Paper LXIII: The Higgs Mass from the Fano Weak Eigenvalue and the QCD Correction: (v/2)(1 + αs(mt)/2π) = 125.23 GeV Paper LXIII

The observed Higgs boson mass mH = 125.25 ± 0.17 GeV has resisted derivation from rst principles in the Standard Model, where it is a free parameter. We show that the brane-bulk octonionic framework derives mH in two steps with no free parameters. Step 1: The quartic self-coupling of the λ = 4 Fano eigenmode (the weak sector mode; Paper LXII) is determined by the anharmonicity of the AdS potential at eigenvalue 4: λH = 1/(2λ2) = 1/(2 × 4) = 1/8. This gives a leading-order Higgs mass m(0) H = v√2λH = v/2 = 123.110 GeV. Step 2: The one-loop QCD correction from the top quark (the heaviest Fano cross-sector excitation, yt ≈1) corrects the self-coupling by ∆λH = λH · αs(mt)/π, giving: mH = v 2 1 + αs(mt) 2π = 123.110 × 1.01719 = 125.226 GeV. The discrepancy from the observed 125.25 GeV is −0.024 GeV (0.019%). The formula requires only the Higgs VEV v = 246.22 GeV (itself set by the Z3 EW freezing of Paper LVI), the Fano eigenvalue λ2 = 4 (from the Fano Laplacian of Paper XLII), and αs(mt) (derivable from the Fano formula of Paper LXII). The correction factor 2.433 identied as unresolved in Paper LXII is now fully explained: 2.392 comes from the ratio v/2 to the leading Paper LXII estimate, and 1.017 from the QCD correction. The Higgs mass sits at mH ≈v/2 because λH = 1/8 is the Fano self-coupling, not because of ne-tuning. The vacuum stability boundary (λH(mPl) →0) is naturally satised in the framework at mH ≈129 GeV, placing the observed 125.25 GeV in the metastable regime consistent with the δM/M tilt of Paper LVI being non-zero but small. Three new predictions follow (Predictions 120122). Part of the One-Octonion Brane-Bulk Framework series. Anchor DOI: 10.5281/zenodo.19120873. Community: one-octonion-brane-bulk. Author: Bharathi Dasan Jagadeesan, M.D., University of Minnesota. ORCID: 0000-0002-1143-941X.