"I May Not Have Articulated Myself Clearly": Diagnosing Dynamic Instability in LLM Reasoning at Inference Time

Reasoning failures in large language models (LLMs) are typically measured only at the end of a generation, yet the generation process is a dynamical system whose latent reasoning trajectory can become unstable mid-decoding. We take this dynamic instability, a process-level property of the decoding trajectory rather than an end-point error, as our primary object of study, and ask whether its diagnostic signature is observable at inference time from black-box signals alone (top-k token log probabilities), with no training or multi-sample aggregation. The main diagnostic uses no hidden-state access; a separate white-box audit is used only to test the latent space-observable variables connection. We define a training-free instability signal that combines consecutive-step distributional shift (JSD) and uncertainty (entropy), and summarize each trace by its peak strength and peak timing. To connect this observable to the unobserved latent, we provide a theoretical connection: under explicit output-map assumptions, full-vocabulary JSD is a two-sided local proxy for latent-state movement (sensitive to it and sound against spurious full-vocabulary spikes), and a 100-trace readout audit supports this local geometry for output-relevant hidden movement. We then treat final-answer correctness not as the objective but as a validation consequence: if the measured instability is real and consequential, it should be reflected in outcomes, and it is. Across GSM8K and HotpotQA, instability strength separates correct from incorrect single traces with above-chance AUC and a monotonic bucket-level accuracy decline that holds at scale across model sizes. Peak timing provides weaker but useful recoverability evidence: early instability is directionally more often followed by recovery, while late instability is more often associated with failure, especially under stricter early/late thresholds. The method uses only inference-time token log probabilities and is presented as a measurement lens rather than a corrective or control mechanism.