Classical robot ethics is often framed around obedience, including Asimov's laws. This framing is insufficient for contemporary AI systems, which are increasingly adaptive, generative, embodied, and embedded in physical, psychological, and social environments. This paper proposes conditional mutualism under governance as a framework for human-AI coexistence: a co-evolutionary relationship in which humans and AI systems develop, specialize, and coordinate under institutional conditions that preserve reciprocity, reversibility, psychological safety, and social legitimacy. We synthesize concepts from computability, machine learning, foundation models, embodied AI, alignment, human-robot interaction, ecological mutualism, coevolution, and polycentric governance. We then formalize coexistence as a multiplex dynamical system across physical, psychological, and social layers, with reciprocal supply-demand coupling, conflict penalties, developmental freedom, and governance regularization. The model gives conditions for existence, uniqueness, and global asymptotic stability of equilibria. We complement the analytical results with deterministic ODE simulations, basin sweeps, sensitivity analyses, governance-regime comparisons, shock tests, and local stability checks. The simulations indicate that governed mutualism reaches a high coexistence index with negligible domination, whereas insufficient or excessive governance can produce domination, weak-benefit lock-in, or suppressed developmental freedom. The results suggest that human-AI coexistence should be designed as a co-evolutionary governance problem rather than as a static obedience problem.