A Unified Operator Framework for Emergent Gravity and Gauge Interactions with Weakly Non-Commuting Mass–Charge Corrections

We present an operator-based framework in which mass and charge are encoded in a single complex operator Z = M+iQ allowing the simultaneous emergence of all four fundamental interactions. The real sector, M, generates gravity through an entropy-maximizing projection, while the imaginary sector, Q produces electromagnetism and accommodates weak and strong interactions via non-Abelian extensions. We focus on the weakly non-commuting regime, [M,Q]≠0, which introduces subtle mass–charge correlations observable in nuclear binding energies. Comparison between theoretical predictions and experimental nuclear data confirms the quantitative validity of these corrections. This framework naturally accounts for the hierarchy of forces and links microscopic operator structure to macroscopic phenomena including nuclear physics, astrophysics, and emergent gauge dynamics.