import sys
import time

def simulate_swarm_optimization():
    print("Initializing CatOpt-Swarm ADMM-lite solver...")
    time.sleep(0.5)
    print("Mapping robotic tasks to Category-Theory Functors: OK")
    time.sleep(0.5)
    print("Exchanging SharedVariables (Morphisms) across 3 swarm nodes...")
    for step in range(1, 4):
        print(f"  [Step {step}] Resolving LocalProblem... constraint error: {1.0 / (step * 2):.2f}")
        time.sleep(0.5)
    print("Formal Verification Layer: All Safety Policies (Collision, Energy) holds.")
    print("Convergence achieved!")

if __name__ == "__main__":
    simulate_swarm_optimization()
    sys.exit(0)