Latent reasoning models compress chain-of-thought into hidden states, but whether these representations retain usable self-knowledge about correctness remains unclear. We study two compression-based paradigms, Latent-SFT and CoLaR, and find a sharp distinction between problem-level and trajectory-level self-knowledge. A lightweight attention probe predicts which problems the model will solve (AUC 0.805/0.853) and transfers across datasets and compression ratios, yet cannot reliably rank rollouts of the same problem; distribution-matched retraining does not recover this signal. This distinction maps directly to downstream use: selective prediction improves accuracy by 20–25pp at 50% coverage, and adaptive routing outperforms either solver while reducing token cost, whereas latent best-of-N yields negligible gains despite available oracle headroom. The problem-level signal also persists on a 7B math checkpoint but vanishes on StrategyQA. These results identify an algorithm–paradigm boundary for exploiting self-knowledge in latent reasoning. Code is available at https://github.com/Arthas777/latent-probe.