Wrong Prediction, Right Answer: Recovering Evidence from Collapsed LLM Sequence Scores

When a large language model fails a reasoning task, it is often assumed to lack the underlying capability. However, this conflates a genuine absence of reasoning with a late-stage output bottleneck. We observe a consistent readout gap across diverse reasoning benchmarks: hidden-state probes successfully decode correct answers even when native sequence scoring completely collapses due to structural biases. To test whether instance-specific logic survives this collapse, we introduce a diagnostic protocol using a minimal, target-label-free additive correction. Fitting just two parameters on as few as 25 unlabeled examples recovers 9--34 accuracy points for Qwen3.5 models, transferring successfully to OLMo-2-1B and Llama-3.1-8B. Crucially, these recovered decisions persist on hard instances unresolved by simple lexical overlap and significantly exceed count-preserving permutation baselines. Our results show that many apparent zero-shot reasoning deficits are expression failures masking intact internal logic, urging a narrower interpretation of benchmark evaluations.