Normalized Scheduling-Degree Truncation

1. Exact integration point: insert the truncation in a scheduling-conditioned MLP, state-space model, or latent world model immediately before the dynamics matrices are generated. Normalize scheduling channels using training-set statistics, enumerate monomials up to degree h, and use them as inputs to a linear hypernetwork or factorized bilinear dynamics layer. 2. Pseudocode: estimate mu and s on the training split; compute tilde p=(p-mu)/s; generate every multi-index alpha with |alpha|<=h; form phi_alpha; calculate A(tilde p)=A_0+sum_alpha phi_alpha A_alpha; calculate B(tilde p) similarly or with a lower degree; update z_{k+1}=A(tilde p_k)z_k+B(tilde p_k)u_k; and train with one-step and multi-step latent losses. Add spectral normalization or rescale A(tilde p) so its estimated spectral radius is below a target rho_star<1 when bounded stable rollouts are desired. 3. Computed from the paper: scheduling normalization and removal of rows or features with excessive scheduling products. Estimated empirically: degree h, coefficient regularization, and spectral-radius target. 4. First cheap experiment: use a two-dimensional Duffing or cart-pole system with one or two time-varying parameters, comparing h=0,1,2,3,4 against a full multiplicative MLP and a GRU. Measure validation one-step error, 50-step rollout error, feature count, and runtime. The prediction is that the first degree at which residual error stops falling identifies a truncation point; feature count must follow binomial(n_p+h,h). For the spectrally constrained version, the empirical latent Jacobian spectral radius should remain below rho_star and stable-trajectory rollout norms should decay approximately as rho_star^t.