Unifies CCLII (Δm² ratio + PMNS via Class III Gudermannian blend at framework angles) and CCLIII (absolute neutrino mass scale via Higgs Yukawa with G₂ root closure) into a single mass formula. The key insight: ν₁ has no G₂ orbit closure on the 4D brane at any order (the only neutrino with n_long = 0 in the framework PMNS structure), so its mass cannot come from G₂-orbit closure on the brane. The mass acquisition must instead be W-boson mediated: the W lives in 5D effective phase space (4D brane + 1D e₇ direction, since the W crosses the brane-bulk separator under CXLIX), and its action on the 4D brane is the projection of that 5D phase space. The dimensional ratio 5/4 enters as the angular projection factor. For ν₁, this fixes φ₁ = (5/4)·Θ_G₂ = 10.110°, replacing CCLII's tilt-based −Θ_tilt = −4.044°. Evaluating the Gudermannian blend at this corrected angle gives m_ν₁ = 0.5047 meV, matching CCLIII's separate α⁷·√7 channel (0.5071 meV) at 0.48% agreement. The α⁷·√7 of CCLIII is therefore not a separate physical mechanism but the small-angle limit of the unified blend. One formula handles all three masses: m_νᵢ = (f_III·sinh²(φᵢ) + (1−f_III)·sin²(φᵢ)) × scale, with φ = (10.110°, 40.956°, 85.956°). Σm_ν = 59.30 meV. Framework now makes the structural prediction that the W boson lives in 5D effective phase space, falsifiable via anomalous W-neutrino couplings at >1% precision. Closes the OOB neutrino sector under a single physical mechanism. 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.