## Problem 268 — rank:258

**Title:** Minimal genome problem

**Added binding assumptions (LaTeX):**

```latex
The background class must not supply uncounted essential genes or alternative genetic machinery that trivializes the gene-count objective. State copy-number, gene-definition, regulatory-element and hereditary-component counting conventions. Use sufficiently many passages to distinguish sustained autonomous reproduction from transient rescue by inherited material. A viable construction is an upper bound; a lower bound is only relative to the fixed catalogue, background and nutrient class, not all chemically possible cells.
```

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