Hadronic Mass from Confinement, Transition Structure and Matrix State Realization

The prediction of hadronic masses remains one of the most challenging problems in modern physics. While lattice quantum chromodynamics (LQCD) has achieved remarkable success, its accuracy varies significantly across the hadron spectrum. Certain regions achieve strong agreement, while others—particularly in excited states and meson sectors—can deviate by 5–10% or more. Alternative phenomenological approaches often improve performance within specific subgroups but struggle to maintain consistency across the full spectrum. In this work, we present a compact phenomenological mass equation that achieves an average error of 0.128% across a dataset of 281 hadrons, including over 90 baryons, 180 mesons, quarks, and exotic states. The model maintains a tightly bounded error distribution, with no deviations exceeding approximately 1.51%. The formulation separates intrinsic quark contributions, transition energies, and state-dependent excitation into a unified framework, enabling consistent performance across diverse hadronic systems. The full computational implementation is provided, allowing direct reproducibility of all results. Despite its simplicity, the model demonstrates an unexpectedly high level of accuracy across the complete hadron spectrum. The construction of such a compact and efficient equation raises a natural question: How can a phenomenological model achieve this level of agreement across such a wide range of systems? This paper presents the full formulation, dataset, python code to reproduce and results.