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

The Koide relation Q = (mₑ + m_ + m_) / (√mₑ + √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. Keywords: Koide formula, lepton masses, SO (8) triality, three generations, G2 algebra, charged leptons, mass relations