Psychohistory holds for the mass — until one individual is off the distribution entirely. The Mule is the mutation the equations never budgeted for: a single agent whose leverage tips the whole forecast. Inject it and watch the plan, so accurate a moment ago, come apart.
A population of 'typical citizens' is drawn from one distribution; the forecast is their running mean, and while everyone is in-distribution the forecast error stays near 0 (the mass is lawful). Inject the Mule — one agent placed far outside the distribution with high weight — and the mean, and thus the forecast, is dragged off by exactly its leverage; the error jumps discontinuously. A single out-of-distribution point's influence on the mean, shown live.
'The Mule', 'the plan comes apart' is Asimov. The mechanism is the non-robustness of the sample mean to an outlier (its breakdown point is 0) — a real statistical fact. The 'forecast' is just the mean; no society is modelled.
This is what psychohistory admits it cannot hold: the individual off the distribution. A model fit to the typical is blind to the exceptional by construction — and the exceptional is exactly what moves history. The plan works precisely until it doesn't.