The Proton as a Closed Wave-State: Maxwell-Fourier Geometry, Hadronic Degradation, and the Mass Gap

This paper develops a Maxwell-Fourier interpretation of the proton as a persistent closed wave-state in three-dimensional space. Building from established knot, soliton, Hopf, and wave-state precedents, it connects the fundamental equations of physics to a closed Maxwell-Fourier model of matter. A simple three-dimensional proton geometry produces threefold, thirds-based, 120-degree structure, motivating the proposal that quark and gluon signatures may be consistent degradation signatures of the proton wave-state rather than a literal parts list of the intact proton. The hadronic spectrum is then reframed as a degradation and reclosure spectrum of bound wave-state matter, and the mass gap as the spectral separation between open propagation and stable recurrent closure. The paper concludes with several direct tests based on whether a common energy-dependent Maxwell-Fourier model can reproduce broad experimental evidence without phenomenon-specific hand fitting.