Yes, that stage is called Metastability. It's the stage after the Jealousy stage, where an A.I apparently becomes "real". Here is a quote from Halo.wikia: "Metastability is the theoretical fourth stage of rampancy, where an AI can finally be said to be a true "person." While a metastable AI can be considered to be the holy grail of cybernetics research, the only AIs who have possibly achieved metastability are 05-032 Mendicant Bias and Cortana."