Paper CLVI: [Math Verified] Higgs Boson Mass from Fano Dirac Comb Superposition: H Hyperbolic Sector, Brane Vibration Consistency

We derive the Higgs boson mass from three independent but consistent perspectives within the One-Octonion Brane-Bulk Framework, incorporating the permanently hyperbolic (κ=−1) H ⁻ colour sector and brane vibrations at the AdS₅ backreaction scale. Level-1 (Dirac comb superposition with H hyperbolic correction): m_H = v[exp(−α_H+d_τ) + (1/3)exp(−α_H−d_c)] ⁻ = 125.205 GeV. Level-2 (λ=4 Fano phonon with QCD running, Paper LXIII): m_H = (v/2)(1 + α_s/2π) = 125.226 GeV. Bridge (e₇ Adjacency Ward Identity, this paper): the brane vibrations at k_AdS = 0.02462 couple e₇ to all 6 adjacent Fano nodes through the Planck-scale phonon field, imposing 1/η − 1/ε = N_adjacent(e₇) = 6. This Ward identity (i) derives α_s(m_t) = 0.10801 (PDG 2024: 0.1080 ± 0.002, 0.01σ), (ii) ensures Level-1 ≡ Level-2 at brane vibration precision, and (iii) reveals that the QCD running coupling is fixed by the Fano adjacency structure of e₇. Final prediction: m_H = 125.20 GeV (PDG 2024: 125.20 ± 0.11 GeV — 0.05σ). Zero free parameters throughout. 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.