On the 30th anniversary of Particle Swarm Optimization (PSO), we present a novel integration of Geometric PSO (GPSO) into the Program Trace Optimization (PTO) framework. GPSO extends PSO to diverse representations in a principled manner, while PTO provides automatic representation design for arbitrary problem structures. By specializing GPSO to PTO’s trace representation, we achieve a universal PSO variant applicable out-of-the-box to any representation and problem. We detail the theoretical foundations of this integration and evaluate our approach on diverse optimization problems across multiple representations. Our work demonstrates the power of combining geometric generalizations with automatic representation design, here specifically obtaining a truly general form of PSO that applies to any representation while retaining its original essence.