Understanding the 200 Years Mystery of ‘Gram Mole’ via 4G Model of Final Unification and Its Applications

The ultimate goal of theoretical physics is unifying the microscopic quantum realm with macroscopic general relativity. This paper proposes the 4G Model of Final Unification (having 3+1 interaction dependent gravitational constants) to bridge this gap. Central to this framework is resolving the historical mystery of the gram mole. Rather than an arbitrary chemical convention, the mole is redefined as a fundamental, intrinsic gravitational charge. Consequently, the Avogadro number is physically derived as a structural limit dictated by strong force saturation and nuclear binding energy. By treating the atom as an electromagnetic particle, the model establishes a direct equivalence between microscopic and macroscopic gravitational scales. To formalize this, honouring Einstein, Perrin, Loschmidt, Avogadro and Newton, we introduce the dimensionless EPLAN ratio. This universal scaling factor authenticates the SI-defined magnitude of the Avogadro constant and extends directly into astrophysics. Integrating this ratio with nuclear magic numbers yields a quantized mass spectrum for celestial bodies. This introduces a bottom-up geometric construction of stars, successfully deriving boundaries like the Chandrasekhar mass limit from first principles and suggesting compact objects settle into discrete gravitational orbitals. Finally, the framework reveals that the four fundamental constants corresponding to the strong, weak, electromagnetic, and Newtonian forces are not isolated. Instead, they operate as synchronized gears in a cosmic clockwork. The precise interaction of these quantum gears drives the macroscopic rotation of Newtonian gravity, proving that the subatomic stability of the atom is perfectly interwoven with the grand scale stability of the entire universe. By grounding the pursuit of unification in testable, multi-disciplinary outcomes, this framework offers a practical alternative to highly abstract theoretical models, and we respectfully present it for the physics community’s serious consideration.