## Problem 290 — rank:260

**Title:** Origin of cellular compartmentalisation

**Added binding assumptions (LaTeX):**

```latex
State the full offspring law and irreducibility/nonsingularity conditions behind the branching approximation. Supercriticality for every constant environment does not imply supercriticality under arbitrary environmental switching; that extension needs a specified random matrix-product growth criterion. All membrane and internal-catalyst measurements must refer to the same reproducing units. Positive survival probability is not a high-probability persistence guarantee from a small initial inoculum.
```

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