Reachable Global Optimization in AI Systems: How Global Is Global?

AI systems increasingly claim to optimize prompts, policies, architectures, plans, tool-use trajectories, reasoning traces, and test-time computation. This paper argues that such claims are underspecified unless they state the region actually reachable by the system that performed the optimization. We introduce Reachability-Induced Optimization (RIO), a model in which a generator, verifier, controller, memory, tools, and budget induce a reachable candidate region. The returned solution is therefore a best visited point, an approximate reachable optimum, or an exact global optimum only when additional certificates relate the reachable region to the full formal space. We prove reachable-optimality, false-globality, gap- decomposition, certificate, escape, pruning, and control-value results.