arXiv:2608.17124 defines decodability that predicts hidden-state selection gains over voting at r=0.75

The paper introduces CASE, a linear gate trained on answer-token hidden states that selects the highest-scoring candidate from LLM samples. It defines decodability as a leakage-free ranking metric over correct versus incorrect candidates for each question. Conventional probes lose accuracy under question-grouped splits, confirming identity leakage as the source of prior over-optimism. CASE improves accuracy by up to 19 points on medium-difficulty items and 16.8 points on hard items across general and medical models. Decodability depends on recall of aligned knowledge rather than parameter count. The metric transfers to an unseen scientific domain with a maximum drop of 3.8 points. Hidden-state selection therefore replaces voting only when decodability exceeds the 0.60 AUC threshold on a calibration set. This supplies an a-priori test that avoids repeated sampling on difficult questions where correlated errors dominate. Future deployments can compute decodability once per model-task pair before choosing the combiner.