Theoretical Guarantees

The theory establishes limited sufficient conditions rather than a full proof for the deployed RASP-Tuner system. The guarantees are conditional and local rather than universal. The analysis does not prove a universal positive lower bound for the planner-memory useful-basin probability. The RA-GD regret bound is uniform in the time horizon and grows at most linearly with the number of regimes. The theoretical analysis separates frozen-stage local contraction from event-level improvement. Under stated local assumptions, frozen-stage dynamics converge exponentially to equilibrium when port input vanishes. The finite-budget proposition bounds stage improvement probability by the product of planner proposal probability and rollout reach probability. If transformed metric badness scores are bounded in [0,1] and monotone in hidden true loss, any positive-weight convex average preserves those properties. In the idealized finite-regime model, nearest-neighbor retrieval recovers the active regime after memory contains at least one context from each regime. The Lyapunov function adds a small cross term to the Hamiltonian gap because damping acts on momentum rather than directly on the gradi…