This paper extends IGUP to include internal gauge symmetries. We construct principal fiber bundles over the quantum information manifold M. We define gauge potentials as affine connections, derive field strengths as bundle curvatures in full component detail, and show that the Yang–Mills Lagrangian is a natural geometric invariant of IGUP. We unify U (1), SU (2), SU (3) within the information geometry framework, and write the full Lagrangian unifying gravity, quantum theory, and the Standard Model. All derivations are explicit and self-contained.
Y. Li (Sun,) studied this question.