class RDoDEngine:
    def __init__(self, sigma=1.0):
        self.sigma = sigma
        self.levels = {
            "OBSERVER": 0.1,
            "PARTICIPANT": 0.5,
            "COORDINATOR": 0.8,
            "SOVEREIGN": 0.9999
        }

    def calculate_saturation(self, phi_recursive_factor, drift=0.0):
        # RDoD formula from README invariants
        # simplified for implementation
        saturation = self.sigma * phi_recursive_factor * (1 - drift)
        return min(saturation, 1.0)

    def get_authorization(self, saturation):
        if saturation >= self.levels["SOVEREIGN"]:
            return "SOVEREIGN"
        elif saturation >= self.levels["COORDINATOR"]:
            return "COORDINATOR"
        elif saturation >= self.levels["PARTICIPANT"]:
            return "PARTICIPANT"
        return "OBSERVER"

if __name__ == "__main__":
    engine = RDoDEngine()
    saturation = engine.calculate_saturation(0.999997)
    auth = engine.get_authorization(saturation)
    print(f"RDoD Saturation: {saturation:.6f}")
    print(f"Authorization Level: {auth}")