Geometric Model of the Mass Gap in Yang–Mills Theory and the Wave Structure of Nucleons Based on the Method of Central-Disk Sectioning in Euclidean Space

This preprint introduces a classical geometric model of the Yang–Mills mass gap and the wave structure of nucleons in flat 3D Euclidean space, eliminating the need for point-like quarks, confinement postulates, and curved spacetime metrics. Key contributions of this work: Method of Central-Disk Sectioning: Demonstrates that any great-circle arc on a sphere lies in a flat secant disk passing through the origin, and the true chord triangle inside these disks always has an angle sum of 180°. Geometric Origin of the Mass Gap & Color Charges: Models nucleons as spherically closed standing-wave resonators formed by three flat disks intersecting at 120° (2π/3), naturally yielding the 1/3 normalized power invariant and the (+2/3, +2/3, -1/3) force profile. Spatial Interpretation of Spin-1/2 (720°): Explains half-integer spin as a continuous phase transition across two orthogonal secant disks (360° + 360° = 720°) combined with classical vortex energy flux (Umov–Poynting vector). Cross-Scale Structural Unity: Connects the 120° ternary resonance of nucleons with macroscale barycentric dynamics and the critical symmetry axis of the Riemann zeta function. Related preprints by the author: Wave model of nucleons: https://doi.org/10.5281/zenodo.22675117 Barycentric dynamics and 120° ternary geometry: https://doi.org/10.5281/zenodo.22898768 Arithmetic proof of the Riemann Hypothesis : https://doi.org/10.5281/zenodo.23666677