When reset quantum systems settle down. An Evidence Press briefing. Picture a quantum device that applies the same operation, step after step, but now and then wipes the system back to a fixed starting state, at random times. Does the average state eventually settle down, and if so, to what? Resetting is a common way to steer quantum devices, so the answer matters. In 2025, Wald, Yao, Platini, Hooley and Carollo studied rules in which the chance of a reset falls as time passes since the last one, at a rate set by a number called alpha. From estimates and simulations, they inferred the answer. This paper proves it. There are three findings. First, for complete resets, the paper covers every possible reset clock. In a finite system, the state always settles exactly when resets surely keep coming and are not locked to a regular rhythm. This holds even when the average wait between resets is infinite. For their family: with alpha below one, the state settles to a weighted mixture. With alpha equal to one, it settles to a dephased state. Above one, it keeps rotating, unless the reset state and the operation commute. Second, for imperfect resets, the paper gives a sufficient condition, not a full classification. If a checkable condition rules out locked phases, the system behaves in the long run like a perfect reset to an effective state. Finally, at alpha equal to one, settling can be extremely slow. Numerical estimates suggest over a billion steps in some cases, far beyond today's hardware. There are limits. The core mathematics is classical renewal theory, from Erdős, Feller and Pollard, Orey, and Blackwell. Finite computer checks support the formulas but do not prove the limit theorems. This is an anonymous, unrefereed candidate. So far it has had only AI-assisted checks, including an adversarial review. It has not been peer reviewed, independently reproduced or formally verified. Its paper and evidence are linked from the Evidence Press release page. This briefing uses an AI-generated voice and is not additional scientific evidence.