Hierarchical Fractional Quantization in Atomic Nuclei: A Unified Framework Based on Symmetry Breaking

We present a systematic extension of the Hierarchical Fractional Quantization (HFQ) framework to nuclear structure physics. This work demonstrates that the empirical regularity of energy ratios approaching small-denominator rational numbers in nuclear spectra originates from universal sequential symmetry breaking in nuclear many-body systems. The framework provides a priori predictions of rational coefficients based on group representation theory for various nuclear phenomena.