Wave-Source Theory: Magnetic Self-Energy Closure of the Proton Mass (938.272 MeV) and a Neutron Mass Candidate (939.565 MeV)

We present a candidate framework ("wave-source theory") in which the proton is modeled as ten synchronized pulse sources and the neutron as eleven, each alternating between a magnetic energy layer and an interstitial vacuum layer with symmetric duty ratio tau_b = tau_i = 0.5. An analytic magnetic self-energy expression E_self = (25/4) h c^3 / (pi^4 tau_b r^3 f0^2), evaluated at the proton charge radius r_p = 0.84 fm (PDG 0.8407 fm), the duty ratio tau_b = 0.5 and the base frequency f0 = 1.60353e23 Hz, closes at 938.267 MeV (ratio 0.999994 to the measured proton mass 938.272 MeV). Applied at the mass-scaled radius r_n = r_p (m_p/m_n)^(1/3) = 0.8396 fm, the same expression closes at 939.560 MeV (ratio 0.999995 to the measured neutron mass 939.565 MeV). Honesty disclaimer: this is a consistency closure, not a first-principles prediction. The base frequency f0 and duty ratio tau_b are reverse-solved from the proton mass itself (circular constraint chain; internal audit grade FAIL), and the neutron radius scaling is an ansatz. The contribution is (i) a compact, exactly reproducible analytic closing of both nucleon masses, (ii) an explicit circularity audit, and (iii) a falsifiable research program: breathing sideband spectroscopy of the hydrogen 1S-2S transition, where phase-modulation sidebands at the breathing frequency should appear with strength J1^2 ~ 1.3e-5 for f_vib = 6.8e13 Hz (within the EGB-allowed window; energy offset +/- 0.28 eV), currently unsearched and decisive in both directions. All numbers are reproducible with the included verification script verify_nucleon_mass.py (CODATA constants).