The blue dot is where the model says the next latent must land; contraction + noise bound it to a reachable set (the ring). Now encode what reality actually did and drag it around. Inside the ring → an ordinary belief update, and a free reality-grounded training target. Outside the ring → the world did something the model swore was impossible. That isn't a big MSE to average away — it's news: out-of-distribution or an unmodelled disturbance, a high-value event that should fire surprise, trigger replanning, or mark this state for data collection. A plain loss blurs these two cases together; the certificate keeps them apart.