Nuclear Particle Masses from Photon-Flow Probability Kernels

The electron is modelled as a two-photon bound system rather than a point particle, admitting a discrete set of stable orbital states selected by a single standing-wave closure condition; the nuclear-particle mass spectrum then follows as products of these kernel states with no particle-by-particle fitted parameters. The atomic and nuclear domains appear as the two lowest exact solutions of one closure condition—the closed full-orbit kernel and the open half-orbit kernel—rather than as independently postulated structures. The neutron mass, computed independently of the proton, agrees to 0.268 ppm raw and +0.0013 ppm with a derived one-loop coefficient; the charged pion agrees with PDG 2024 at 1.5σ of its ±1.3 ppm measurement; the top quark agrees to 25 ppm; the muon closes to +0.030 ppm; and the tauon carries a single falsifiable prediction, 3477.2269 electron masses, resolvable by Belle II. The proton mass is reproduced to eleven significant figures through an exact closed form, disclosed as the calibration identity fixing the Anomalous fNuclear Ratio. All results follow from the fine-structure constant and the electron gyromagnetic anomaly alone, presented as evidence that the nuclear mass hierarchy has a geometric origin in electron structure.