Chain-of-thought (CoT) reasoning in large language models often produces redundant steps that increase generation cost and obscure when reasoning has effectively completed. Existing stopping methods rely on output-level or token-level signals, overlooking internal representation dynamics that reflect reasoning progress. We propose STARS (STate-Aware Reasoning Stopping), a framework that leverages spectral analysis of hidden-state representations to detect transitions in reasoning phases. Our key insight is that structural changes in the representation space capture shifts in reasoning states, enabling early and reliable stopping decisions. To address representation instability, where semantically similar steps can induce different hidden states, we focus on spectral structure rather than raw activations, improving robustness to context-dependent drift. Experiments on four mathematical and logical reasoning benchmarks show that STARS reduces generation cost by over 45% under fixed token budgets while improving accuracy over standard CoT baselines.