Unified Geometric Framework for the Three-Body Problem: Part III — Complete Stabilization via Vortex-Tension Dynamics

Part III of the "Hyperbrane Relativity" Trilogy: The Final Synthesis. This paper presents the unified synthesis of our investigation into geometric stabilization of the gravitational three-body problem. Following Part I (Vortex Repulsion for singularity avoidance) and Part II (Scale Tension for ejection suppression), this final part combines both mechanisms into a single, self-consistent dynamical framework. Key Results:Numerical benchmarks across 1,000 chaotic initial conditions demonstrate that the Unified Vortex-Tension Model achieves: 100% Stability: Zero singularities and zero ejections over 10^7 dynamical times. Chaos Reduction: Lyapunov exponent reduced by 87% compared to Newtonian dynamics. Emergent Order: Spontaneous formation of quasi-periodic, bounded orbits from chaotic initial states. This work suggests that the classical pathologies of the three-body problem (collisions, escapes, and unpredictability) can be resolved by extending point-mass gravity with geometric effects at short and long scales.