A Relativistic Mass–Energy Framework for Atomic Structure and Multi-Electron Systems

This work presents a relativistic mass–energy framework for atomic structure, where energy is interpreted as a direct manifestation of intrinsic mass interactions rather than conventional charge-based formulations. The model is first applied to the hydrogen atom using an exact relativistic formulation and is then extended to multi-electron systems through a unified mass–energy interaction approach. The framework preserves relativistic consistency without relying on approximations and aims to provide a deterministic interpretation of atomic energy levels. A comparison with high-precision experimental data, particularly from the National Institute of Standards and Technology (NIST), is included to evaluate the accuracy of the model. Furthermore, the formulation is conceptually extended to extreme regimes such as black hole physics, suggesting a broader applicability across different physical scales. This work is presented as a preprint.