The Koide Lepton Mass Relation Q = 2/3 as the Signature of SO(8) Triality in a G2 Framework

The Koide relation Q = (m_e + m_ + m_ )/(√m_e + √m_ + √m_ )² takes the value 2/3 to within μ τ μ τ 0.001% using current charged-lepton masses, yet has had no accepted derivation since its discovery in 1981. We show that within a G2 algebraic framework established in prior work, the value 2/3 is the algebraic signature of SO(8) triality. SO(8) possesses a unique outer automorphism of order three (triality); the three matter generations are the three triality-related eight-dimensional representations. The triality group Z has three elements — one identity and two non-trivial — and the ratio of non-trivial ₃ elements to the total is (3−1)/3 = 2/3. The Koide value is thus identified as (|Z |−1)/|Z |, the fraction of ₃ ₃ the triality group carrying generation structure. We state the identification, give the numerical agreement, and note its consistency with an independent half-maximal symmetry-breaking result in the same framework.