Psychohistory's second axiom: the population must stay ignorant of the analysis. A prediction that reaches the predicted stops being true — they steer by it, and the forecast folds back on itself. Reveal the plan and watch it break the very thing it measured.
Agents follow a latent trend; the forecast is that trend. While the prediction is HIDDEN, actual tracks predicted and the error stays ~0 — the forecast is valid. REVEAL it and each agent adjusts by the prediction (away from it in self-defeating mode, toward it in self-fulfilling), so actual departs from predicted and the error grows: a real model of reflexivity — a prediction that changes the system it predicts. The error jumping on reveal is the measured effect.
Asimov's 'the people must not know psychohistory' is the frame. The mechanism is reflexive prediction (Merton's self-fulfilling/self-defeating prophecy), rendered as agents shifting by a revealed forecast. The 'society' is a toy trend; the point is only that observation can perturb the observed.