## Problem 297 — rank:194

**Title:** Coupling protocell growth to division

**Added binding assumptions (LaTeX):**

```latex
The partition kernel obeys a declared material budget, including any loss or chemistry during division, and fixes joint daughter correlations. A single-type mean criterion applies only when viable parents have the same offspring law or a validated reduction; heterogeneous viability requires the multitype model. Define the probability of persistence and functional-material retention across the same fixed cycles, not a separate favorable conditioning sample of successful divisions.
```

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