Paper CLVI of the Brane-Bulk Series 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): mH = vexp (−αH+d_τ) + (1/3) exp (−αH−dc) ⁻ = 125. 205 GeV. Level-2 (λ=4 Fano phonon with QCD running, Paper LXIII): mH = (v/2) (1 + αₛ/2π) = 125. 226 GeV. Bridge (e₇ Adjacency Ward Identity, this paper): the brane vibrations at kAdS = 0. 02462 couple e₇ to all 6 adjacent Fano nodes through the Planck-scale phonon field, imposing 1/η − 1/ε = Nₐdjacent (e₇) = 6. This Ward identity (i) derives αₛ (mₜ) = 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: mH = 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.