## Problem 286 — rank:313

**Title:** Error threshold for first replicators

**Added binding assumptions (LaTeX):**

```latex
For a fixed finite irreducible mutation--selection matrix, the Perron equilibrium is a known construction and varies smoothly under ordinary smooth parameter changes with preserved irreducibility. A sharp nonanalytic error threshold generally needs a specified limiting procedure or a change of support; the level set at functional mass $\rho$ is an operational threshold. Distinguish this from stochastic loss and finite-horizon survival in a finite population.
```

**Direct edits:** 0. **Fresh external checks:** SC10, SC11