The NeuralChaos paper develops methods for approximating stochastic processes using neural network architectures that respect the information flow encoded in a filtration. A central open question emerging from this work is whether there exists a universal rate at which such adapted approximations converge to the true process, or whether the geometry and complexity of the filtration itself fundamentally governs the best achievable approximation error. In other words, does the filtration structure impose an intrinsic curse of dimensionality on adapted approximation that cannot be overcome by any architecture, no matter how expressive? This question asks for a sharp minimax lower bound that accounts not just for the smoothness of the target process but for the information-theoretic complexity of the conditional expectations that define adaptedness. The problem is open and hard because adapted approximation is strictly harder than ordinary function approximation: the approximant must at each time step depend only on the past, which creates a nested constraint structure that classical approximation theory does not handle. Standard tools such as Kolmogorov entropy and VC dimension apply to static function classes, but the sequential and conditional nature of predictable processes means that errors at early times propagate and compound in ways that are not yet well understood at a theoretical level. The filtration can itself be highly complex, generated by path-dependent or non-Markovian signals, and there is no established framework connecting filtration complexity to approximation rates in the way that smoothness classes connect to rates in classical nonparametric estimation. Resolving this question would unlock a rigorous theoretical foundation for the use of neural networks in stochastic control, financial derivatives pricing, and reinforcement learning. It would tell practitioners exactly when expressive architectures can overcome the adaptedness constraint and when they fundamentally cannot, guiding algorithm design and providing non-asymptotic guarantees for learned stochastic policies in safety-critical applications.