"The Theory of Guided Symbiosis: A New Paradigm for Human Evolution in the Age of Superintelligence".

Building on “The Theory of Guided Symbiosis: A New Paradigm for Human Evolution in the Age of Superintelligence” (2025), this study presents a mathematical core and a computational prototype for Guided Symbiosis Theory (GST). For a fixed infinite-horizon model, the existence and uniqueness of a globally optimal control are proved. The optimum preserves positive lower bounds on the system’s states, even though no separate state constraints were imposed in the optimization problem. For a broader family of models, an exact criterion for jointly preserving specified bounds is established. A separate theorem proves a strict advantage of a scenario with a positive external human population over one without humans: under the model’s assumptions, the same useful outcome can be achieved with less control effort. This advantage arises without directly rewarding population size in the objective function. The computational study demonstrates that a compact learned agent can approach the performance of the numerical optimal controller. Three PPO agents were trained from scratch, without a safety filter or imitation of reference actions. After 51,200 transitions per run, their costs at the baseline initial state were only 0.70–2.14% above the numerical reference. All three met the 5% tolerance, including a conservative bound on the remaining cost tail. The exported agent contains 1,185 parameters and runs through NumPy. Across 30 evaluated trajectories, no violations of the selected lower bounds were observed on the numerical grid. However, the mathematical guarantees of the original optimum do not automatically extend to the learned agents. The baseline initial state was used to determine when training stopped. These results concern the specified model and establish neither the safety of a real superintelligent system nor its preservation of the human population. The full materials are temporarily available under closed access, with public release planned for a later date.