K⁺ Decay Branching Fraction Hierarchy from V−A Helicity, G₂ Cabibbo Suppression, and Fano Phase Space

Paper CXLIII established the K⁺ decay channel structure from G₂ Fano geometry: 3 two-body + 4 three-body = 7 channels, identified by Fano line incidence at the s̅ decay vertex e₅. The present paper derives the branching fraction hierarchy within each sector. The dominant result is the leptonic ratio R(μ⁺νμ / e⁺νₑ): helicity suppression (V−A chirality) forces R = (mμ/mₑ)² × kinematic factor. Using masses derived in Paper CXXV (mμ = 105.646 MeV, mₑ = 0.4995 MeV), the framework gives R = 40,730, within +1.38 % of PDG observed 40,177 — with zero free parameters. The V−A chirality itself is a theorem: Arf(B₁,₄) = 1 forces left-handed neutrinos (Theorem P_S2, Paper CXVIII), and the chirality angle τ = arccos(1/√7) governs the W-boson vertex coupling. The three-body semileptonic ratio R(π⁰μ⁺νμ / π⁰e⁺νₑ) = 0.616 from bare Fano phase space (PDG 0.661; the residual requires the helicity weight (1−mμ²/q²) integrated over the Dalitz boundary). Hadronic channel ratios (π⁺π⁰/μ⁺νμ, π⁺π⁺π⁻/π⁰e⁺νₑ) require Λ₂ᴀᴋ from the sump geometry and are deferred to Paper CXLV. 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.