## Problem 042 — rank:23

**Title:** Multiscale closure

**Added binding assumptions (LaTeX):**

```latex
Fix the initial conditional microscopic ensemble associated with each coarse state and the law, covariance and initial-state dependence of $\eta$. The displayed ordinary derivative requires an integrable colored forcing; white noise instead requires a stochastic integral formulation. A time-convolution kernel is an ansatz, not a general exact closure for every nonlinear projection. The corrected bound normalizes each observable's tolerance separately.
```

**Direct edits:** 1. **Fresh external checks:** None; supplied sources retained as provenance.