Paper CLXIII: One-Octonion Positron-Mediated Muon-Antimuon Lepton Fusion via the G₂ Klein Ladder: True Muonium Formation by Charge Exchange, the π γ Channel Prediction

Toyama et al. (2026, Science Advances, DOI: 10.1126/sciadv.aed3321) report the first direct observation of muonic molecular resonance states critical to muon-catalyzed fusion (μCF). We use this result as a starting point to develop a qualitatively different framework: positron-mediated μ μ lepton fusion, in which the α- ⁺ ⁻ sticking problem that limits standard μCF is structurally absent. In the One-Octonion Brane-Bulk Framework (Paper CVII), the muon is the 5D-transited pion — mμ = mπ × √(3/5) — and both μ and μ are ⁺ ⁻ brane solitons (Paper CLX) at nodes e₂ (H sector) and e₆ (H sector) of the G₂-symmetric Fano plane. The ⁺ ⁻ positron (e , H sector) forms an e μ bound state ('muonic anti-hydrogen') with Bohr radius 0.53 Å and ⁺ ⁺ ⁺ ⁻ binding energy 13.5 eV. This system undergoes exothermic charge exchange with a passing μ : e μ + μ ⁺ ⁺ ⁻ ⁺ → (μ μ ) + e , releasing 1.4 keV to the freed positron. The resulting true muonium (μ μ ) has Bohr radius ⁺ ⁻ ⁺ ⁺ ⁻ 512 fm and binding energy 1.4 keV and annihilates via the G₂ Klein ladder (Paper CXLII) at node e₂, which gives exactly 3 two-body + 4 three-body final state channels. The key prediction is a two-body channel μ μ → π + γ, yielding a primary photon at Eγ = 62.55 MeV and a π at 148.77 MeV that subsequently ⁺ ⁻ ⁰ ⁰ decays to 2γ at 105.7 + 43.1 MeV (boosted asymmetric). This channel is strongly suppressed in the Standard Model (OZI rule) but predicted to be non-negligible by the framework because the muon is the 5D-transited pion — making μ μ → π γ the time-reverse of π γ → μ μ pair production at the e₂ Fano node. The ⁺ ⁻ ⁰ ⁰ ⁺ ⁻ positron plays three roles: (1) it shepherds μ into a bound state that accepts μ via charge exchange; (2) it ⁻ ⁺ prepares the para (μ μ ) spin-singlet state via B₀ field and RF π-pulse (the positron resonator cavity, Paper ⁺ ⁻ XXIV); and (3) it is released by the charge exchange and cycles, unlike the muon in standard μCF which sticks to α 0.6% of the time. A complete thermodynamic breakeven analysis identifies three conditions: (1) muon production cost must decrease from 5,000 MeV to 106 MeV (47×); (2) the π γ Klein ladder ∼ ∼ ⁰ channel produces a 105.7 MeV forward photon that is exactly at the γγ → μ μ threshold, enabling a closed ⁺ ⁻ recycling loop; and (3) cavity gain G > 2 at MeV-scale photon frequencies closes the energy balance. The framework's 5D transit interpretation of the muon (no neutrino emission in π→μ) is the path to eliminating the 21% neutrino tax that makes the... 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.