K⁺ Decay Phenomenology from G₂ Node Assignment: Quark Mass Ratios and the Cabibbo Director, Center for Magnetic Resonance Research (CMRR)

Using the quark-to-node assignment derived in Paper CXXV from the Ursa Major Yukawa theorem, we place the K⁺ meson (us̅) on the Fano line {e₅, e₆, e₁} (strange, up, down). Applying the Klein ladder theorem of Paper CXLII to the s̅ weak-decay vertex at node e₅, we reproduce the complete K⁺ PDG decay table: exactly 3 two-body channels (Fano lines through e₅) and 4 three-body channels (Fano lines not through e₅), totalling 7. The ratio of derived Yukawa couplings yₙ/yₛ = 2.741×10⁻⁵/5.508×10⁻⁴ = 0.04976 closes the Gatto–Sartori–Tonin (GST) relation, giving sinθₙ = √(yₙ/yₛ) = 0.2231 — within 0.55 % of PDG 0.22431. All five principal quark mass ratios at the 2-GeV scale are reproduced from the framework Yukawa spectrum with no free parameters. The two independent derivation routes — Fano 4:3 hop topology (Paper V, λ = 0.22481) and the GST closure of this paper (λ = 0.22308) — agree at 0.78 %, bracketing the PDG value. 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.