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 proton drives the electron at coupling α⁻¹; in the deuteron, two protons simultaneously drive one shared electron core, doubling the drive to 2α⁻¹. The factor −1 is the self-reference cost: the electron surrenders its bare identity to become the standing wave. No parameters are fitted. The neutron mass excess is derived as m_n − m_p = m_π/108 = 1.2920 MeV (observed: 1.29333 MeV, 0.10%). The denominator 108 is the geometric identity of the electron itself: charge is geometric orientation relative to the 108° pentagonal face, so the occupation cost is the bridge resonance energy divided by the electron's own geometric address. The binding energy ratio m_π/E_bind = 62.8 ≈ 63 matches the nucleation threshold from Bootstrap prime geometry. Four testable predictions are identified, including EMC-effect asymmetry between the two protons in polarised DIS and suppression of the anti-shadowing peak relative to free-nucleon A^(1/3) scaling.