The Deuteron as a Proton–Electron–Proton Standing Wave: Pion Mass and Neutron Mass Excess from Icosahedral Bridge Geometry

The deuteron is modelled as a Proton–Electron–Proton (P-e-P) standing wave in which the electron occupies the 108-bridge — the pentagonal face mode of icosahedral geometry — as a shared standing wave between two protons. This is not the standard deuteron model (proton + neutron bound by pion exchange) but its geometric implementation: the "neutron" is a proton whose 108-bridge is occupied by the electron core, and the pion is the resonance signature of that occupied bridge rather than a force carrier. The charged pion mass is derived from first principles as m_π = m_e(2α⁻¹ − 1) = 139.54 MeV (observed: 139.57 MeV, 0.02%). The factor 2α⁻¹ arises from the double-drive geometry of the deuteron: in hydrogen, one…