QCD Corrections to the Koide Formula from Information-Theoretic Principles

The Koide formula Q = 2/3 for the charged lepton masses is confirmed to |Q - 2/3| = 6.2 × 10⁻⁶ but fails for quarks, where Q_u = 0.849 and Q_d = 0.731. We argue that the color degree of freedom carries log₂(N_c) = 1.585 bits of Shannon information, which distributes over d_c × N_gen = 21 structural channels, producing a universal color correction Δ_color = 0.0755. Combined with electromagnetic hierarchy corrections, this yieldsQ_u^pred = 0.848 and Q_d^pred = 0.737 with no continuously adjustable parameters (conditional on a companion framework). The predicted–observed differences (0.001 and 0.005) are small compared to the dominant uncertainty from renormalization scheme mixing (~3%). The Koide parameter satisfies an exact Rényientropy identity Q = exp(−H1/2), which provides a self-contained perturbation framework for the QCD correction. Quark Koide parameters converge to 2/3 at high energy scales as α_s → 0. An exact enumeration over 665 discrete parameter combinations gives p = 0.0015 for parameter coincidence; accounting for structural look-elsewhere effects gives p ≲ 0.03. Companion paper: "Fermion Mixing Angles from Three Algebraic Parameters" (Paper 1), DOI:10.5281/zenodo.18675985.