Field Symmetry Theory: A Phenomenological Model for Nuclear Binding Energy with 99.9% Accuracy for Heavy Nuclei

We present a phenomenological model for nuclear binding energy, termed Field Symmetry Theory (FST), based on an effective nuclear field derived from the Heisenberg uncertainty relation. The model incorporates volume, Coulomb, symmetry, and pairing terms as physical corrections, with the logarithmic term ln A justified through renormalization group arguments. A Lorentzian correction is introduced to account for few-body effects in light nuclei, with a physical justification based on finite-size effects in quantum systems. With only eight adjustable parameters, the model achieves a mean absolute error of 0.0388 MeV per nucleon and R² = 0.99996 when compared to 3554 nuclei from the Atomic Mass Evaluation 2020 (AME2020) dataset. The model performs reasonably well for light nuclei (A < 8: MAE = 1.15 MeV/n, accuracy 65.8\%) and achieves 99.9\% accuracy for heavy nuclei (A > 150), with uranium isotopes reaching 99.9% precision. Cross-validation confirms no overfitting (generalization gap < 10^-6 MeV/n), and correlation analysis reveals expected interdependencies among base parameters while confirming the stability of correction parameters. The complete computational code is provided as supplementary material accompanying this manuscript.