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 Qᵤ = 0. 849 and Qd = 0. 731. We argue that the color degree of freedom carries log₂ (Nc) = 1. 585 bits of Shannon information, which distributes over dc × Ngen = 21 structural channels, producing a universal color correction Δcolor = 0. 0755. Combined with electromagnetic hierarchy corrections, this yieldsQᵤᵖred = 0. 848 and Qdᵖred = 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 αₛ → 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.