Forecast Error Is Not a Certificate: Fixed-Point Quantization Destroys Chaotic Climate Before It Degrades Accuracy

Reservoir surrogates of chaotic systems are increasingly deployed to fixed-point hardware, and the compression literature certifies the resulting low-precision models using forecast error. We show this certificate is invalid. Sweeping an echo state network trained on Lorenz-63 across a fixed-point precision ladder, we find that the model's invariant measure -- its climate -- collapses below 19 total bits, while one-step forecast RMSE at that precision remains at $2.2 \times 10^{-3}$, under an order of magnitude above its full-precision floor, and does not exceed $5 \times 10^{-2}$ until below 15 total bits. Critically, the RMSE curve is smooth and monotone across the entire ladder: it exhibits no feature at the precision where the climate dies. The failure is therefore not one that a tighter forecast-error threshold could detect. We further find an ordering -- climate collapses first, the largest Lyapunov exponent crosses zero two bits later, and forecast error responds last -- and that quantization-aware training of the readout, optimized on a one-step objective, degrades climate fidelity below post-training quantization, an effect a full-precision control isolates to the quantizer rather than to the change in objective. All distributional claims are calibrated against the sampling noise floor of the metric itself.