Particle Stability and Spin from the Geometry of Closed Null Orientations

This work develops a geometric interpretation of particle stability and intrinsic angular momentum based on configurations of null orientations in Minkowski spacetime. Building on earlier results showing that non-collinear combinations of null directions necessarily generate a timelike invariant, the paper investigates the structural conditions under which such configurations can form stable particle-like realizations. The analysis demonstrates that the existence of a timelike invariant alone is insufficient for stability. A stable realization requires the geometric closure of the spatial orientation structure, meaning that the spatial components of the null directions must cancel. The minimal non-degenerate configuration satisfying this closure condition consists of three orientations whose spatial vectors sum to zero, forming a triangular structure on the unit sphere. Within this framework, particle-like states emerge as minimal stable closures of null orientation configurations. The closure condition not only stabilizes the structure but also introduces a natural dynamical degree of freedom: collective rotation of the orientation configuration. These rotational modes preserve the closure relation and therefore represent the lowest-energy perturbations of the system. As a consequence, intrinsic angular momentum (spin) arises naturally from the rotational symmetry of the closed configuration rather than being introduced as an independent quantum postulate. The work further connects these geometric structures to the temporal organization of realizable states. Stable massive realizations are proposed to occur when the intrinsic Compton frequency of the configuration forms a rational phase relation with a global relaxation scale of spacetime, Ω ≈ 31 nHz. This condition provides a possible mechanism for the appearance of discrete particle masses within the broader realization framework. Taken together, the results suggest a unified geometric picture in which several fundamental features of physics arise from the same underlying structure: Light corresponds to open null realizations on the light-cone boundary. Mass emerges when multiple null orientations form a timelike invariant. Particles correspond to minimal stable closures of these orientations. Spin arises from the rotational symmetry of the closed configuration. The framework preserves the standard geometry of Minkowski spacetime and introduces no new fields or forces. Instead, it proposes that the invariant geometric structure of spacetime constrains which configurations of null orientations can appear as stable physical realizations.