## Problem 047 — rank:60

**Title:** Causality from observational omics

**Added binding assumptions (LaTeX):**

```latex
For an outcome functional $\psi$, define width as $\sup_{Q\in\mathcal I_x}\psi(Q)-\inf_{Q\in\mathcal I_x}\psi(Q)$; distributions themselves do not have an unspecified scalar width. Specify the feasible design menu, its cost and the finite-sample enlargement of the identified set. Empty sets reject the assumed causal model class; singleton observational fits need not imply an identified intervention effect.
```

**Direct edits:** 0. **Fresh external checks:** None; supplied sources retained as provenance.