Large reasoning models achieve strong performance on complex tasks by generating extended chains of thought, but they often “overthink”: continuing to reason long after they internally have enough information to answer correctly. This wastes inference-time compute and can even hurt accuracy. Existing attempts to stop early either manipulate decoding with extra sampling and heuristics, rely on auxiliary verifier models, or operate only as post-hoc analysis pipelines without formal guarantees. We introduce LYNX, an online early-exit mechanism that turns a model’s own hidden-state awareness into confidence-controlled stopping decisions. LYNX attaches exit decisions to naturally occurring reasoning cues (e.g., “hmm”, “wait”) during generation, trains a lightweight probe on hidden states at those cue tokens using supervision from forced exits, and wraps the resulting scores in split conformal prediction to obtain distribution-free control over the rate of premature exits. Crucially, we train and calibrate this probe once on a generic mathematical corpus and then reuse it unchanged across benchmarks, decoding temperatures, and even non-mathematical tasks. Across three model families spanning 1.5B to 32B parameters (DeepSeek-R1-1.5B, QwQ-32B, and Llama-3.1-Nemotron-8B), a single mathematically trained probe per base model yields strong accuracy–efficiency tradeoffs. On GSM8K, LYNX matches or improves baseline accuracy while reducing tokens by 40–65%; on MATH-500 it improves accuracy by up to 12 points with roughly 35–60% fewer tokens; on AIME 2024 it recovers baseline accuracy with more than 50% token savings; and on CommonsenseQA, a non-math benchmark, it transfers zero-shot with modest accuracy gains and up to 70% fewer tokens. Compared to state-of-the-art early-exit methods, LYNX offers competitive or superior Pareto frontiers while remaining fully online, requiring no proxy models at inference, and providing explicit, user-tunable confidence guarantees. Code is available at https://github.com/farukakgul/LYNX.