence with some positive energy.
However, from the equal rates of fall of electrons, protons, and neutrons we cannot extract quantitative conclusions for the rates of fall of the self-energies locked up in the rest masses, because we have no way of calculating the magnitudes of these self-energies. A naive calculation of the, say, gravitational self-energy of the electron gives an infinite value; this, of course, proves only that the calculation is wrong and that our understanding of the quantum dynamics is faulty.
Do you see a connection between "minimal size of existence" and the ratio of masses? Using a simplified ideal example: Let an electron and proton be positioned closer and closer to one another with the magnitude of their forces determined by Coulomb's force equation. The forces go to infinity while their accelerations have the inverse ratio of their masses. This is the question stated differently: If the ratio of their masses is maintained, the forces cannot become infinite?

James A Putnam