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A nonce carries the window it was minted in, not the instant, and is accepted for that window and the one before it. So a peer re-stamped at least once per window can never be left holding one outside the accepted pair, whenever it was last served and however much life its own nonce had left. That is the whole reason management tracks nothing per peer, and it was resting on an argument rather than a test. The phases are part of the property, not decoration: accounts are deliberately given a refresh phase of their own, so the guarantee has to hold off the window boundary too. The negative case shows why that matters — a cadence of exactly two windows lands inside the grace window when it is aligned to the boundary and leaves a gap when it is not.