Paper CXXII · One-Octonion Brane-Bulk Framework · Prediction P206–P207 The Charge Wave at B (1, 4): A Triangle Relation Between α, mₑ, and m_π via the Fano Secant √7

The electron traverses the quark–lepton boundary B (1, 4) with two distinct waves: the mass wave (Dirac oscillation, fermionic, anti-periodic, two traversals from the Arf = 1 spin structure) and the charge wave (electromagnetic field configuration, bosonic, periodic, one traversal to close). The mass wave was addressed in Paper CXXI: it gives the correction 2α√7 to mₑ. Here we analyse the charge wave. The key result: the mass formula mₑ = (αm_π/2) (1 + 2α√7) is a quadratic equation in α — it creates a triangle relation between three quantities mₑ, m_π, and α, mediated by the Fano factor √7. Any two determine the third. Inverting for α given observed mₑ = 0. 51100 MeV and m_π = 134. 977 MeV: alpha^-1 = 137. 17 (observed: 137. 036, 0. 10% discrepancy) inversion result The 0. 10% discrepancy is exactly the same order as the mass formula's own 0. 098% error — the system is self-consistent at first order. This is not a derivation of α from pure geometry, but it demonstrates that the framework contains α, mₑ, and m_π in a single constraint surface: the Fano secant √7 mediates between the QCD scale and the electromagnetic scale. A full derivation of α = 1/137. 036 from the G₂ structure constants at the B (1, 4) boundary is identified as structurally possible and is deferred. 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.