Where does a randomly reset process end up after a very high peak? An Evidence Press briefing. Many random processes are reset from time to time: a searcher returns to base, a queue is emptied, an insurer's reserve is topped up. Suppose such a process is watched for a fixed window and, during it, climbs unusually high. Where is it at the end of the window? This release answers that question for a broad family of processes that can jump down but never up, reset at random times. Once the peak is high, there are essentially only two stories. Either no reset has happened yet, and the process ends just below its peak; or it has been reset, and it ends at an ordinary level, as if nothing had happened. The paper gives the odds of the two stories, about fifty-three to forty-seven in the standard Brownian example, the full endpoint law in each case, and the law of the whole path. The height of the peak above the threshold turns out to be memoryless. The leading constants come from a standard calculation. What is new is an explicit error bound that holds for every question one could ask about the endpoint at once. For Brownian motion this also supplies a constant that a 2026 paper by Dębicki, Hashorva and Michna left open, and shows that their two bounds on it are strict. The evidence is written proofs, checked against exact simulation of the process. This is an anonymous, AI-assisted, unrefereed candidate. It has not been peer reviewed or independently reproduced, and processes with upward jumps are not covered. Published on 27 October 2026, the paper and evidence are linked from the Evidence Press release page. This briefing uses an AI-generated voice and is not additional scientific evidence.