Lipschitz-Inflated Conformal Trajectory Tube

Integrate this as an inference-time wrapper around a neural ODE, latent SSM, GRU, or world model. The base model receives irregular observations and produces a continuous prediction function X_hat(t); do not change its weights initially. Split trajectories into training and calibration sets. For every calibration trajectory, evaluate the model at its observed times, compute S_i=max_j ||X_i(t_ij)-X_hat_i(t_ij)||, and store the finite-sample conformal quantile q. Estimate L_hat from a separate high-frequency calibration set by computing the maximum finite-difference slope of the true trajectories, optionally applying a safety multiplier. Estimate L_hat_pred from dense solver evaluations of the neural predictor. At inference, for any requested time t, compute delta(t), the distance to the nearest observed input time, and return center X_hat(t) with radius q+(L_hat+L_hat_pred)delta(t). Pseudocode is: q=conformal_quantile(S); Gamma=L_hat+L_pred_hat; delta=min(abs(t-T_obs)); radius=q+Gamma*delta. The first cheap experiment is a GRU or neural ODE on noisy pendulum trajectories with randomly deleted observation times, comparing pointwise intervals against this tube. The quantitative prediction is dense-grid empirical coverage near 1-alpha-alpha_L, up to finite-sample slack, and approximately linear median radius growth with delta, with fitted slope near Gamma. Artificially using a sublinear gap inflation should cause coverage failures at the largest gaps.