Rivers remember what outlasts them: a phase diagram of mechanical memory

Rivers are pulse-driven machines, yet after a century of dam building we still lack a framework for how long a channel remembers an individual hydrological event. Here we show that river memory has two stages: an event is written into channel form only when it outlasts the reach-scale water residence time, and it is kept only when the sediment regime that follows does not erase it. A global layer of reach-scale timescales for 79,073 reaches maps where short events can register; regime shifts across five dam systems and a climate-stripped double difference over 898 dam sites show regulation shifting rivers along the measured writing axis of this phase space; nine controlled floods on the Colorado River show one-year retention set by post-flood tributary sediment supply (Spearman = 0.90), not by the flood itself; and 31 analysable Yellow River regulation events — from the only programme decoupling water from sediment pulses — all write in full yet split on retention, three-fifths of scour writes reburied within months while starved-year writes persist. Controlled floods and environmental flows should therefore be designed by hydrodynamics-based memory phase, not by water volume alone.