Psychohistory forecasts the mass, not the man — and its confidence has a horizon. The plan is sharp for the next crisis and blurs into a widening cone beyond it. You cannot forecast a thousand years as well as ten; the cone is the honest shape of that.
The predicted trajectory is a drift with diffusion: the uncertainty band grows as ±σ·√(horizon) — the exact rate at which a random-walk / diffusion forecast loses precision. Near-term the cone is tight (a Seldon crisis is a forced move); far-term it fans out. The band width and the horizon at which it exceeds a threshold ("prediction breaks down") are computed live — degradation with distance, quantified, not hidden.
'The plan', 'crises', 'psychohistory' are Asimov's frame. The instrument shows only that a stochastic forecast's error grows like √t — a real property of diffusion — with 'crises' placed at fixed horizons as narration. It does not model any actual society.