Presence, Not Memory: A Kinetic Framework for Distinguishing Transient and Persistent States in Aqueous Systems

The question whether an aqueous system retains an imprint of past treatment has resisted resolution for four decades, and we argue that the reason is structural rather than empirical: both sides of the dispute argue about structure, an object for which no protocol-defined observable of persistence exists. We propose replacing the disputed concept of memory with an operational one we call presence: the retention of an induced state measured against the time of the drive that produced it, with the source of driving still specified rather than assumed absent. Presence is defined by two measurable quantities — the slowest relaxation time of the system, taken as an eigenvalue of an estimated local generator, and the driving time set by the experimenter — and by their ratio. This reformulation has three consequences. First, the claim becomes falsifiable: a stated fraction of the induced state must survive a stated interval, or it does not. Second, four distinct mechanisms of long-lived order — transient response, kinetic stabilization, flux maintenance, and collective interfacial organization — become separable by three declared axes of measurement rather than by argument. Third, the thermodynamic distinction between a metastable state that costs nothing to maintain and a dissipative structure that is paid for continuously becomes an experimental question rather than a matter of position. We set out the framework, the observables it requires, what each of them cannot decide, and the outcome that would render the framework empty. No experimental data are reported. Preprint.