Every iterative AI optimization process produces a recurring decision after each run: has the system improved enough to keep going, or is further iteration wasting effort? Current practice answers this with fixed score thresholds or manual inspection. Both approaches ignore the shape of the score trajectory over time, which is where the most useful signal sits. I introduce PhaseStop, a framework that detects when an optimization trajectory has stabilized by applying five classical statistical detectors in phase-conditioned sequence. The framework formalizes a three-phase trajectory pattern (activation, growth, saturation) and assigns each detector to the phase where its statistical properties make it most sensitive. Detectors activate in order rather than voting simultaneously, which reduces false-positive stabilization calls on oscillating trajectories. The detector-to-phase assignments are validated on synthetic trajectories with known ground-truth phase boundaries across seven trajectory types (350 instances). A planned real-benchmark validation study on RAG optimization tasks is described in Section 4. The reference implementation is open-sourced at https://github.com/torjoshi/PhaseStop
Rajesh Joshi (Fri,) studied this question.