The G2 Degeneracy Theorem: Koide's Formula, the Genesis Tilt, and Isospin as Topological Invariants of the H−/H+ Boundary

We prove that three fundamental Standard Model quantities — the Koide lepton formula Q = 2/3, the Genesis tilt θG2 = 4.044◦, and the isospin quantum number — are not independent inputs but topological invariants of the H−/H+ boundary in the One-Octonion Brane-Bulk Frame- work. All three follow from a single underlying structure: a two-tier eigenvalue degeneracy of the G2 Klein ladder at the k = 1 (lepton) and k = 2 (pion) rungs, coupled through the brane-bulk transit fraction fbulk = 1 −sinc2(α0) = 3.6917%. Tier 1 (intra-rung degeneracy): all three charged leptons occupy the identical Klein ladder rung k = 1 (λ1 = 2 − √ 3). The Z3 subgroup of W(G2) = Dih6 distributes them at equal angular spacing 2π/3 in weight space. Two trigonometric identities — ∑ℓcos(θ + 2πℓ/3) = 0 and ∑ℓcos2(θ + 2πℓ/3) = 3/2, valid for any θ — force Q = 6/9 = 2/3 exactly, independent of lepton masses. Tier 2 (inter-rung near-degeneracy): the gap ∆λ = λ2 −λ1 = √ 3 −1 = 0.7321 between the pion rung (k = 2, H−) and lepton rung (k = 1, H+) is small enough to be coupled by the B(1, 4) double winding. This coupling generates the Genesis tilt θG2 = 1 2 arctan( √ 6 + √ 2) · fbulk = 4.059◦(observed 4.044◦, residual 0.37%) and the Koide angle δ = (2/3)πx = 12.807◦(observed 12.735◦, 0.57%), where x = (m2 π −m2 µ)/(4m2 π) = 0.10673. The conjectured exact relationship δ = π · θG2 has residual 0.24%, the tightest of all framework conjectures, implying exact θG2 = δ/π = 4.054◦. We designate this Prediction P89. Isospin emerges as the H+ algebraic index of a standing wave after stochastic bulk crossing. 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.