An Absolute Floor for Forecasting, and What It Reveals About Temporal Foundation Models

Every metric in common use for forecasting is relative. Scaled errors and probabilistic scores report that one model beat another and none reports how far either sits from what is achievable because on collected data nobody knows what is achievable. We remove that limitation on a family of systems where the optimum is computable. A chaotic system produces information at a rate equal to the sum of its positive Lyapunov exponents and that rate is the minimum a tracker must be supplied to stay locked onto a trajectory. We build an evaluation around it where a predictor runs on its own output and receives a correction only when it drifts past a chosen precision and the correction stream in bits per unit time is the score. Sweeping the precision separates two causes of drift that error metrics conflate, since the cost of following a deterministic source does not change with precision while the cost of following a model's own mistakes does. On five systems spanning entropy rates from zero to two nats per unit time, four pretrained time series foundation models across a twentyfold range in parameters all spend more information than repeating the last observed value, all show the precision response of a predictor with no internal dynamics, and improve with scale too slowly to reach the floor below $10^{16.8}$ parameters. A delay embedding with a few hundred effective parameters reaches the floor exactly where the floor is zero so the gap belongs to the models themselves rather than to the instrument.