Global Flavor Symmetry and Fractional Quantization in Hadronic Multiplet Mass Sums:ARigorous First-Principles Derivation

We establish a fundamental connection between the breaking pattern of global U(nf) flavor symmetry in quantum chromodynamics (QCD) and the emergence of fractionally quantized ratios in sums of hadron masses within spin-flavor multiplets. Starting from first principles of QCD and group representation theory, we rigorously derive a universal recurrence relation under hierarchical symmetry breaking U(nf) → U(nf −1)×U(1).Weprovide detailed physical interpretations of the model parameters, linking the large mesonic correction slope |ameson| = 88.892±0.005 to spontaneous chiral symmetry breaking and the smaller baryonic slope |abaryon| = 0.600±0.001 to constituent quark model dynamics. Remarkably, the fitted slopes themselves exhibit simple mathematical forms:|ameson| ≈ 9π2 (0.074% accuracy) and |abaryon| = 3/5 (exact within precision).Based on this framework, we present testable predictions for unmeasured multiplets,including U(5) baryons (R = 0.984192±0.000002) and U(6) mesons in the heavy-quark limit (R =0.975610±0.000005). This work establishes fractional quantization of hadronic mass sums as a fundamental organizational principle of QCD and provides a precision tool for testing hadron structure and beyond- standard-Model physics.