QCD Casimir Structure in the Geometric Index of the 59-Dimensional Mass Framework

This paper presents the fourth installment in the 59-Dimensional Series. We solve the circularity problem of Paper I by deriving the geometric index n from first principles for the nine lightest baryons. Central Result: For p, n, Λ, Σ, Ξ, Ω baryons, n is determined by QCD Casimir operators C_R, C_A, T_F, strangeness S, and diquark spin J_diquark, with no free parameters beyond measured α_s. Agreement exceeds 99.7% for all nine baryons. Negative Result: The same approach fails for mesons due to dynamical chiral symmetry breaking dominance. We report both findings with equal clarity. The work connects particle masses to the 59 = 29+1+29 geometric partition and the Riemann Hypothesis critical line Re(s) = 1/2. This provides the first derivation of hadron masses from pure geometry and group theory.