State-space models are accurate and efficient neural operators for dynamical systems

The paper specifies the SSM/Mamba recurrence, its ZOH discretization, and the Mamba block architecture, and asserts linear-time inference and encoded temporal causality, contrasting this with generic neural operators like DeepONet; it also empirically demonstrates linear scaling and OOD robustness (Ex+/Ex-) rather than providing formal proofs. The model supplies rigorous versions of these points: an inductive causality proof for the Mamba scan, a clear O(N) time/activation-memory analysis, and an explicit construction showing DeepONet need not be causal. Thus the paper’s claims are substantively correct but informal, while the model provides the missing formal details. See the SSM/Mamba formulation and block description, the linear-time claim, the causality contrast with neural operators, and Ex+/Ex- evidence in the paper.