The Higgs boson mass and its quartic self-coupling are free parameters of the Standard Model. We show that within a G2 algebraic framework established in prior work, the Higgs quartic self-coupling is fixed at λ = 1/8 = 1/dim(SO(8)_spinor), giving the tree-level prediction m_H = v/2 = 123.0 GeV, where v = 246 GeV is the electroweak vacuum expectation value. The observed values are = 0.1296 and m_H = 125.25 GeV, λ agreements of 3.7% and 1.8% respectively at tree level. The reciprocal of the eight-dimensional SO(8) spinor representation — the representation in which the framework's electroweak sector sits — fixes the self-coupling with no free parameter. Radiative corrections of the expected size and sign (order +2 GeV from top-quark and gauge-boson loops) account for the small residual. We give the identification, the numerical comparison, and the relation to the framework's wider electroweak-sector results. Keywords: Higgs boson, Higgs mass, quartic self-coupling, electroweak symmetry breaking, SO(8), G2 algebra, Standard Model