Based on the shape-invariant standing waves on S³ and traveling waves on Z⁴ introduced in companion papers, we classify shape-invariant waves by the number κ of nonzero wavevector components into three stable modes: direction-constrained waves (κ=2), spherical waves (κ=0), and standing waves (κ=1). The signed area of the two-axis plane for κ=2 yields the geometric origin of the Pauli exclusion principle, while the (spatial, t) versus (spatial, spatial) plane structure determines chirality and the Majorana condition. Acceleration is derived intrinsically from the geodesic curvature of child-space central projection.
Noriaki Kihara (Thu,) studied this question.